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