YES(?,O(n^1))

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

 notEmpty > odd, notEmpty > even, evenodd > odd, evenodd > even,
 odd ~ even, notEmpty ~ evenodd .

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))