NO Problem 1: (VAR v_NonEmpty:S N:S X:S XS:S) (RULES after(0,XS:S) -> XS:S after(s(N:S),cons(X:S,XS:S)) -> after(N:S,XS:S) from(X:S) -> cons(X:S,from(s(X:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,XS:S) FROM(X:S) -> FROM(s(X:S)) -> Rules: after(0,XS:S) -> XS:S after(s(N:S),cons(X:S,XS:S)) -> after(N:S,XS:S) from(X:S) -> cons(X:S,from(s(X:S))) Problem 1: Infinite Processor: -> Pairs: AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,XS:S) FROM(X:S) -> FROM(s(X:S)) -> Rules: after(0,XS:S) -> XS:S after(s(N:S),cons(X:S,XS:S)) -> after(N:S,XS:S) from(X:S) -> cons(X:S,from(s(X:S))) -> Pairs in cycle: FROM(X:S) -> FROM(s(X:S)) The problem is infinite.