YES 1 decompositions #1 ----------- 1: +(x1,0()) -> x1 2: +(s(x1),x2) -> s(+(x2,x1)) 3: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 4: +(x1,x2) -> +(x2,x1) @Jouannaud and Kirchner's criterion --- R 1: +(x1,0()) -> x1 2: +(s(x1),x2) -> s(+(x2,x1)) 3: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 4: +(x1,x2) -> +(x2,x1) --- S 1: +(x1,0()) -> x1 2: +(s(x1),x2) -> s(+(x2,x1)) 3: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 4: +(x1,x2) -> +(x2,x1)