YES
Input TRS:
      1: a__f(f(X)) -> a__c(f(g(f(X))))
      2: a__c(X) -> d(X)
      3: a__h(X) -> a__c(d(X))
      4: mark(f(X)) -> a__f(mark(X))
      5: mark(c(X)) -> a__c(X)
      6: mark(h(X)) -> a__h(mark(X))
      7: mark(g(X)) -> g(X)
      8: mark(d(X)) -> d(X)
      9: a__f(X) -> f(X)
      10: a__c(X) -> c(X)
      11: a__h(X) -> h(X)
Number of strict rules: 11
Direct POLO(bPol) ... removes: 8 1 3 5 10 7 11 9 6 2
      h 	w: 2 * x1 + 8
      d 	w: x1 + 1
      a__h	w: 2 * x1 + 14
      a__f	w: x1 + 8
      c 	w: x1 + 1
      f 	w: x1 + 4
      mark	w: 2 * x1 + 1
      g 	w: x1 + 1
      a__c	w: x1 + 2
Number of strict rules: 1
Direct POLO(bPol) ... removes: 4
      h 	w: 2 * x1 + 21246
      d 	w: x1 + 1
      a__h	w: 2 * x1 + 42491
      a__f	w: x1 + 1705
      c 	w: x1 + 5
      f 	w: x1 + 853
      mark	w: 2 * x1 + 1
      g 	w: x1 + 841
      a__c	w: x1 + 11
Number of strict rules: 0