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 = 8
  a__c#_A = 9
  a__f_A(x1) = max{2, 1 + x1}
  a__f#_A(x1) = max{5, x1}
  g_A(x1) = max{3, -9 + x1}
  g#_A(x1) = max{7, 8}
  c_A = 8
  c#_A = 0
  mark_A(x1) = max{0, 2 + x1}
  mark#_A(x1) = max{6, 2 + x1}
  f_A(x1) = max{2, -1 + x1}
  f#_A(x1) = max{1, -1}

precedence:

  g > mark > a__c > a__f = c > f