YES(?,POLY)

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

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(?,POLY)

The input was oriented with the instance of 'Polynomial Path Order'
as induced by the safe mapping

 safe(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {},
 safe(b) = {}, safe(v) = {}, safe(a) = {1}

and precedence

 d > b, d > v, c > b, c > v, b > v, d ~ c .

Following symbols are considered recursive:

 {d, c, b}

The recursion depth is 2.

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(?,POLY)