YES
*** Computating Strongly Quasi-Reducible Parts ***
TRS:
   [ +(0,?y) -> ?y,
     +(s(0),?y) -> s(?y),
     s(s(?x)) -> ?x ]
Constructors: {0,s}
Defined function symbols: {+}
Constructor subsystem:
   [ s(s(?x)) -> ?x ]
Rule part & Conj Part:
   [ s(s(?x)) -> ?x,
     +(0,?y) -> ?y,
     +(s(0),?y) -> s(?y) ]
   [ ]
*** Ground Confluence Check by Rewriting Induction ***
Sort: {Nat}
Signature:
   [ + : Nat,Nat -> Nat,
     s : Nat -> Nat,
     0 : Nat ]
Rule Part:
   [ s(s(?x)) -> ?x,
     +(0,?y) -> ?y,
     +(s(0),?y) -> s(?y) ]
Conjecture Part:
   [ ]
Precedence (by weight): {(+,3),(0,1),(s,0)}
Rule part is confluent.
R0 is ground confluent.
Conjucture part is empty.
examples/additions/plus4.trs: Success(GCR)
(8 msec.)