YES(?,PRIMREC)

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

Strict Trs:
  { a__f(X) -> f(X)
  , a__f(f(X)) -> a__c(f(g(f(X))))
  , a__c(X) -> d(X)
  , a__c(X) -> c(X)
  , a__h(X) -> a__c(d(X))
  , a__h(X) -> h(X)
  , mark(f(X)) -> a__f(mark(X))
  , mark(g(X)) -> g(X)
  , mark(d(X)) -> d(X)
  , mark(c(X)) -> a__c(X)
  , mark(h(X)) -> a__h(mark(X)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,PRIMREC)

The input was oriented with the instance of'multiset path order' as
induced by the precedence

 a__f > f, a__f > a__c, a__f > g, a__f > d, a__f > c, a__f > h,
 a__c > f, a__c > d, a__c > c, a__c > h, g > f, g > a__c, g > d,
 g > c, g > h, d > f, d > h, a__h > a__f, a__h > f, a__h > a__c,
 a__h > g, a__h > d, a__h > c, a__h > h, mark > a__f, mark > f,
 mark > a__c, mark > g, mark > d, mark > a__h, mark > c, mark > h,
 c > f, c > h, f ~ h, d ~ c .

Hurray, we answered YES(?,PRIMREC)