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)

max/plus interpretations on N:

  a__c_A = 7
  a__c#_A = 7
  a__f_A(x1) = max{6, 3 + x1}
  a__f#_A(x1) = max{6, 3 + x1}
  g_A(x1) = max{0, x1}
  g#_A(x1) = max{0, x1}
  c_A = 3
  c#_A = 3
  mark_A(x1) = max{8, 5 + x1}
  mark#_A(x1) = max{8, 5 + x1}
  f_A(x1) = max{0, 2 + x1}
  f#_A(x1) = max{0, 2 + x1}

precedence:

  a__c > a__f = c > g = f > mark