YES 1 decompositions #1 ----------- 1: +(0(),x1) -> x1 2: +(1(),-(1())) -> 0() 3: -(0()) -> 0() 4: -(-(x1)) -> x1 5: -(+(x1,x2)) -> +(-(x1),-(x2)) 6: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 7: +(x1,x2) -> +(x2,x1) @Jouannaud and Kirchner's criterion --- R 1: +(0(),x1) -> x1 2: +(1(),-(1())) -> 0() 3: -(0()) -> 0() 4: -(-(x1)) -> x1 5: -(+(x1,x2)) -> +(-(x1),-(x2)) 6: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 7: +(x1,x2) -> +(x2,x1) --- S 1: +(0(),x1) -> x1 2: +(1(),-(1())) -> 0() 3: -(0()) -> 0() 4: -(-(x1)) -> x1 5: -(+(x1,x2)) -> +(-(x1),-(x2)) 6: +(+(x1,x2),x3) -> +(x1,+(x2,x3)) 7: +(x1,x2) -> +(x2,x1)