YES

TRS:

  a__g(X) -> a__h(X)
  a__c() -> d()
  a__h(d()) -> a__g(c())
  mark(g(X)) -> a__g(X)
  mark(h(X)) -> a__h(X)
  mark(c()) -> a__c()
  mark(d()) -> d()
  a__g(X) -> g(X)
  a__h(X) -> h(X)
  a__c() -> c()

max/plus interpretations on N:

  a__g_A(x1) = max{16, 15 + x1}
  a__g#_A(x1) = max{5, 8 + x1}
  a__h_A(x1) = max{16, 11 + x1}
  a__h#_A(x1) = max{4, 6 + x1}
  a__c_A = 4
  a__c#_A = 2
  d_A = 4
  d#_A = 1
  c_A = 1
  c#_A = 0
  mark_A(x1) = max{3, 4 + x1}
  mark#_A(x1) = max{3, -4 + x1}
  g_A(x1) = max{10, 12 + x1}
  g#_A(x1) = max{0, 0}
  h_A(x1) = max{12, 11 + x1}
  h#_A(x1) = max{6, 6}

precedence:

  mark > a__h = a__c > d = h > a__g = c > g