YES 1 decompositions #0 ----------- 1: +(0(),y) -> y 2: +(x,0()) -> x 3: +(s(x),y) -> s(+(y,x)) 4: +(x,s(y)) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z) 6: +(x,y) -> +(y,x) @Jouannaud and Kirchner's criterion --- R 1: +(0(),y) -> y 2: +(x,0()) -> x 3: +(s(x),y) -> s(+(y,x)) 4: +(x,s(y)) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z) 6: +(x,y) -> +(y,x) --- S 1: +(0(),y) -> y 2: +(x,0()) -> x 3: +(s(x),y) -> s(+(y,x)) 4: +(x,s(y)) -> s(+(x,y)) 5: +(x,+(y,z)) -> +(+(x,y),z) 6: +(x,y) -> +(y,x)