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) = x1 + 3
  a__g#_A(x1) = x1 + 3
  a__h_A(x1) = x1 + 2
  a__h#_A(x1) = x1 + 2
  a__c_A = 6
  a__c#_A = 6
  d_A = 5
  d#_A = 5
  c_A = 1
  c#_A = 1
  mark_A(x1) = x1 + 6
  mark#_A(x1) = x1 + 6
  g_A(x1) = x1 + 1
  g#_A(x1) = x1 + 1
  h_A(x1) = x1 + 1
  h#_A(x1) = x1 + 1

precedence:

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