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