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)

max/plus interpretations on N:

  a__f_A(x1) = max{31, 11 + x1}
  a__f#_A(x1) = max{37, 42}
  f_A(x1) = max{21, 11 + x1}
  f#_A(x1) = max{35, 33}
  a__c_A(x1) = max{32, 11 + x1}
  a__c#_A(x1) = max{34, 15 + x1}
  g_A(x1) = max{6, 7}
  g#_A(x1) = max{41, 38}
  d_A(x1) = max{19, -13 + x1}
  d#_A(x1) = max{0, 1}
  a__h_A(x1) = max{32, x1}
  a__h#_A(x1) = max{34, 2 + x1}
  mark_A(x1) = max{32, 31 + x1}
  mark#_A(x1) = max{43, 33 + x1}
  c_A(x1) = max{0, -18 + x1}
  c#_A(x1) = max{16, 0}
  h_A(x1) = max{0, x1}
  h#_A(x1) = max{3, 0}

precedence:

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