YES 2 decompositions #1 ----------- 3: hd(:(x3,x4)) -> x3 #2 ----------- 1: nats() -> :(0(),inc(nats())) 2: inc(:(x1,x2)) -> :(s(x1),inc(x2)) 4: tl(:(x5,x6)) -> x6 5: inc(tl(nats())) -> tl(inc(nats())) @Knuth and Bendix' criterion --- R 3: hd(:(x3,x4)) -> x3 --- S 3: hd(:(x3,x4)) -> x3 @Rule Labeling --- R 1: nats() -> :(0(),inc(nats())) 2: inc(:(x1,x2)) -> :(s(x1),inc(x2)) 4: tl(:(x5,x6)) -> x6 5: inc(tl(nats())) -> tl(inc(nats())) --- S 1: nats() -> :(0(),inc(nats())) 2: inc(:(x1,x2)) -> :(s(x1),inc(x2)) 4: tl(:(x5,x6)) -> x6 5: inc(tl(nats())) -> tl(inc(nats()))