MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__fib(N) -> a__sel(mark(N), a__fib1(s(0()), s(0()))) , a__fib(X) -> fib(X) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) , a__sel(0(), cons(X, XS)) -> mark(X) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(fib1(X1, X2)) -> a__fib1(mark(X1), mark(X2)) , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) , mark(fib(X)) -> a__fib(mark(X)) , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , a__fib1(X, Y) -> cons(mark(X), fib1(Y, add(X, Y))) , a__fib1(X1, X2) -> fib1(X1, X2) , a__add(X1, X2) -> add(X1, X2) , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y))) , a__add(0(), X) -> mark(X) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..