YES(?,O(n^1))

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

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

The input was oriented with the instance of 'Small Polynomial Path
Order (PS,1-bounded)' as induced by the safe mapping

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

and precedence

 v > u, w > u, v ~ w .

Following symbols are considered recursive:

 {v, w}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

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

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