YES (ignored inputs)COMMENT translated from Cops 208 *** Computating Strongly Quasi-Reducible Parts *** TRS: [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), +(?x,?y) -> +(?y,?x), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), *(?x,?y) -> *(?y,?x), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)) ] Constructors: {0,s} Defined function symbols: {*,+} Constructor subsystem: [ ] Rule part & Conj Part: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x) ] Rule part & Conj Part: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x) ] [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x) ] Rule part & Conj Part: [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x) ] Rule part & Conj Part: [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x) ] [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x) ] *** Ground Confluence Check by Rewriting Induction *** Sort: {Nat} Signature: [ * : Nat,Nat -> Nat, + : Nat,Nat -> Nat, 0 : Nat, s : Nat -> Nat ] Rule Part: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] Conjecture Part: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] Precedence (by weight): {(*,3),(+,2),(0,1),(s,0)} Rule part is confluent. R0 is ground confluent. Check conj part consists of inductive theorems of R0. Rules: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] Conjectures: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] STEP 0 ES: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS: [ ] ES0: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS0: [ ] ES1: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS1: [ ] Expand +(?x,0) = ?x [ 0 = 0, s(+(?x_2,0)) = s(?x_2) ] ES2: [ 0 = 0, s(+(?x_2,0)) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ +(?x,0) -> ?x ] STEP 1 ES: [ 0 = 0, s(+(?x_2,0)) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ +(?x,0) -> ?x ] ES0: [ 0 = 0, s(?x_2) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS0: [ +(?x,0) -> ?x ] ES1: [ *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS1: [ +(?x,0) -> ?x ] Expand *(?x,0) = 0 [ 0 = 0, +(*(?x_4,0),0) = 0 ] ES2: [ 0 = 0, *(?x_4,0) = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS2: [ *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 2 ES: [ 0 = 0, *(?x_4,0) = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS: [ *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, 0 = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS0: [ *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS1: [ *(?x,0) -> 0, +(?x,0) -> ?x ] Expand *(?x,?y) = *(?y,?x) [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] ES2: [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 3 ES: [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS0: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS1: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(?x,?y) = +(?y,?x) [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)) ] ES2: [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS2: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 4 ES: [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ ?y_1 = ?y_1, s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS0: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS1: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(?y_2,s(?x_2)) = s(+(?x_2,?y_2)) [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))) ] ES2: [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 5 ES: [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ s(?x) = s(?x), s(s(+(?x,?x_2))) = s(s(+(?x_2,?x))), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), s(+(?y,?x)) = s(+(?x,?y)) ] HS0: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x) ] HS1: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand *(?y_4,s(?x_4)) = +(*(?x_4,?y_4),?y_4) [ 0 = +(*(?x,0),0), +(*(?x_4,s(?x)),s(?x)) = +(*(?x,s(?x_4)),s(?x_4)) ] ES2: [ 0 = +(*(?x,0),0), s(+(?x,*(?x_4,s(?x)))) = +(*(?x,s(?x_4)),s(?x_4)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS2: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 6 ES: [ 0 = +(*(?x,0),0), s(+(?x,*(?x_4,s(?x)))) = +(*(?x,s(?x_4)),s(?x_4)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(*(?y,?x),?x) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS0: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS1: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(?x,?y),?z) = +(?x,+(?y,?z)) [ +(?y_1,?z) = +(0,+(?y_1,?z)), +(s(+(?x_2,?y_2)),?z) = +(s(?x_2),+(?y_2,?z)) ] ES2: [ +(?y_1,?z) = +(0,+(?y_1,?z)), s(+(+(?x_2,?y_2),?z)) = +(s(?x_2),+(?y_2,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS2: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 7 ES: [ +(?y_1,?z) = +(0,+(?y_1,?z)), s(+(+(?x_2,?y_2),?z)) = +(s(?x_2),+(?y_2,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_1,?z) = +(?y_1,?z), s(+(+(?x_2,?y_2),?z)) = s(+(?x_2,+(?y_2,?z))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS0: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS1: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand *(*(?x,?y),?z) = *(?x,*(?y,?z)) [ *(0,?z) = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)) ] ES2: [ 0 = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS2: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 8 ES: [ 0 = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS0: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS1: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), *(s(+(?x_2,?y_2)),?z) = +(*(s(?x_2),?z),*(?y_2,?z)) ] ES2: [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), +(*(+(?x_2,?y_2),?z),?z) = +(*(s(?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS2: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 9 ES: [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), +(*(+(?x_2,?y_2),?z),?z) = +(*(s(?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ *(?y_1,?z) = *(?y_1,?z), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), +(*(*(?x_4,?y_4),?z),*(?y_4,?z)) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS0: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) ] HS1: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), *(?x,s(+(?x_2,?y_2))) = +(*(?x,s(?x_2)),*(?x,?y_2)) ] ES2: [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,s(?x_2)),*(?x,?y_2)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)) ] HS2: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 10 ES: [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,s(?x_2)),*(?x,?y_2)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)) ] HS: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ *(?x,?y_1) = *(?x,?y_1), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)) ] HS0: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)) ] HS1: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand s(+(?x,+(*(?x,?x_4),?x_4))) = s(+(?x_4,+(*(?x_4,?x),?x))) [ s(+(0,+(0,?y_7))) = s(+(?y_7,+(*(?y_7,0),0))), s(+(s(?x_8),+(+(*(?x_8,?y_8),?y_8),?y_8))) = s(+(?y_8,+(*(?y_8,s(?x_8)),s(?x_8)))) ] ES2: [ s(?y_7) = s(+(?y_7,+(*(?y_7,0),0))), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(+(?y_8,+(*(?y_8,s(?x_8)),s(?x_8)))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)) ] HS2: [ s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 11 ES: [ s(?y_7) = s(+(?y_7,+(*(?y_7,0),0))), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(+(?y_8,+(*(?y_8,s(?x_8)),s(?x_8)))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)) ] HS: [ s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ s(?y_7) = s(?y_7), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)) ] HS0: [ s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)) ] HS1: [ s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(+(*(?x_2,?z),?z),*(?y_2,?z)) [ +(0,+(*(?y_2,?y_5),?y_5)) = +(+(*(0,?y_5),?y_5),*(?y_2,?y_5)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_2,?y_6)) ] ES2: [ +(*(?y_2,?y_5),?y_5) = +(+(*(0,?y_5),?y_5),*(?y_2,?y_5)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_2,?y_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS2: [ +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 12 ES: [ +(*(?y_2,?y_5),?y_5) = +(+(*(0,?y_5),?y_5),*(?y_2,?y_5)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_2,?y_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS: [ +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y_2,?y_5),?y_5) = +(?y_5,*(?y_2,?y_5)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS0: [ +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS1: [ +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x_2,?x),?x),*(?x,?y_2)) [ +(0,+(*(?y_2,?y_5),?y_5)) = +(+(*(0,?y_5),?y_5),*(?y_5,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_6,?y_2)) ] ES2: [ +(*(?y_2,?y_5),?y_5) = +(+(*(0,?y_5),?y_5),*(?y_5,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)) ] HS2: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 13 ES: [ +(*(?y_2,?y_5),?y_5) = +(+(*(0,?y_5),?y_5),*(?y_5,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(s(?x_6),?y_6),?y_6),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)) ] HS: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y_2,?y_5),?y_5) = +(?y_5,*(?y_5,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)) ] HS0: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y_2,?y_5),?y_5) = +(?y_5,*(?y_5,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)) ] HS1: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y_2,?y_5),?y_5) = +(?y_5,*(?y_5,?y_2)) [ +(0,?y_6) = +(?y_6,*(?y_6,0)), +(+(*(?x_7,?y_7),?y_7),?y_7) = +(?y_7,*(?y_7,s(?x_7))) ] ES2: [ ?y_6 = +(?y_6,*(?y_6,0)), +(*(?x_7,?y_7),+(?y_7,?y_7)) = +(?y_7,*(?y_7,s(?x_7))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)) ] HS2: [ +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 14 ES: [ ?y_6 = +(?y_6,*(?y_6,0)), +(*(?x_7,?y_7),+(?y_7,?y_7)) = +(?y_7,*(?y_7,s(?x_7))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)) ] HS: [ +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ ?y_6 = ?y_6, +(*(?x_7,?y_7),+(?y_7,?y_7)) = +(*(?x_7,?y_7),+(?y_7,?y_7)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)) ] HS0: [ +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)) ] HS1: [ +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)) [ +(+(0,?y_7),+(*(?y,?y_7),?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y,?y_7)), +(+(+(*(?x_8,?y_8),?y_8),?y_8),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y,?y_8)) ] ES2: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y,?y_7)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y,?y_8)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS2: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 15 ES: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y,?y_7)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y,?y_8)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(?y_7,?y_7),*(?y,?y_7)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS0: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) ] HS1: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) = +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)) [ +(+(0,?y_7),+(*(?y,?y_7),?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y_7,?y)), +(+(+(*(?x_8,?y_8),?y_8),?y_8),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y_8,?y)) ] ES2: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y_7,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS2: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 16 ES: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(*(0,?y_7),+(?y_7,?y_7)),*(?y_7,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(s(?x_8),?y_8),+(?y_8,?y_8)),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS0: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS1: [ +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_7),+(?y_7,?y_7)) = +(+(?y_7,?y_7),*(?y_7,?y)) [ +(0,+(?y_10,?y_10)) = +(+(?y_10,?y_10),*(?y_10,0)), +(+(*(?x_11,?y_11),?y_11),+(?y_11,?y_11)) = +(+(?y_11,?y_11),*(?y_11,s(?x_11))) ] ES2: [ +(?y_10,?y_10) = +(+(?y_10,?y_10),*(?y_10,0)), +(*(?x_11,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,?y_11),*(?y_11,s(?x_11))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)) ] HS2: [ +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 17 ES: [ +(?y_10,?y_10) = +(+(?y_10,?y_10),*(?y_10,0)), +(*(?x_11,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,?y_11),*(?y_11,s(?x_11))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)) ] HS: [ +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_10,?y_10) = +(?y_10,?y_10), +(*(?x_11,?y_11),+(?y_11,+(?y_11,?y_11))) = +(*(?x_11,?y_11),+(?y_11,+(?y_11,?y_11))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)) ] HS0: [ +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)) ] HS1: [ +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))) [ s(s(+(0,+(+(?y_3,?y_3),0)))) = s(s(+(*(0,?y_3),+(?y_3,+(0,?y_3))))), s(s(+(+(*(?x_4,?y_4),?y_4),+(+(?y_4,?y_4),s(?x_4))))) = s(s(+(*(s(?x_4),?y_4),+(?y_4,+(s(?x_4),?y_4))))) ] ES2: [ s(s(+(?y_3,?y_3))) = s(s(+(*(0,?y_3),+(?y_3,+(0,?y_3))))), s(s(s(+(+(+(?y_4,?y_4),+(?x_4,?y_4)),*(?x_4,?y_4))))) = s(s(+(*(s(?x_4),?y_4),+(?y_4,+(s(?x_4),?y_4))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS2: [ s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 18 ES: [ s(s(+(?y_3,?y_3))) = s(s(+(*(0,?y_3),+(?y_3,+(0,?y_3))))), s(s(s(+(+(+(?y_4,?y_4),+(?x_4,?y_4)),*(?x_4,?y_4))))) = s(s(+(*(s(?x_4),?y_4),+(?y_4,+(s(?x_4),?y_4))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS: [ s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ s(s(+(?y_3,?y_3))) = s(s(+(?y_3,?y_3))), s(s(s(+(+(+(?y_4,?y_4),+(?x_4,?y_4)),*(?x_4,?y_4))))) = s(s(s(+(+(+(?x_4,?y_4),+(?y_4,?y_4)),*(?x_4,?y_4))))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS0: [ s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS1: [ s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)) [ +(+(0,+(?y_11,?y_11)),+(*(?y,?y_11),?y_11)) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y_11,?y)), +(+(+(*(?x_12,?y_12),?y_12),+(?y_12,?y_12)),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y_12,?y)) ] ES2: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y_11,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y_12,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS2: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 19 ES: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y_11,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y_12,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS0: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) ] HS1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)) [ +(0,+(?y_14,+(?y_14,?y_14))) = +(+(?y_14,+(?y_14,?y_14)),*(?y_14,0)), +(+(*(?x_15,?y_15),?y_15),+(?y_15,+(?y_15,?y_15))) = +(+(?y_15,+(?y_15,?y_15)),*(?y_15,s(?x_15))) ] ES2: [ +(?y_14,+(?y_14,?y_14)) = +(+(?y_14,+(?y_14,?y_14)),*(?y_14,0)), +(*(?x_15,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,?y_15)),*(?y_15,s(?x_15))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS2: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 20 ES: [ +(?y_14,+(?y_14,?y_14)) = +(+(?y_14,+(?y_14,?y_14)),*(?y_14,0)), +(*(?x_15,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,?y_15)),*(?y_15,s(?x_15))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_14,+(?y_14,?y_14)) = +(?y_14,+(?y_14,?y_14)), +(*(?x_15,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(*(?x_15,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS0: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS1: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) = +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)) [ +(+(0,+(?y_11,?y_11)),+(*(?y,?y_11),?y_11)) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y,?y_11)), +(+(+(*(?x_12,?y_12),?y_12),+(?y_12,?y_12)),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y,?y_12)) ] ES2: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y,?y_11)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y,?y_12)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS2: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 21 ES: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(*(0,?y_11),+(?y_11,+(?y_11,?y_11))),*(?y,?y_11)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(s(?x_12),?y_12),+(?y_12,+(?y_12,?y_12))),*(?y,?y_12)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) = +(+(?y_11,+(?y_11,?y_11)),*(?y,?y_11)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS0: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS1: [ +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)) [ +(+(0,+(?y_15,+(?y_15,?y_15))),+(*(?y,?y_15),?y_15)) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y,?y_15)), +(+(+(*(?x_16,?y_16),?y_16),+(?y_16,+(?y_16,?y_16))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y,?y_16)) ] ES2: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y,?y_15)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y,?y_16)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS2: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 22 ES: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y,?y_15)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y,?y_16)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y,?y_15)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS0: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) ] HS1: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) = +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)) [ +(+(0,+(?y_15,+(?y_15,?y_15))),+(*(?y,?y_15),?y_15)) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y_15,?y)), +(+(+(*(?x_16,?y_16),?y_16),+(?y_16,+(?y_16,?y_16))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y_16,?y)) ] ES2: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y_15,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)) ] HS2: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 23 ES: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(*(0,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))),*(?y_15,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(s(?x_16),?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)) ] HS: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)) ] HS0: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)) ] HS1: [ +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) = +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)) [ +(0,+(?y_18,+(?y_18,+(?y_18,?y_18)))) = +(+(?y_18,+(?y_18,+(?y_18,?y_18))),*(?y_18,0)), +(+(*(?x_19,?y_19),?y_19),+(?y_19,+(?y_19,+(?y_19,?y_19)))) = +(+(?y_19,+(?y_19,+(?y_19,?y_19))),*(?y_19,s(?x_19))) ] ES2: [ +(?y_18,+(?y_18,+(?y_18,?y_18))) = +(+(?y_18,+(?y_18,+(?y_18,?y_18))),*(?y_18,0)), +(*(?x_19,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,?y_19))),*(?y_19,s(?x_19))), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS2: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 24 ES: [ +(?y_18,+(?y_18,+(?y_18,?y_18))) = +(+(?y_18,+(?y_18,+(?y_18,?y_18))),*(?y_18,0)), +(*(?x_19,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,?y_19))),*(?y_19,s(?x_19))), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_18,+(?y_18,+(?y_18,?y_18))) = +(?y_18,+(?y_18,+(?y_18,?y_18))), +(*(?x_19,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(*(?x_19,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS0: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS1: [ +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)) [ +(+(0,+(?y_19,+(?y_19,+(?y_19,?y_19)))),+(*(?y,?y_19),?y_19)) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y,?y_19)), +(+(+(*(?x_20,?y_20),?y_20),+(?y_20,+(?y_20,+(?y_20,?y_20)))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y,?y_20)) ] ES2: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y,?y_19)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y,?y_20)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS2: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 25 ES: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y,?y_19)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y,?y_20)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y,?y_19)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS0: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) ] HS1: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) = +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)) [ +(+(0,+(?y_19,+(?y_19,+(?y_19,?y_19)))),+(*(?y,?y_19),?y_19)) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y_19,?y)), +(+(+(*(?x_20,?y_20),?y_20),+(?y_20,+(?y_20,+(?y_20,?y_20)))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y_20,?y)) ] ES2: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y_19,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)) ] HS2: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 26 ES: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(*(0,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))),*(?y_19,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(s(?x_20),?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)) ] HS: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)) ] HS0: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)) ] HS1: [ +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) = +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)) [ +(0,+(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22))))) = +(+(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))),*(?y_22,0)), +(+(*(?x_23,?y_23),?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))),*(?y_23,s(?x_23))) ] ES2: [ +(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))) = +(+(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))),*(?y_22,0)), +(*(?x_23,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))),*(?y_23,s(?x_23))), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS2: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 27 ES: [ +(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))) = +(+(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))),*(?y_22,0)), +(*(?x_23,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))),*(?y_23,s(?x_23))), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))) = +(?y_22,+(?y_22,+(?y_22,+(?y_22,?y_22)))), +(*(?x_23,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(*(?x_23,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS0: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS1: [ +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)) [ +(+(0,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),+(*(?y,?y_23),?y_23)) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y,?y_23)), +(+(+(*(?x_24,?y_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y,?y_24)) ] ES2: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y,?y_23)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y,?y_24)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS2: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 28 ES: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y,?y_23)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y,?y_24)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y,?y_23)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS0: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) ] HS1: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) = +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)) [ +(+(0,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),+(*(?y,?y_23),?y_23)) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y_23,?y)), +(+(+(*(?x_24,?y_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y_24,?y)) ] ES2: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y_23,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)) ] HS2: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 29 ES: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(*(0,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))),*(?y_23,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(s(?x_24),?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)) ] HS: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)) ] HS0: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)) ] HS1: [ +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) = +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)) [ +(0,+(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26)))))) = +(+(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))),*(?y_26,0)), +(+(*(?x_27,?y_27),?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))),*(?y_27,s(?x_27))) ] ES2: [ +(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))) = +(+(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))),*(?y_26,0)), +(*(?x_27,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))),*(?y_27,s(?x_27))), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS2: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 30 ES: [ +(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))) = +(+(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))),*(?y_26,0)), +(*(?x_27,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))),*(?y_27,s(?x_27))), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))) = +(?y_26,+(?y_26,+(?y_26,+(?y_26,+(?y_26,?y_26))))), +(*(?x_27,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(*(?x_27,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS0: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS1: [ +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)) [ +(+(0,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),+(*(?y,?y_27),?y_27)) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y,?y_27)), +(+(+(*(?x_28,?y_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y,?y_28)) ] ES2: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y,?y_27)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y,?y_28)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS2: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 31 ES: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y,?y_27)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y,?y_28)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y,?y_27)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS0: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) ] HS1: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) = +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)) [ +(+(0,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),+(*(?y,?y_27),?y_27)) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y_27,?y)), +(+(+(*(?x_28,?y_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y_28,?y)) ] ES2: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y_27,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)) ] HS2: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 32 ES: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(*(0,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))),*(?y_27,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(s(?x_28),?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)) ] HS: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)) ] HS0: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)) ] HS1: [ +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) = +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)) [ +(0,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30))))))) = +(+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))),*(?y_30,0)), +(+(*(?x_31,?y_31),?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))),*(?y_31,s(?x_31))) ] ES2: [ +(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))) = +(+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))),*(?y_30,0)), +(*(?x_31,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))),*(?y_31,s(?x_31))), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS2: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 33 ES: [ +(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))) = +(+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))),*(?y_30,0)), +(*(?x_31,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))),*(?y_31,s(?x_31))), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))) = +(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,+(?y_30,?y_30)))))), +(*(?x_31,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(*(?x_31,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS0: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS1: [ +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)) [ +(+(0,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),+(*(?y,?y_31),?y_31)) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y,?y_31)), +(+(+(*(?x_32,?y_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y,?y_32)) ] ES2: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y,?y_31)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y,?y_32)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS2: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 34 ES: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y,?y_31)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y,?y_32)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y,?y_31)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS0: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) ] HS1: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) = +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)) [ +(+(0,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),+(*(?y,?y_31),?y_31)) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y_31,?y)), +(+(+(*(?x_32,?y_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y_32,?y)) ] ES2: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y_31,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)) ] HS2: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 35 ES: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(*(0,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))),*(?y_31,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(s(?x_32),?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)) ] HS: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)) ] HS0: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)) ] HS1: [ +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) = +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)) [ +(0,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34)))))))) = +(+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))),*(?y_34,0)), +(+(*(?x_35,?y_35),?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))),*(?y_35,s(?x_35))) ] ES2: [ +(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))) = +(+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))),*(?y_34,0)), +(*(?x_35,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))),*(?y_35,s(?x_35))), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS2: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 36 ES: [ +(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))) = +(+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))),*(?y_34,0)), +(*(?x_35,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))),*(?y_35,s(?x_35))), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))) = +(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,+(?y_34,?y_34))))))), +(*(?x_35,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(*(?x_35,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS0: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS1: [ +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)) [ +(+(0,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),+(*(?y,?y_35),?y_35)) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y,?y_35)), +(+(+(*(?x_36,?y_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y,?y_36)) ] ES2: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y,?y_35)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y,?y_36)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS2: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 37 ES: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y,?y_35)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y,?y_36)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y,?y_35)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS0: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) ] HS1: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) = +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)) [ +(+(0,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),+(*(?y,?y_35),?y_35)) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y_35,?y)), +(+(+(*(?x_36,?y_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y_36,?y)) ] ES2: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y_35,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)) ] HS2: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 38 ES: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(*(0,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))),*(?y_35,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(s(?x_36),?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)) ] HS: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)) ] HS0: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)) ] HS1: [ +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) = +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)) [ +(0,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38))))))))) = +(+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))),*(?y_38,0)), +(+(*(?x_39,?y_39),?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))),*(?y_39,s(?x_39))) ] ES2: [ +(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))) = +(+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))),*(?y_38,0)), +(*(?x_39,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))),*(?y_39,s(?x_39))), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS2: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 39 ES: [ +(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))) = +(+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))),*(?y_38,0)), +(*(?x_39,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))),*(?y_39,s(?x_39))), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))) = +(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,+(?y_38,?y_38)))))))), +(*(?x_39,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(*(?x_39,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS0: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS1: [ +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)) [ +(+(0,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),+(*(?y,?y_39),?y_39)) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y,?y_39)), +(+(+(*(?x_40,?y_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y,?y_40)) ] ES2: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y,?y_39)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y,?y_40)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS2: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 40 ES: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y,?y_39)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y,?y_40)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y,?y_39)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS0: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) ] HS1: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) = +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)) [ +(+(0,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),+(*(?y,?y_39),?y_39)) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y_39,?y)), +(+(+(*(?x_40,?y_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y_40,?y)) ] ES2: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y_39,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)) ] HS2: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 41 ES: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(*(0,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))),*(?y_39,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(s(?x_40),?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)) ] HS: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)) ] HS0: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)) ] HS1: [ +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) = +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)) [ +(0,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42)))))))))) = +(+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))),*(?y_42,0)), +(+(*(?x_43,?y_43),?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))),*(?y_43,s(?x_43))) ] ES2: [ +(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))) = +(+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))),*(?y_42,0)), +(*(?x_43,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))),*(?y_43,s(?x_43))), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS2: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 42 ES: [ +(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))) = +(+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))),*(?y_42,0)), +(*(?x_43,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))),*(?y_43,s(?x_43))), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))) = +(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,+(?y_42,?y_42))))))))), +(*(?x_43,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(*(?x_43,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS0: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS1: [ +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)) [ +(+(0,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),+(*(?y,?y_43),?y_43)) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y,?y_43)), +(+(+(*(?x_44,?y_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y,?y_44)) ] ES2: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y,?y_43)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y,?y_44)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS2: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 43 ES: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y,?y_43)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y,?y_44)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y,?y_43)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS0: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) ] HS1: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) = +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)) [ +(+(0,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),+(*(?y,?y_43),?y_43)) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y_43,?y)), +(+(+(*(?x_44,?y_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y_44,?y)) ] ES2: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y_43,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y_44,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)) ] HS2: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 44 ES: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(*(0,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))),*(?y_43,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(s(?x_44),?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),*(?y_44,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)) ] HS: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)) ] HS0: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)) ] HS1: [ +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) = +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)) [ +(0,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46))))))))))) = +(+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))),*(?y_46,0)), +(+(*(?x_47,?y_47),?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47))))))))))) = +(+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))),*(?y_47,s(?x_47))) ] ES2: [ +(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))) = +(+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))),*(?y_46,0)), +(*(?x_47,?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))))) = +(+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))),*(?y_47,s(?x_47))), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)) ] HS2: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) -> +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] STEP 45 ES: [ +(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))) = +(+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))),*(?y_46,0)), +(*(?x_47,?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))))) = +(+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))),*(?y_47,s(?x_47))), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)) ] HS: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) -> +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))) = +(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,+(?y_46,?y_46)))))))))), +(*(?x_47,?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))))) = +(*(?x_47,?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))))), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)) ] HS0: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) -> +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] ES1: [ +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)), +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y_44,?y)) ] HS1: [ +(*(?y,?y_43),+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43))))))))))) -> +(+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,+(?y_43,?y_43)))))))))),*(?y_43,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y_40,?y)), +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40)))))))))),+(*(?y,?y_40),?y_40)) -> +(+(*(?x_40,?y_40),+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,+(?y_40,?y_40))))))))))),*(?y,?y_40)), +(*(?y,?y_39),+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39)))))))))) -> +(+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,+(?y_39,?y_39))))))))),*(?y_39,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y_36,?y)), +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36))))))))),+(*(?y,?y_36),?y_36)) -> +(+(*(?x_36,?y_36),+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,+(?y_36,?y_36)))))))))),*(?y,?y_36)), +(*(?y,?y_35),+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35))))))))) -> +(+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,+(?y_35,?y_35)))))))),*(?y_35,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y_32,?y)), +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32)))))))),+(*(?y,?y_32),?y_32)) -> +(+(*(?x_32,?y_32),+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,+(?y_32,?y_32))))))))),*(?y,?y_32)), +(*(?y,?y_31),+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31)))))))) -> +(+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,+(?y_31,?y_31))))))),*(?y_31,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y_28,?y)), +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28))))))),+(*(?y,?y_28),?y_28)) -> +(+(*(?x_28,?y_28),+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,+(?y_28,?y_28)))))))),*(?y,?y_28)), +(*(?y,?y_27),+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27))))))) -> +(+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,+(?y_27,?y_27)))))),*(?y_27,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y_24,?y)), +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24)))))),+(*(?y,?y_24),?y_24)) -> +(+(*(?x_24,?y_24),+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,+(?y_24,?y_24))))))),*(?y,?y_24)), +(*(?y,?y_23),+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23)))))) -> +(+(?y_23,+(?y_23,+(?y_23,+(?y_23,+(?y_23,?y_23))))),*(?y_23,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y_20,?y)), +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20))))),+(*(?y,?y_20),?y_20)) -> +(+(*(?x_20,?y_20),+(?y_20,+(?y_20,+(?y_20,+(?y_20,+(?y_20,?y_20)))))),*(?y,?y_20)), +(*(?y,?y_19),+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19))))) -> +(+(?y_19,+(?y_19,+(?y_19,+(?y_19,?y_19)))),*(?y_19,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y_16,?y)), +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,?y_16)))),+(*(?y,?y_16),?y_16)) -> +(+(*(?x_16,?y_16),+(?y_16,+(?y_16,+(?y_16,+(?y_16,?y_16))))),*(?y,?y_16)), +(*(?y,?y_15),+(?y_15,+(?y_15,+(?y_15,?y_15)))) -> +(+(?y_15,+(?y_15,+(?y_15,?y_15))),*(?y_15,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y_12,?y)), +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,?y_12))),+(*(?y,?y_12),?y_12)) -> +(+(*(?x_12,?y_12),+(?y_12,+(?y_12,+(?y_12,?y_12)))),*(?y,?y_12)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y,?y_8)), +(*(?y,?y_11),+(?y_11,+(?y_11,?y_11))) -> +(+(?y_11,+(?y_11,?y_11)),*(?y_11,?y)), +(+(*(?x_8,?y_8),+(?y_8,?y_8)),+(*(?y,?y_8),?y_8)) -> +(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?y_8))),*(?y_8,?y)), s(s(+(*(?x_8,?y_8),+(+(?y_8,?y_8),?x_8)))) -> s(s(+(*(?x_8,?y_8),+(?y_8,+(?x_8,?y_8))))), +(*(?y,?y_7),+(?y_7,?y_7)) -> +(+(?y_7,?y_7),*(?y_7,?y)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_6,?y_2)), +(+(*(?x_6,?y_6),?y_6),+(*(?y_2,?y_6),?y_6)) -> +(+(*(?x_6,?y_6),+(?y_6,?y_6)),*(?y_2,?y_6)), +(*(?y_2,?y_5),?y_5) -> +(?y_5,*(?y_5,?y_2)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x_2,?x),?x),*(?x,?y_2)), +(*(?x_2,?z),+(*(?y_2,?z),?z)) -> +(+(*(?x_2,?z),?z),*(?y_2,?z)), s(+(?x,+(*(?x,?x_4),?x_4))) -> s(+(?x_4,+(*(?x_4,?x),?x))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44))))))))))),+(*(?y,?y_44),?y_44)) = +(+(*(?x_44,?y_44),+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,+(?y_44,?y_44)))))))))))),*(?y,?y_44)) [ +(+(0,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47))))))))))),+(*(?y,?y_47),?y_47)) = +(+(*(0,?y_47),+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,+(?y_47,?y_47)))))))))))),*(?y,?y_47)), +(+(+(*(?x_48,?y_48),?y_48),+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,?y_48))))))))))),+(*(?y,?y_48),?y_48)) = +(+(*(s(?x_48),?y_48),+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,+(?y_48,?y_48)))))))))))),*(?y,?y_48)) ] rewriting induction stopped because of timeout. *** Ground Confluence Check by Rewriting Induction *** Sort: {Nat} Signature: [ * : Nat,Nat -> Nat, + : Nat,Nat -> Nat, 0 : Nat, s : Nat -> Nat ] Rule Part: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x) ] Conjecture Part: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(0,?y) = 0, *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] Precedence (by weight): {(*,3),(+,2),(0,1),(s,0)} Rule part is confluent. R0 is ground confluent. Check conj part consists of inductive theorems of R0. Rules: [ +(0,?y) -> ?y, +(s(?x),?y) -> s(+(?x,?y)), *(?x,0) -> 0, *(?x,s(?y)) -> +(*(?x,?y),?x) ] Conjectures: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(0,?y) = 0, *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] STEP 0 ES: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(0,?y) = 0, *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS: [ ] ES0: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(0,?y) = 0, *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS0: [ ] ES1: [ +(?x,0) = ?x, +(?x,s(?y)) = s(+(?x,?y)), *(0,?y) = 0, *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS1: [ ] Expand +(?x,0) = ?x [ 0 = 0, s(+(?x_2,0)) = s(?x_2) ] ES2: [ 0 = 0, s(+(?x_2,0)) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), *(0,?y) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ +(?x,0) -> ?x ] STEP 1 ES: [ 0 = 0, s(+(?x_2,0)) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), *(0,?y) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ +(?x,0) -> ?x ] ES0: [ 0 = 0, s(?x_2) = s(?x_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), *(0,?y) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS0: [ +(?x,0) -> ?x ] ES1: [ *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), *(0,?y) = 0, +(?x,s(?y)) = s(+(?x,?y)) ] HS1: [ +(?x,0) -> ?x ] Expand *(0,?y) = 0 [ 0 = 0, +(*(0,?y_4),0) = 0 ] ES2: [ 0 = 0, *(0,?y_4) = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS2: [ *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 2 ES: [ 0 = 0, *(0,?y_4) = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS: [ *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, 0 = 0, +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS0: [ *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(?x,s(?y)) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS1: [ *(0,?y) -> 0, +(?x,0) -> ?x ] Expand *(?x,?y) = *(?y,?x) [ 0 = *(0,?x_3), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4) ] ES2: [ 0 = *(0,?x_3), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 3 ES: [ 0 = *(0,?x_3), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS0: [ *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS1: [ *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(?x,?y) = +(?y,?x) [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)) ] ES2: [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4) ] HS2: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 4 ES: [ ?y_1 = +(?y_1,0), s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4) ] HS: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ ?y_1 = ?y_1, s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4) ] HS0: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(+(?x_2,?y_2)) = +(?y_2,s(?x_2)), +(?x,s(?y)) = s(+(?x,?y)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4) ] HS1: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(?y_2,s(?x_2)) = s(+(?x_2,?y_2)) [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))) ] ES2: [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS2: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 5 ES: [ s(?x) = s(+(?x,0)), s(+(?x_2,s(?x))) = s(+(?x,s(?x_2))), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), +(?x,s(?y)) = s(+(?x,?y)) ] HS: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ s(?x) = s(?x), s(s(+(?x,?x_2))) = s(s(+(?x_2,?x))), +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y), s(+(?y,?x)) = s(+(?x,?y)) ] HS0: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_4,?y_4),?x_4) = *(s(?y_4),?x_4), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(s(?x),?y) = +(*(?x,?y),?y) ] HS1: [ +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand *(s(?y_4),?x_4) = +(*(?x_4,?y_4),?x_4) [ 0 = +(*(0,?y),0), +(*(s(?y),?y_4),s(?y)) = +(*(s(?y_4),?y),s(?y_4)) ] ES2: [ 0 = +(*(0,?y),0), s(+(?y,*(s(?y),?y_4))) = +(*(s(?y_4),?y),s(?y_4)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS2: [ *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 6 ES: [ 0 = +(*(0,?y),0), s(+(?y,*(s(?y),?y_4))) = +(*(s(?y_4),?y),s(?y_4)), *(s(?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS: [ *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(*(?y,?x),?y) = +(*(?x,?y),?y), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS0: [ *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS1: [ *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(?x,?y),?z) = +(?x,+(?y,?z)) [ +(?y_1,?z) = +(0,+(?y_1,?z)), +(s(+(?x_2,?y_2)),?z) = +(s(?x_2),+(?y_2,?z)) ] ES2: [ +(?y_1,?z) = +(0,+(?y_1,?z)), s(+(+(?x_2,?y_2),?z)) = +(s(?x_2),+(?y_2,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS2: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 7 ES: [ +(?y_1,?z) = +(0,+(?y_1,?z)), s(+(+(?x_2,?y_2),?z)) = +(s(?x_2),+(?y_2,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?y_1,?z) = +(?y_1,?z), s(+(+(?x_2,?y_2),?z)) = s(+(?x_2,+(?y_2,?z))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS0: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS1: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand *(*(?x,?y),?z) = *(?x,*(?y,?z)) [ *(0,?z) = *(?x_3,*(0,?z)), *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,*(s(?y_4),?z)) ] ES2: [ 0 = *(?x_3,*(0,?z)), *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,*(s(?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS2: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 8 ES: [ 0 = *(?x_3,*(0,?z)), *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,*(s(?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS0: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS1: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), *(s(+(?x_2,?y_2)),?z) = +(*(s(?x_2),?z),*(?y_2,?z)) ] ES2: [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), +(*(?z,+(?x_2,?y_2)),?z) = +(*(s(?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS2: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 9 ES: [ *(?y_1,?z) = +(*(0,?z),*(?y_1,?z)), +(*(?z,+(?x_2,?y_2)),?z) = +(*(s(?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?x_4),?z) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ *(?y_1,?z) = *(?y_1,?z), +(*(?z,+(?x_2,?y_2)),?z) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS0: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?z,+(?x_2,?y_2)),?z) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = *(?x_4,+(*(?z,?y_4),?z)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) ] HS1: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), *(?x,s(+(?x_2,?y_2))) = +(*(?x,s(?x_2)),*(?x,?y_2)) ] ES2: [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,s(?x_2)),*(?x,?y_2)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = *(?x_4,+(*(?z,?y_4),?z)), +(*(?z,+(?x_2,?y_2)),?z) = +(+(*(?z,?x_2),?z),*(?y_2,?z)) ] HS2: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 10 ES: [ *(?x,?y_1) = +(*(?x,0),*(?x,?y_1)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,s(?x_2)),*(?x,?y_2)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = *(?x_4,+(*(?z,?y_4),?z)), +(*(?z,+(?x_2,?y_2)),?z) = +(+(*(?z,?x_2),?z),*(?y_2,?z)) ] HS: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ *(?x,?y_1) = *(?x,?y_1), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)) ] HS0: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)) ] HS1: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand s(+(?y,+(*(?y_4,?y),?y_4))) = s(+(?y_4,+(*(?y,?y_4),?y))) [ s(+(0,+(0,?x_7))) = s(+(?x_7,+(*(0,?x_7),0))), s(+(s(?y_8),+(+(*(?x_8,?y_8),?x_8),?x_8))) = s(+(?x_8,+(*(s(?y_8),?x_8),s(?y_8)))) ] ES2: [ s(?x_7) = s(+(?x_7,+(*(0,?x_7),0))), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(+(?x_8,+(*(s(?y_8),?x_8),s(?y_8)))), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)) ] HS2: [ s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 11 ES: [ s(?x_7) = s(+(?x_7,+(*(0,?x_7),0))), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(+(?x_8,+(*(s(?y_8),?x_8),s(?y_8)))), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)) ] HS: [ s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ s(?x_7) = s(?x_7), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)) ] HS0: [ s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)) ] HS1: [ s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?z,?x_2),+(*(?z,?y_2),?z)) = +(+(*(?z,?x_2),?z),*(?y_2,?z)) [ +(0,+(*(?x_5,?y_2),?x_5)) = +(+(*(?x_5,0),?x_5),*(?y_2,?x_5)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,s(?y_6)),?x_6),*(?y_2,?x_6)) ] ES2: [ +(*(?x_5,?y_2),?x_5) = +(+(*(?x_5,0),?x_5),*(?y_2,?x_5)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,s(?y_6)),?x_6),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS2: [ +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 12 ES: [ +(*(?x_5,?y_2),?x_5) = +(+(*(?x_5,0),?x_5),*(?y_2,?x_5)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,s(?y_6)),?x_6),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS: [ +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_5,?y_2),?x_5) = +(?x_5,*(?y_2,?x_5)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS0: [ +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_5,?y_2),?x_5) = +(?x_5,*(?y_2,?x_5)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS1: [ +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_5,?y_2),?x_5) = +(?x_5,*(?y_2,?x_5)) [ +(0,?x_6) = +(?x_6,*(0,?x_6)), +(+(*(?x_7,?y_7),?x_7),?x_7) = +(?x_7,*(s(?y_7),?x_7)) ] ES2: [ ?x_6 = +(?x_6,*(0,?x_6)), +(*(?x_7,?y_7),+(?x_7,?x_7)) = +(?x_7,*(s(?y_7),?x_7)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)) ] HS2: [ +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 13 ES: [ ?x_6 = +(?x_6,*(0,?x_6)), +(*(?x_7,?y_7),+(?x_7,?x_7)) = +(?x_7,*(s(?y_7),?x_7)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)) ] HS: [ +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ ?x_6 = ?x_6, +(*(?x_7,?y_7),+(?x_7,?x_7)) = +(*(?x_7,?y_7),+(?x_7,?x_7)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)) ] HS0: [ +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)) ] HS1: [ +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) = +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)) [ +(*(0,?z),*(?x_7,?z)) = +(*(?x_7,*(?z,0)),*(?x_7,?z)), +(*(+(*(?x_8,?y_8),?x_8),?z),*(?x_8,?z)) = +(*(?x_8,*(?z,s(?y_8))),*(?x_8,?z)) ] ES2: [ *(?x_7,?z) = +(*(?x_7,*(?z,0)),*(?x_7,?z)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,s(?y_8))),*(?x_8,?z)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS2: [ +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 14 ES: [ *(?x_7,?z) = +(*(?x_7,*(?z,0)),*(?x_7,?z)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,s(?y_8))),*(?x_8,?z)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS: [ +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ *(?x_7,?z) = *(?x_7,?z), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS0: [ +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) ] HS1: [ +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(+(*(?x,?x_2),?x),*(?x,?y_2)) [ +(0,+(*(?y_2,0),0)) = +(+(*(0,?x_5),0),*(0,?y_2)), +(+(*(?x_6,?y_6),?x_6),+(*(?y_2,s(?y_6)),s(?y_6))) = +(+(*(s(?y_6),?x_6),s(?y_6)),*(s(?y_6),?y_2)) ] ES2: [ 0 = +(+(*(0,?x_5),0),*(0,?y_2)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = +(+(*(s(?y_6),?x_6),s(?y_6)),*(s(?y_6),?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS2: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 15 ES: [ 0 = +(+(*(0,?x_5),0),*(0,?y_2)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = +(+(*(s(?y_6),?x_6),s(?y_6)),*(s(?y_6),?y_2)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ 0 = 0, s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS0: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS1: [ +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) = s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))) [ s(s(+(0,+(+(?x_3,?x_3),0)))) = s(s(+(*(?x_3,0),+(?x_3,+(0,?x_3))))), s(s(+(+(*(?x_4,?y_4),?x_4),+(+(?x_4,?x_4),s(?y_4))))) = s(s(+(*(?x_4,s(?y_4)),+(?x_4,+(s(?y_4),?x_4))))) ] ES2: [ s(s(+(?x_3,?x_3))) = s(s(+(*(?x_3,0),+(?x_3,+(0,?x_3))))), s(s(s(+(+(+(?x_4,?x_4),+(?y_4,?x_4)),*(?x_4,?y_4))))) = s(s(+(*(?x_4,s(?y_4)),+(?x_4,+(s(?y_4),?x_4))))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS2: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 16 ES: [ s(s(+(?x_3,?x_3))) = s(s(+(*(?x_3,0),+(?x_3,+(0,?x_3))))), s(s(s(+(+(+(?x_4,?x_4),+(?y_4,?x_4)),*(?x_4,?y_4))))) = s(s(+(*(?x_4,s(?y_4)),+(?x_4,+(s(?y_4),?x_4))))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ s(s(+(?x_3,?x_3))) = s(s(+(?x_3,?x_3))), s(s(s(+(+(+(?x_4,?x_4),+(?y_4,?x_4)),*(?x_4,?y_4))))) = s(s(s(+(+(+(?y_4,?x_4),+(?x_4,?x_4)),*(?x_4,?y_4))))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS0: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS1: [ s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) = +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)) [ +(+(0,?x_7),+(*(?x_7,?y),?x_7)) = +(+(*(?x_7,0),+(?x_7,?x_7)),*(?y,?x_7)), +(+(+(*(?x_8,?y_8),?x_8),?x_8),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,s(?y_8)),+(?x_8,?x_8)),*(?y,?x_8)) ] ES2: [ +(*(?x_7,?y),+(?x_7,?x_7)) = +(+(*(?x_7,0),+(?x_7,?x_7)),*(?y,?x_7)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,s(?y_8)),+(?x_8,?x_8)),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS2: [ +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 17 ES: [ +(*(?x_7,?y),+(?x_7,?x_7)) = +(+(*(?x_7,0),+(?x_7,?x_7)),*(?y,?x_7)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,s(?y_8)),+(?x_8,?x_8)),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS: [ +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_7,?y),+(?x_7,?x_7)) = +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS0: [ +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_7,?y),+(?x_7,?x_7)) = +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) ] HS1: [ +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_7,?y),+(?x_7,?x_7)) = +(+(?x_7,?x_7),*(?y,?x_7)) [ +(0,+(?x_10,?x_10)) = +(+(?x_10,?x_10),*(0,?x_10)), +(+(*(?x_11,?y_11),?x_11),+(?x_11,?x_11)) = +(+(?x_11,?x_11),*(s(?y_11),?x_11)) ] ES2: [ +(?x_10,?x_10) = +(+(?x_10,?x_10),*(0,?x_10)), +(*(?x_11,?y_11),+(?x_11,+(?x_11,?x_11))) = +(+(?x_11,?x_11),*(s(?y_11),?x_11)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)) ] HS2: [ +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 18 ES: [ +(?x_10,?x_10) = +(+(?x_10,?x_10),*(0,?x_10)), +(*(?x_11,?y_11),+(?x_11,+(?x_11,?x_11))) = +(+(?x_11,?x_11),*(s(?y_11),?x_11)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)) ] HS: [ +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_10,?x_10) = +(?x_10,?x_10), +(*(?x_11,?y_11),+(?x_11,+(?x_11,?x_11))) = +(*(?x_11,?y_11),+(?x_11,+(?x_11,?x_11))), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)) ] HS0: [ +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)) ] HS1: [ +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) = +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))) [ +(*(0,?z),+(*(?x_11,?z),*(?x_11,?z))) = +(*(?x_11,*(?z,0)),+(*(?x_11,?z),*(?x_11,?z))), +(*(+(*(?x_12,?y_12),?x_12),?z),+(*(?x_12,?z),*(?x_12,?z))) = +(*(?x_12,*(?z,s(?y_12))),+(*(?x_12,?z),*(?x_12,?z))) ] ES2: [ +(*(?x_11,?z),*(?x_11,?z)) = +(*(?x_11,*(?z,0)),+(*(?x_11,?z),*(?x_11,?z))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,s(?y_12))),+(*(?x_12,?z),*(?x_12,?z))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS2: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 19 ES: [ +(*(?x_11,?z),*(?x_11,?z)) = +(*(?x_11,*(?z,0)),+(*(?x_11,?z),*(?x_11,?z))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,s(?y_12))),+(*(?x_12,?z),*(?x_12,?z))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_11,?z),*(?x_11,?z)) = +(*(?x_11,?z),*(?x_11,?z)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS0: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) ] HS1: [ +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) = +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)) [ +(+(0,+(?x_11,?x_11)),+(*(?x_11,?y),?x_11)) = +(+(*(?x_11,0),+(?x_11,+(?x_11,?x_11))),*(?y,?x_11)), +(+(+(*(?x_12,?y_12),?x_12),+(?x_12,?x_12)),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,s(?y_12)),+(?x_12,+(?x_12,?x_12))),*(?y,?x_12)) ] ES2: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) = +(+(*(?x_11,0),+(?x_11,+(?x_11,?x_11))),*(?y,?x_11)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,s(?y_12)),+(?x_12,+(?x_12,?x_12))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS2: [ +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 20 ES: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) = +(+(*(?x_11,0),+(?x_11,+(?x_11,?x_11))),*(?y,?x_11)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,s(?y_12)),+(?x_12,+(?x_12,?x_12))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS: [ +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) = +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS0: [ +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) = +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS1: [ +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) = +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)) [ +(0,+(?x_14,+(?x_14,?x_14))) = +(+(?x_14,+(?x_14,?x_14)),*(0,?x_14)), +(+(*(?x_15,?y_15),?x_15),+(?x_15,+(?x_15,?x_15))) = +(+(?x_15,+(?x_15,?x_15)),*(s(?y_15),?x_15)) ] ES2: [ +(?x_14,+(?x_14,?x_14)) = +(+(?x_14,+(?x_14,?x_14)),*(0,?x_14)), +(*(?x_15,?y_15),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(?x_15,+(?x_15,?x_15)),*(s(?y_15),?x_15)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)) ] HS2: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 21 ES: [ +(?x_14,+(?x_14,?x_14)) = +(+(?x_14,+(?x_14,?x_14)),*(0,?x_14)), +(*(?x_15,?y_15),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(?x_15,+(?x_15,?x_15)),*(s(?y_15),?x_15)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)) ] HS: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_14,+(?x_14,?x_14)) = +(?x_14,+(?x_14,?x_14)), +(*(?x_15,?y_15),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(*(?x_15,?y_15),+(?x_15,+(?x_15,+(?x_15,?x_15)))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)) ] HS0: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)) ] HS1: [ +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) = s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))) [ s(+(+(?y_5,*(?y_5,0)),+(*(?x_4,0),?x_4))) = s(+(+(*(?x_4,0),+(?x_4,0)),+(*(?y_5,0),?y_5))), s(+(+(s(+(?x_6,?y_6)),*(?y_6,s(?x_6))),+(*(?x_4,s(?x_6)),?x_4))) = s(+(+(*(?x_4,s(?x_6)),+(?x_4,s(?x_6))),+(*(?y_6,s(?x_6)),?y_6))) ] ES2: [ s(+(?y_5,?x_4)) = s(+(+(*(?x_4,0),+(?x_4,0)),+(*(?y_5,0),?y_5))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(+(+(*(?x_4,s(?x_6)),+(?x_4,s(?x_6))),+(*(?y_6,s(?x_6)),?y_6))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS2: [ s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 22 ES: [ s(+(?y_5,?x_4)) = s(+(+(*(?x_4,0),+(?x_4,0)),+(*(?y_5,0),?y_5))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(+(+(*(?x_4,s(?x_6)),+(?x_4,s(?x_6))),+(*(?y_6,s(?x_6)),?y_6))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS: [ s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ s(+(?y_5,?x_4)) = s(+(?x_4,?y_5)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS0: [ s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) ] HS1: [ s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) = +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)) [ +(+(0,+(?x_15,+(?x_15,?x_15))),+(*(?x_15,?y),?x_15)) = +(+(*(?x_15,0),+(?x_15,+(?x_15,+(?x_15,?x_15)))),*(?y,?x_15)), +(+(+(*(?x_16,?y_16),?x_16),+(?x_16,+(?x_16,?x_16))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,s(?y_16)),+(?x_16,+(?x_16,+(?x_16,?x_16)))),*(?y,?x_16)) ] ES2: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(*(?x_15,0),+(?x_15,+(?x_15,+(?x_15,?x_15)))),*(?y,?x_15)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,s(?y_16)),+(?x_16,+(?x_16,+(?x_16,?x_16)))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS2: [ +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 23 ES: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(*(?x_15,0),+(?x_15,+(?x_15,+(?x_15,?x_15)))),*(?y,?x_15)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,s(?y_16)),+(?x_16,+(?x_16,+(?x_16,?x_16)))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS: [ +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS0: [ +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS1: [ +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) = +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)) [ +(0,+(?x_18,+(?x_18,+(?x_18,?x_18)))) = +(+(?x_18,+(?x_18,+(?x_18,?x_18))),*(0,?x_18)), +(+(*(?x_19,?y_19),?x_19),+(?x_19,+(?x_19,+(?x_19,?x_19)))) = +(+(?x_19,+(?x_19,+(?x_19,?x_19))),*(s(?y_19),?x_19)) ] ES2: [ +(?x_18,+(?x_18,+(?x_18,?x_18))) = +(+(?x_18,+(?x_18,+(?x_18,?x_18))),*(0,?x_18)), +(*(?x_19,?y_19),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(?x_19,+(?x_19,+(?x_19,?x_19))),*(s(?y_19),?x_19)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)) ] HS2: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 24 ES: [ +(?x_18,+(?x_18,+(?x_18,?x_18))) = +(+(?x_18,+(?x_18,+(?x_18,?x_18))),*(0,?x_18)), +(*(?x_19,?y_19),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(?x_19,+(?x_19,+(?x_19,?x_19))),*(s(?y_19),?x_19)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)) ] HS: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_18,+(?x_18,+(?x_18,?x_18))) = +(?x_18,+(?x_18,+(?x_18,?x_18))), +(*(?x_19,?y_19),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(*(?x_19,?y_19),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)) ] HS0: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)) ] HS1: [ +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) = +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) [ +(*(0,?z),+(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z)))) = +(*(?x_15,*(?z,0)),+(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z)))), +(*(+(*(?x_16,?y_16),?x_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z)))) = +(*(?x_16,*(?z,s(?y_16))),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z)))) ] ES2: [ +(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z))) = +(*(?x_15,*(?z,0)),+(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z)))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,s(?y_16))),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS2: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 25 ES: [ +(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z))) = +(*(?x_15,*(?z,0)),+(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z)))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,s(?y_16))),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z)))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z))) = +(*(?x_15,?z),+(*(?x_15,?z),*(?x_15,?z))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS0: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) ] HS1: [ +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) = +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)) [ +(+(0,+(?x_19,+(?x_19,+(?x_19,?x_19)))),+(*(?x_19,?y),?x_19)) = +(+(*(?x_19,0),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))),*(?y,?x_19)), +(+(+(*(?x_20,?y_20),?x_20),+(?x_20,+(?x_20,+(?x_20,?x_20)))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,s(?y_20)),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),*(?y,?x_20)) ] ES2: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(*(?x_19,0),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))),*(?y,?x_19)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,s(?y_20)),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS2: [ +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 26 ES: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(*(?x_19,0),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))),*(?y,?x_19)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,s(?y_20)),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS: [ +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS0: [ +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS1: [ +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) = +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)) [ +(0,+(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22))))) = +(+(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))),*(0,?x_22)), +(+(*(?x_23,?y_23),?x_23),+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))),*(s(?y_23),?x_23)) ] ES2: [ +(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))) = +(+(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))),*(0,?x_22)), +(*(?x_23,?y_23),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))),*(s(?y_23),?x_23)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)) ] HS2: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 27 ES: [ +(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))) = +(+(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))),*(0,?x_22)), +(*(?x_23,?y_23),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))),*(s(?y_23),?x_23)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)) ] HS: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))) = +(?x_22,+(?x_22,+(?x_22,+(?x_22,?x_22)))), +(*(?x_23,?y_23),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(*(?x_23,?y_23),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)) ] HS0: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)) ] HS1: [ +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) = s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))) [ s(s(+(+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2))),+(*(0,?x_2),0)))) = s(s(+(+(+(+(?x_2,0),0),*(0,?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))), s(s(+(+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2))),+(*(s(?x_4),?x_2),s(+(?x_4,s(?x_4))))))) = s(s(+(+(+(+(?x_2,s(?x_4)),s(?x_4)),*(s(?x_4),?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))) ] ES2: [ s(s(+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2))))) = s(s(+(+(+(+(?x_2,0),0),*(0,?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(+(+(+(+(?x_2,s(?x_4)),s(?x_4)),*(s(?x_4),?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS2: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 28 ES: [ s(s(+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2))))) = s(s(+(+(+(+(?x_2,0),0),*(0,?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(+(+(+(+(?x_2,s(?x_4)),s(?x_4)),*(s(?x_4),?x_2)),+(*(?y_2,?x_2),+(?y_2,?y_2))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ s(s(+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2))))) = s(s(+(*(?y_2,?x_2),+(+(?y_2,?y_2),?x_2)))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS0: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) ] HS1: [ s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) = +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)) [ +(+(0,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),+(*(?x_23,?y),?x_23)) = +(+(*(?x_23,0),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))),*(?y,?x_23)), +(+(+(*(?x_24,?y_24),?x_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,s(?y_24)),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),*(?y,?x_24)) ] ES2: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(*(?x_23,0),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))),*(?y,?x_23)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,s(?y_24)),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS2: [ +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 29 ES: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(*(?x_23,0),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))),*(?y,?x_23)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,s(?y_24)),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS: [ +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS0: [ +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS1: [ +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) = +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)) [ +(0,+(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26)))))) = +(+(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))),*(0,?x_26)), +(+(*(?x_27,?y_27),?x_27),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))),*(s(?y_27),?x_27)) ] ES2: [ +(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))) = +(+(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))),*(0,?x_26)), +(*(?x_27,?y_27),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))),*(s(?y_27),?x_27)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)) ] HS2: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 30 ES: [ +(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))) = +(+(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))),*(0,?x_26)), +(*(?x_27,?y_27),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))),*(s(?y_27),?x_27)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)) ] HS: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))) = +(?x_26,+(?x_26,+(?x_26,+(?x_26,+(?x_26,?x_26))))), +(*(?x_27,?y_27),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(*(?x_27,?y_27),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)) ] HS0: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)) ] HS1: [ +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) = +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) [ +(*(0,?z),+(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z))))) = +(*(?x_19,*(?z,0)),+(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z))))), +(*(+(*(?x_20,?y_20),?x_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z))))) = +(*(?x_20,*(?z,s(?y_20))),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z))))) ] ES2: [ +(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z)))) = +(*(?x_19,*(?z,0)),+(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,s(?y_20))),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS2: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 31 ES: [ +(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z)))) = +(*(?x_19,*(?z,0)),+(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,s(?y_20))),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z)))) = +(*(?x_19,?z),+(*(?x_19,?z),+(*(?x_19,?z),*(?x_19,?z)))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS0: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) ] HS1: [ +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) = +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)) [ +(+(0,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),+(*(?x_27,?y),?x_27)) = +(+(*(?x_27,0),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))),*(?y,?x_27)), +(+(+(*(?x_28,?y_28),?x_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,s(?y_28)),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),*(?y,?x_28)) ] ES2: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(*(?x_27,0),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))),*(?y,?x_27)), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,s(?y_28)),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),*(?y,?x_28)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) ] HS2: [ +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 32 ES: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(*(?x_27,0),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))),*(?y,?x_27)), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,s(?y_28)),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),*(?y,?x_28)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) ] HS: [ +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) ] HS0: [ +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) ] HS1: [ +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) = +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)) [ +(0,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30))))))) = +(+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))),*(0,?x_30)), +(+(*(?x_31,?y_31),?x_31),+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31))))))) = +(+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))),*(s(?y_31),?x_31)) ] ES2: [ +(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))) = +(+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))),*(0,?x_30)), +(*(?x_31,?y_31),+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))))) = +(+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))),*(s(?y_31),?x_31)), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)) ] HS2: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) -> +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] STEP 33 ES: [ +(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))) = +(+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))),*(0,?x_30)), +(*(?x_31,?y_31),+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))))) = +(+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))),*(s(?y_31),?x_31)), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)) ] HS: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) -> +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES0: [ +(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))) = +(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,+(?x_30,?x_30)))))), +(*(?x_31,?y_31),+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))))) = +(*(?x_31,?y_31),+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,+(?x_31,?x_31)))))))), +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)) ] HS0: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) -> +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] ES1: [ +(*(*(?x_20,?y_20),?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))) = +(*(?x_20,*(?z,?y_20)),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),+(*(?x_20,?z),*(?x_20,?z)))))), s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))), +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28))))))),+(*(?x_28,?y),?x_28)) = +(+(*(?x_28,?y_28),+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,+(?x_28,?x_28)))))))),*(?y,?x_28)) ] HS1: [ +(*(?x_27,?y),+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27))))))) -> +(+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,+(?x_27,?x_27)))))),*(?y,?x_27)), +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24)))))),+(*(?x_24,?y),?x_24)) -> +(+(*(?x_24,?y_24),+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,+(?x_24,?x_24))))))),*(?y,?x_24)), +(*(*(?x_16,?y_16),?z),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))) -> +(*(?x_16,*(?z,?y_16)),+(*(?x_16,?z),+(*(?x_16,?z),+(*(?x_16,?z),*(?x_16,?z))))), +(*(?x_23,?y),+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23)))))) -> +(+(?x_23,+(?x_23,+(?x_23,+(?x_23,+(?x_23,?x_23))))),*(?y,?x_23)), +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20))))),+(*(?x_20,?y),?x_20)) -> +(+(*(?x_20,?y_20),+(?x_20,+(?x_20,+(?x_20,+(?x_20,+(?x_20,?x_20)))))),*(?y,?x_20)), s(s(+(+(*(?y_6,?x_6),+(?y_6,+(?x_6,?y_6))),+(*(?x_4,?x_6),+(?x_4,?x_4))))) -> s(s(+(+(+(+(?x_6,?x_4),?x_4),*(?x_4,?x_6)),+(*(?y_6,?x_6),+(?y_6,?y_6))))), +(*(?x_19,?y),+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19))))) -> +(+(?x_19,+(?x_19,+(?x_19,+(?x_19,?x_19)))),*(?y,?x_19)), +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,?x_16)))),+(*(?x_16,?y),?x_16)) -> +(+(*(?x_16,?y_16),+(?x_16,+(?x_16,+(?x_16,+(?x_16,?x_16))))),*(?y,?x_16)), +(*(*(?x_12,?y_12),?z),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))) -> +(*(?x_12,*(?z,?y_12)),+(*(?x_12,?z),+(*(?x_12,?z),*(?x_12,?z)))), +(*(?x_15,?y),+(?x_15,+(?x_15,+(?x_15,?x_15)))) -> +(+(?x_15,+(?x_15,+(?x_15,?x_15))),*(?y,?x_15)), +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,?x_12))),+(*(?x_12,?y),?x_12)) -> +(+(*(?x_12,?y_12),+(?x_12,+(?x_12,+(?x_12,?x_12)))),*(?y,?x_12)), s(+(+(+(?y_6,?y_2),*(?y_2,?y_6)),+(*(?x_6,?y_6),?x_6))) -> s(+(+(*(?x_6,?y_6),+(?x_6,?y_6)),+(*(?y_2,?y_6),?y_2))), +(*(?x_11,?y),+(?x_11,+(?x_11,?x_11))) -> +(+(?x_11,+(?x_11,?x_11)),*(?y,?x_11)), +(+(*(?x_8,?y_8),+(?x_8,?x_8)),+(*(?x_8,?y),?x_8)) -> +(+(*(?x_8,?y_8),+(?x_8,+(?x_8,?x_8))),*(?y,?x_8)), +(*(*(?x_8,?y_8),?z),+(*(?x_8,?z),*(?x_8,?z))) -> +(*(?x_8,*(?z,?y_8)),+(*(?x_8,?z),*(?x_8,?z))), +(*(?x_7,?y),+(?x_7,?x_7)) -> +(+(?x_7,?x_7),*(?y,?x_7)), +(+(*(?x_6,?y_6),?x_6),+(*(?x_6,?y_2),?x_6)) -> +(+(*(?x_6,?y_6),+(?x_6,?x_6)),*(?y_2,?x_6)), s(s(+(*(?x_8,?y_8),+(+(?x_8,?x_8),?y_8)))) -> s(s(+(*(?x_8,?y_8),+(?x_8,+(?y_8,?x_8))))), +(*(?x_2,?x),+(*(?y_2,?x),?x)) -> +(+(*(?x,?x_2),?x),*(?x,?y_2)), +(*(*(?x_4,?y_4),?z),*(?x_4,?z)) -> +(*(?x_4,*(?z,?y_4)),*(?x_4,?z)), +(*(?x_5,?y_2),?x_5) -> +(?x_5,*(?y_2,?x_5)), +(*(?z,?x_2),+(*(?z,?y_2),?z)) -> +(+(*(?z,?x_2),?z),*(?y_2,?z)), s(+(?y,+(*(?y_4,?y),?y_4))) -> s(+(?y_4,+(*(?y,?y_4),?y))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(s(?y_4),?x_4) -> +(*(?x_4,?y_4),?x_4), +(?y_2,s(?x_2)) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(0,?y) -> 0, +(?x,0) -> ?x ] Expand s(s(s(s(+(+(*(?x_2,?x_4),+(?x_2,+(?x_4,?x_4))),+(*(?y_2,?x_2),+(?y_2,+(?x_2,?y_2)))))))) = s(s(s(s(+(+(*(?x_2,?x_4),+(+(?x_4,?x_2),+(?x_4,?x_2))),+(*(?y_2,?x_2),+(?y_2,?y_2))))))) [ s(s(s(s(+(+(*(0,?x_2),+(0,+(?x_2,?x_2))),+(0,+(?x_5,+(0,?x_5)))))))) = s(s(s(s(+(+(*(0,?x_2),+(+(?x_2,0),+(?x_2,0))),+(*(?x_5,0),+(?x_5,?x_5))))))), s(s(s(s(+(+(*(s(?y_6),?x_2),+(s(?y_6),+(?x_2,?x_2))),+(+(*(?x_6,?y_6),?x_6),+(?x_6,+(s(?y_6),?x_6)))))))) = s(s(s(s(+(+(*(s(?y_6),?x_2),+(+(?x_2,s(?y_6)),+(?x_2,s(?y_6)))),+(*(?x_6,s(?y_6)),+(?x_6,?x_6))))))) ] rewriting induction stopped because of timeout. *** Ground Confluence Check by Rewriting Induction *** Sort: {Nat} Signature: [ * : Nat,Nat -> Nat, + : Nat,Nat -> Nat, 0 : Nat, s : Nat -> Nat ] Rule Part: [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] Conjecture Part: [ +(0,?y) = ?y, +(s(?x),?y) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] Precedence (by weight): {(*,3),(+,2),(0,1),(s,0)} Rule part is confluent. R0 is ground confluent. Check conj part consists of inductive theorems of R0. Rules: [ +(?x,0) -> ?x, +(?x,s(?y)) -> s(+(?x,?y)), *(0,?y) -> 0, *(s(?x),?y) -> +(*(?x,?y),?y) ] Conjectures: [ +(0,?y) = ?y, +(s(?x),?y) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] STEP 0 ES: [ +(0,?y) = ?y, +(s(?x),?y) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS: [ ] ES0: [ +(0,?y) = ?y, +(s(?x),?y) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS0: [ ] ES1: [ +(0,?y) = ?y, +(s(?x),?y) = s(+(?x,?y)), *(?x,0) = 0, *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x), *(?x,?y) = *(?y,?x) ] HS1: [ ] Expand +(0,?y) = ?y [ 0 = 0, s(+(0,?y_2)) = s(?y_2) ] ES2: [ 0 = 0, s(+(0,?y_2)) = s(?y_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(s(?x),?y) = s(+(?x,?y)) ] HS2: [ +(0,?y) -> ?y ] STEP 1 ES: [ 0 = 0, s(+(0,?y_2)) = s(?y_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(s(?x),?y) = s(+(?x,?y)) ] HS: [ +(0,?y) -> ?y ] ES0: [ 0 = 0, s(?y_2) = s(?y_2), *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(s(?x),?y) = s(+(?x,?y)) ] HS0: [ +(0,?y) -> ?y ] ES1: [ *(?x,?y) = *(?y,?x), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), *(?x,0) = 0, +(s(?x),?y) = s(+(?x,?y)) ] HS1: [ +(0,?y) -> ?y ] Expand *(?x,0) = 0 [ 0 = 0, +(*(?x_4,0),0) = 0 ] ES2: [ 0 = 0, *(?x_4,0) = 0, +(s(?x),?y) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS2: [ *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 2 ES: [ 0 = 0, *(?x_4,0) = 0, +(s(?x),?y) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS: [ *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ 0 = 0, 0 = 0, +(s(?x),?y) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS0: [ *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ +(s(?x),?y) = s(+(?x,?y)), *(?x,?y) = *(?y,?x), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(?x,?y) = +(?y,?x) ] HS1: [ *(?x,0) -> 0, +(0,?y) -> ?y ] Expand *(?x,?y) = *(?y,?x) [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] ES2: [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS2: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 3 ES: [ 0 = *(?y_3,0), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ 0 = 0, +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS0: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), +(?x,?y) = +(?y,?x), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS1: [ *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand +(?x,?y) = +(?y,?x) [ ?x_1 = +(0,?x_1), s(+(?x_2,?y_2)) = +(s(?y_2),?x_2) ] ES2: [ ?x_1 = +(0,?x_1), s(+(?x_2,?y_2)) = +(s(?y_2),?x_2), +(s(?x),?y) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS2: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 4 ES: [ ?x_1 = +(0,?x_1), s(+(?x_2,?y_2)) = +(s(?y_2),?x_2), +(s(?x),?y) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ ?x_1 = ?x_1, s(+(?x_2,?y_2)) = +(s(?y_2),?x_2), +(s(?x),?y) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS0: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ s(+(?x_2,?y_2)) = +(s(?y_2),?x_2), +(s(?x),?y) = s(+(?x,?y)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)) ] HS1: [ +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand +(s(?y_2),?x_2) = s(+(?x_2,?y_2)) [ s(?y) = s(+(0,?y)), s(+(s(?y),?y_2)) = s(+(s(?y_2),?y)) ] ES2: [ s(?y) = s(+(0,?y)), s(+(s(?y),?y_2)) = s(+(s(?y_2),?y)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS2: [ +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 5 ES: [ s(?y) = s(+(0,?y)), s(+(s(?y),?y_2)) = s(+(s(?y_2),?y)), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), +(s(?x),?y) = s(+(?x,?y)) ] HS: [ +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ s(?y) = s(?y), s(s(+(?y_2,?y))) = s(s(+(?y,?y_2))), +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x), s(+(?y,?x)) = s(+(?x,?y)) ] HS0: [ +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ +(*(?x_4,?y_4),?y_4) = *(?y_4,s(?x_4)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(?x,s(?y)) = +(*(?x,?y),?x) ] HS1: [ +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand *(?y_4,s(?x_4)) = +(*(?x_4,?y_4),?y_4) [ 0 = +(*(?x,0),0), +(*(?x_4,s(?x)),s(?x)) = +(*(?x,s(?x_4)),s(?x_4)) ] ES2: [ 0 = +(*(?x,0),0), s(+(*(?x_4,s(?x)),?x)) = +(*(?x,s(?x_4)),s(?x_4)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS2: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 6 ES: [ 0 = +(*(?x,0),0), s(+(*(?x_4,s(?x)),?x)) = +(*(?x,s(?x_4)),s(?x_4)), *(?x,s(?y)) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ 0 = 0, s(+(+(*(?x,?x_4),?x_4),?x)) = s(+(+(*(?x_4,?x),?x),?x_4)), +(*(?y,?x),?x) = +(*(?x,?y),?x), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS0: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ s(+(+(*(?x,?x_4),?x_4),?x)) = s(+(+(*(?x_4,?x),?x),?x_4)), +(+(?x,?y),?z) = +(?x,+(?y,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS1: [ *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand +(+(?x,?y),?z) = +(?x,+(?y,?z)) [ +(?x_1,?z) = +(?x_1,+(0,?z)), +(s(+(?x_2,?y_2)),?z) = +(?x_2,+(s(?y_2),?z)) ] ES2: [ +(?x_1,?z) = +(?x_1,+(0,?z)), s(+(?z,+(?x_2,?y_2))) = +(?x_2,+(s(?y_2),?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(+(*(?x,?x_4),?x_4),?x)) = s(+(+(*(?x_4,?x),?x),?x_4)) ] HS2: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 7 ES: [ +(?x_1,?z) = +(?x_1,+(0,?z)), s(+(?z,+(?x_2,?y_2))) = +(?x_2,+(s(?y_2),?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(+(*(?x,?x_4),?x_4),?x)) = s(+(+(*(?x_4,?x),?x),?x_4)) ] HS: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ +(?x_1,?z) = +(?x_1,?z), s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS0: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(*(?x,?y),?z) = *(?x,*(?y,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS1: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand *(*(?x,?y),?z) = *(?x,*(?y,?z)) [ *(0,?z) = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)) ] ES2: [ 0 = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS2: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 8 ES: [ 0 = *(0,*(?y_3,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = *(s(?x_4),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ 0 = 0, *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS0: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) ] HS1: [ *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand s(+(?z,+(?x_2,?y_2))) = s(+(?x_2,+(?z,?y_2))) [ s(+(?z,?x_3)) = s(+(?x_3,+(?z,0))), s(+(?z,s(+(?x_4,?y_4)))) = s(+(?x_4,+(?z,s(?y_4)))) ] ES2: [ s(+(?z,?x_3)) = s(+(?x_3,+(?z,0))), s(s(+(?z,+(?x_4,?y_4)))) = s(+(?x_4,+(?z,s(?y_4)))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS2: [ s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 9 ES: [ s(+(?z,?x_3)) = s(+(?x_3,+(?z,0))), s(s(+(?z,+(?x_4,?y_4)))) = s(+(?x_4,+(?z,s(?y_4)))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS: [ s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ s(+(?z,?x_3)) = s(+(?x_3,?z)), s(s(+(?z,+(?x_4,?y_4)))) = s(s(+(?x_4,+(?z,?y_4)))), *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS0: [ s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS1: [ s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand *(+(?x,?y),?z) = +(*(?x,?z),*(?y,?z)) [ *(?x_1,?z) = +(*(?x_1,?z),*(0,?z)), *(s(+(?x_2,?y_2)),?z) = +(*(?x_2,?z),*(s(?y_2),?z)) ] ES2: [ *(?x_1,?z) = +(*(?x_1,?z),*(0,?z)), +(*(+(?x_2,?y_2),?z),?z) = +(*(?x_2,?z),*(s(?y_2),?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS2: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 10 ES: [ *(?x_1,?z) = +(*(?x_1,?z),*(0,?z)), +(*(+(?x_2,?y_2),?z),?z) = +(*(?x_2,?z),*(s(?y_2),?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), *(+(*(?x_4,?y_4),?y_4),?z) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ *(?x_1,?z) = *(?x_1,?z), +(*(?x_2,?z),+(*(?y_2,?z),?z)) = +(*(?x_2,?z),+(*(?y_2,?z),?z)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), +(*(*(?x_4,?y_4),?z),*(?y_4,?z)) = +(*(?x_4,*(?y_4,?z)),*(?y_4,?z)), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS0: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))), *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) ] HS1: [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand *(?x,+(?y,?z)) = +(*(?x,?y),*(?x,?z)) [ *(?x,?x_1) = +(*(?x,?x_1),*(?x,0)), *(?x,s(+(?x_2,?y_2))) = +(*(?x,?x_2),*(?x,s(?y_2))) ] ES2: [ *(?x,?x_1) = +(*(?x,?x_1),*(?x,0)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,?x_2),*(?x,s(?y_2))), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS2: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 11 ES: [ *(?x,?x_1) = +(*(?x,?x_1),*(?x,0)), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,?x_2),*(?x,s(?y_2))), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ *(?x,?x_1) = *(?x,?x_1), +(*(?x_2,?x),+(*(?y_2,?x),?x)) = +(*(?x,?x_2),+(*(?y_2,?x),?x)), s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS0: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) ] HS1: [ *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Expand s(+(*(?x,?x_4),+(?x_4,?x))) = s(+(*(?x_4,?x),+(?x,?x_4))) [ s(+(0,+(?y_7,0))) = s(+(*(?y_7,0),+(0,?y_7))), s(+(+(*(?x_8,?y_8),?y_8),+(?y_8,s(?x_8)))) = s(+(*(?y_8,s(?x_8)),+(s(?x_8),?y_8))) ] ES2: [ s(?y_7) = s(+(*(?y_7,0),+(0,?y_7))), s(s(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?x_8))))) = s(+(*(?y_8,s(?x_8)),+(s(?x_8),?y_8))) ] HS2: [ s(+(*(?x,?x_4),+(?x_4,?x))) -> s(+(*(?x_4,?x),+(?x,?x_4))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] STEP 12 ES: [ s(?y_7) = s(+(*(?y_7,0),+(0,?y_7))), s(s(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?x_8))))) = s(+(*(?y_8,s(?x_8)),+(s(?x_8),?y_8))) ] HS: [ s(+(*(?x,?x_4),+(?x_4,?x))) -> s(+(*(?x_4,?x),+(?x,?x_4))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES0: [ s(?y_7) = s(?y_7), s(s(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?x_8))))) = s(s(+(*(?x_8,?y_8),+(?y_8,+(?y_8,?x_8))))) ] HS0: [ s(+(*(?x,?x_4),+(?x_4,?x))) -> s(+(*(?x_4,?x),+(?x,?x_4))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] ES1: [ ] HS1: [ s(+(*(?x,?x_4),+(?x_4,?x))) -> s(+(*(?x_4,?x),+(?x,?x_4))), *(?x,+(?y,?z)) -> +(*(?x,?y),*(?x,?z)), *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)), s(+(?z,+(?x_2,?y_2))) -> s(+(?x_2,+(?z,?y_2))), *(*(?x,?y),?z) -> *(?x,*(?y,?z)), +(+(?x,?y),?z) -> +(?x,+(?y,?z)), *(?y_4,s(?x_4)) -> +(*(?x_4,?y_4),?y_4), +(s(?y_2),?x_2) -> s(+(?x_2,?y_2)), +(?x,?y) -> +(?y,?x), *(?x,?y) -> *(?y,?x), *(?x,0) -> 0, +(0,?y) -> ?y ] Conj part consisits of inductive theorems of R0. examples/fromCops/cr/208.trs: Success(GCR) (10026 msec.)