YES(?,O(n^1))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { odd(S(x)) -> even(x)
  , odd(0()) -> 0()
  , even(S(x)) -> odd(x)
  , even(0()) -> S(0()) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping

 safe(odd) = {}, safe(S) = {1}, safe(even) = {}, safe(0) = {}

and precedence

 odd ~ even .

Following symbols are considered recursive:

 {odd, even}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

   odd(S(; x);) > even(x;)
                          
      odd(0();) > 0()     
                          
  even(S(; x);) > odd(x;) 
                          
     even(0();) > S(; 0())
                          

Hurray, we answered YES(?,O(n^1))