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