YES

TRS:

  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)

linear polynomial interpretations on N:

  a__f_A(x1) = x1 + 5
  a__f#_A(x1) = x1 + 4
  f_A(x1) = x1 + 5
  f#_A(x1) = x1 + 2
  a__c_A(x1) = 10
  a__c#_A(x1) = 1
  g_A(x1) = x1 + 1
  g#_A(x1) = x1
  d_A(x1) = 10
  d#_A(x1) = 0
  a__h_A(x1) = x1 + 10
  a__h#_A(x1) = x1 + 2
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 1
  c_A(x1) = 10
  c#_A(x1) = 0
  h_A(x1) = x1 + 10
  h#_A(x1) = 0

precedence:

  a__h > h > mark > g = d > a__f > f = a__c > c