NO Problem: +(x,+(y,z)) -> +(+(x,y),z) +(+(x,y),z) -> +(x,+(y,z)) +(x,y) -> +(y,x) +(s(x),y) -> +(x,s(y)) +(x,s(y)) -> +(s(x),y) *(x,s(y)) -> +(x,*(x,y)) *(s(x),y) -> +(*(x,y),y) *(x,y) -> *(y,x) sq(x) -> *(x,x) sq(s(x)) -> +(*(x,x),s(+(x,x))) Proof: Containment Processor: loop length: 1 terms: +(x,y) context: [] substitution: x -> y y -> x Qed