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