YES(?,O(n^1))

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

Strict Trs:
  { a(b(x)) -> b(a(x))
  , a(c(x)) -> x }
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(a) = {}, safe(b) = {1}, safe(c) = {1}

and precedence

 empty .

Following symbols are considered recursive:

 {a}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

  a(b(; x);) > b(; a(x;))
                         
  a(c(; x);) > x         
                         

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