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

Strict Trs:
  { d(x) -> e(u(x))
  , d(u(x)) -> c(x)
  , c(u(x)) -> b(x)
  , b(u(x)) -> a(e(x))
  , v(e(x)) -> x }
Obligation:
  runtime complexity
Answer:
  YES(?,O(1))

The input is overlay and right-linear. Switching to innermost
rewriting.

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

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

and precedence

 d > c, c > b .

Following symbols are considered recursive:

 {}

The recursion depth is 0.

For your convenience, here are the satisfied ordering constraints:

        d(x;) > e(; u(; x))
                           
   d(u(; x);) > c(; x)     
                           
  c(; u(; x)) > b(; x)     
                           
  b(; u(; x)) > a(; e(; x))
                           
   v(e(; x);) > x          
                           

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