YES
Input TRS:
      1: a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
      2: mark(f(X1,X2)) -> a__f(mark(X1),X2)
      3: mark(g(X)) -> g(mark(X))
      4: a__f(X1,X2) -> f(X1,X2)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #mark(f(X1,X2)) -> #a__f(mark(X1),X2)
     #2: #mark(f(X1,X2)) -> #mark(X1)
     #3: #mark(g(X)) -> #mark(X)
     #4: #a__f(g(X),Y) -> #a__f(mark(X),f(g(X),Y))
     #5: #a__f(g(X),Y) -> #mark(X)
Number of SCCs: 1, DPs: 5
  SCC { #1..5 }
POLO(Sum)... succeeded.
      a__f	w: x1 + 1
      f 	w: x1 + 1
      #mark	w: x1 + 23676
      mark	w: x1 + 23676
      #a__f	w: x1
      g 	w: x1 + 23677
    USABLE RULES: { 1..4 }
    Removed DPs: #1..5
Number of SCCs: 0, DPs: 0