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()

linear polynomial interpretations on N:

  a__g_A(x1) = 1
  a__g#_A(x1) = 2
  a__h_A(x1) = 1
  a__h#_A(x1) = 1
  a__c_A = 1
  a__c#_A = 4
  d_A = 1
  d#_A = 3
  c_A = 0
  c#_A = 0
  mark_A(x1) = 1
  mark#_A(x1) = 5
  g_A(x1) = 1
  g#_A(x1) = 0
  h_A(x1) = 1
  h#_A(x1) = 0

precedence:

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