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