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