YES(?,O(n^1))

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

Strict Trs:
  { rec[flip_0][1](E()) -> E()
  , rec[flip_0][1](Z(x1)) -> O(rec[flip_0][1](x1))
  , rec[flip_0][1](O(x1)) -> Z(rec[flip_0][1](x1))
  , main(x1) -> rec[flip_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(E) = {}, safe(rec[flip_0][1]) = {}, safe(Z) = {1},
 safe(O) = {1}, safe(main) = {}

and precedence

 main > rec[flip_0][1] .

Following symbols are considered recursive:

 {rec[flip_0][1]}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

      rec[flip_0][1](E();) > E()                     
                                                     
  rec[flip_0][1](Z(; x1);) > O(; rec[flip_0][1](x1;))
                                                     
  rec[flip_0][1](O(; x1);) > Z(; rec[flip_0][1](x1;))
                                                     
                 main(x1;) > rec[flip_0][1](x1;)     
                                                     

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