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{6, 2 + x1}
  a__f#_A(x1) = max{6, 2 + x1}
  f_A(x1) = max{5, 2 + x1}
  f#_A(x1) = max{5, 2 + x1}
  a__c_A(x1) = max{7, x1}
  a__c#_A(x1) = max{7, x1}
  g_A(x1) = max{1, x1}
  g#_A(x1) = max{1, x1}
  d_A(x1) = max{7, x1}
  d#_A(x1) = max{7, x1}
  a__h_A(x1) = max{5, 7 + x1}
  a__h#_A(x1) = max{5, 7 + x1}
  mark_A(x1) = max{8, 8 + x1}
  mark#_A(x1) = max{8, 8 + x1}
  c_A(x1) = max{7, x1}
  c#_A(x1) = max{7, x1}
  h_A(x1) = max{6, 7 + x1}
  h#_A(x1) = max{6, 7 + x1}

precedence:

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