YES

TRS:

  a__c() -> a__f(g(c()))
  a__f(g(X)) -> g(X)
  mark(c()) -> a__c()
  mark(f(X)) -> a__f(X)
  mark(g(X)) -> g(X)
  a__c() -> c()
  a__f(X) -> f(X)

linear polynomial interpretations on N:

  a__c_A = 5
  a__c#_A = 5
  a__f_A(x1) = x1 + 2
  a__f#_A(x1) = x1 + 2
  g_A(x1) = x1 + 1
  g#_A(x1) = x1 + 1
  c_A = 1
  c#_A = 1
  mark_A(x1) = x1 + 5
  mark#_A(x1) = x1 + 5
  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 1

precedence:

  c > a__c > mark > a__f > g > f