NO Rewrite Rules: [ seteq(?xs,?ys) -> and(subseteq(?xs,?ys),subseteq(?ys,?xs)), subseteq(nil,nil) -> true, subseteq(nil,cons(?y,?ys)) -> false, subseteq(cons(?x,?xs),?ys) -> and(member(?x,?ys),subseteq(?xs,?ys)), member(?x,nil) -> false, member(?x,cons(?y,?ys)) -> or(eq(?x,?y),member(?x,?ys)), eq(0,0) -> true, eq(0,s(?y)) -> false, eq(s(?x),0) -> false, eq(s(?x),s(?y)) -> eq(?x,?y), or(?x,true) -> true, or(true,?y) -> true, or(false,false) -> false, and(true,true) -> true, and(?x,false) -> false, and(false,?y) -> false, app(nil,?ys) -> ?ys, app(cons(?x,?xs),?ys) -> cons(?x,app(?xs,?ys)), seteq(app(?xs,?ys),app(?ys,?xs)) -> true ] Apply Direct Methods... Inner CPs: [ seteq(?ys_12,app(?ys_12,nil)) = true, seteq(app(?ys_12,nil),?ys_12) = true, seteq(cons(?x_13,app(?xs_13,?ys_13)),app(?ys_13,cons(?x_13,?xs_13))) = true, seteq(app(?ys_13,cons(?x_13,?xs_13)),cons(?x_13,app(?xs_13,?ys_13))) = true ] Outer CPs: [ and(subseteq(app(?xs_14,?ys_14),app(?ys_14,?xs_14)),subseteq(app(?ys_14,?xs_14),app(?xs_14,?ys_14))) = true, true = true, false = false ] not Overlay, check Termination... Terminating, not WCR Knuth & Bendix Direct Methods: not CR Final result: not CR new/seteq2.trs: Success(not CR) (29 msec.)