We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { foldl#3(x2, Nil()) -> x2 , foldl#3(x16, Cons(x24, x6)) -> foldl#3(Cons(x24, x16), x6) , main(x1) -> foldl#3(Nil(), x1) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The input was oriented with the instance of 'Small Polynomial Path Order (PS,1-bounded)' as induced by the safe mapping safe(foldl#3) = {1}, safe(Nil) = {}, safe(Cons) = {1, 2}, safe(main) = {} and precedence main > foldl#3 . Following symbols are considered recursive: {foldl#3} The recursion depth is 1. For your convenience, here are the satisfied ordering constraints: foldl#3(Nil(); x2) > x2 foldl#3(Cons(; x24, x6); x16) > foldl#3(x6; Cons(; x24, x16)) main(x1;) > foldl#3(x1; Nil()) Hurray, we answered YES(?,O(n^1))