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:
  { 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),O(n^1))

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

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 }

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(d) = {}, safe(e) = {1}, safe(u) = {1}, safe(c) = {},
   safe(b) = {1}, safe(v) = {}, safe(a) = {1}
  
  and precedence
  
   d ~ c, d ~ b, d ~ v, c ~ b, c ~ v, b ~ v .
  
  Following symbols are considered recursive:
  
   {d, c, b}
  
  The recursion depth is 1.
  
  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          
                             

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:
  { 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),O(1))

Empty rules are trivially bounded

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