YES(O(1),O(n^1))

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

Strict Trs:
  { a(b(x)) -> b(a(x))
  , a(c(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(n^1))

We use the processor 'Small Polynomial Path Order (PS,1-bounded)'
to orient following rules strictly.

Trs:
  { a(b(x)) -> b(a(x))
  , a(c(x)) -> x }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  The input was oriented with the instance of 'Small Polynomial Path
  Order (PS,1-bounded)' 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         
                           

We return to the main proof.

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

Weak Trs:
  { a(b(x)) -> b(a(x))
  , a(c(x)) -> x }
Obligation:
  innermost runtime complexity
Answer:
  YES(O(1),O(1))

Empty rules are trivially bounded

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