MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { natsFrom(N) -> cons(N, n__natsFrom(s(N))) , natsFrom(X) -> n__natsFrom(X) , fst(pair(XS, YS)) -> XS , snd(pair(XS, YS)) -> YS , splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS)) , splitAt(0(), XS) -> pair(nil(), XS) , u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS) , activate(X) -> X , activate(n__natsFrom(X)) -> natsFrom(X) , head(cons(N, XS)) -> N , tail(cons(N, XS)) -> activate(XS) , sel(N, XS) -> head(afterNth(N, XS)) , afterNth(N, XS) -> snd(splitAt(N, XS)) , take(N, XS) -> fst(splitAt(N, XS)) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..