YES 1 decompositions #1 ----------- 2: +(x1,s(x2)) -> s(+(x1,x2)) 3: +(x1,x2) -> +(x2,x1) @Jouannaud and Kirchner's criterion --- R 2: +(x1,s(x2)) -> s(+(x1,x2)) 3: +(x1,x2) -> +(x2,x1) --- S 2: +(x1,s(x2)) -> s(+(x1,x2)) 3: +(x1,x2) -> +(x2,x1) NOTE: input TRS is reduced original is 1: +(s(x1),x2) -> s(+(x1,x2)) 2: +(x1,s(x2)) -> s(+(x1,x2)) 3: +(x1,x2) -> +(x2,x1) reduced to 2: +(x1,s(x2)) -> s(+(x1,x2)) 3: +(x1,x2) -> +(x2,x1)