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