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