We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ list(Cons(x, xs)) -> list(xs)
, list(Nil()) -> True()
, list(Nil()) -> isEmpty[Match](Nil())
, notEmpty(Cons(x, xs)) -> True()
, notEmpty(Nil()) -> False()
, goal(x) -> list(x) }
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(list) = {}, safe(Cons) = {1, 2}, safe(Nil) = {},
safe(True) = {}, safe(isEmpty[Match]) = {1}, safe(notEmpty) = {},
safe(False) = {}, safe(goal) = {}
and precedence
goal > list .
Following symbols are considered recursive:
{list}
The recursion depth is 1.
For your convenience, here are the satisfied ordering constraints:
list(Cons(; x, xs);) > list(xs;)
list(Nil();) > True()
list(Nil();) > isEmpty[Match](; Nil())
notEmpty(Cons(; x, xs);) > True()
notEmpty(Nil();) > False()
goal(x;) > list(x;)
Hurray, we answered YES(?,O(n^1))