YES(?,O(n^1))

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

Strict Trs:
  { rec[even_0][1](0()) -> True()
  , rec[even_0][1](S(0())) -> False()
  , rec[even_0][1](S(S(x2))) -> rec[even_0][1](x2)
  , main(x1) -> rec[even_0][1](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(0) = {}, safe(rec[even_0][1]) = {}, safe(True) = {},
 safe(S) = {1}, safe(False) = {}, safe(main) = {}

and precedence

 main > rec[even_0][1] .

Following symbols are considered recursive:

 {rec[even_0][1]}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

           rec[even_0][1](0();) > True()             
                                                     
      rec[even_0][1](S(; 0());) > False()            
                                                     
  rec[even_0][1](S(; S(; x2));) > rec[even_0][1](x2;)
                                                     
                      main(x1;) > rec[even_0][1](x1;)
                                                     

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