YES 1 decompositions #0 ----------- 1: +(x,y) -> +(y,x) 2: +(0(),y) -> y 3: +(x,0()) -> x 4: +(s(x),y) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z) @Jouannaud and Kirchner's criterion --- R 1: +(x,y) -> +(y,x) 2: +(0(),y) -> y 3: +(x,0()) -> x 4: +(s(x),y) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z) --- S 1: +(x,y) -> +(y,x) 2: +(0(),y) -> y 3: +(x,0()) -> x 4: +(s(x),y) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z)