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