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