YES

Problem:
 a__f(f(X)) -> a__c(f(g(f(X))))
 a__c(X) -> d(X)
 a__h(X) -> a__c(d(X))
 mark(f(X)) -> a__f(mark(X))
 mark(c(X)) -> a__c(X)
 mark(h(X)) -> a__h(mark(X))
 mark(g(X)) -> g(X)
 mark(d(X)) -> d(X)
 a__f(X) -> f(X)
 a__c(X) -> c(X)
 a__h(X) -> h(X)

Proof:
 WPO Processor:
  algebra: Sum
  weight function:
   w0 = 0
   w(h) = w(c) = w(mark) = w(a__h) = w(d) = w(a__c) = w(g) = w(a__f) = w(f) = 0
  status function:
   st(h) = st(c) = st(mark) = st(a__h) = st(d) = st(a__c) = st(g) = st(a__f) = st(f) = [0]
  precedence:
   mark > a__f > a__h > a__c > h ~ c ~ d ~ g ~ f
  problem:
   
  Qed