YES(?,O(1))

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

Strict Trs:
  { f(c(a(), z, x)) -> b(a(), z)
  , b(y, z) -> z
  , b(x, b(z, y)) -> f(b(f(f(z)), c(x, z, y))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(1))

Arguments of following rules are not normal-forms:

{ b(x, b(z, y)) -> f(b(f(f(z)), c(x, z, y))) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { f(c(a(), z, x)) -> b(a(), z)
  , b(y, z) -> z }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS,0-bounded)' as induced by the safe mapping

 safe(f) = {}, safe(c) = {1, 2, 3}, safe(a) = {}, safe(b) = {1, 2}

and precedence

 f > b .

Following symbols are considered recursive:

 {}

The recursion depth is 0.

For your convenience, here are the satisfied ordering constraints:

  f(c(; a(),  z,  x);) > b(; a(),  z)
                                     
            b(; y,  z) > z           
                                     

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