YES
Input TRS:
      1: a__f(X) -> a__if(mark(X),c(),f(true()))
      2: a__if(true(),X,Y) -> mark(X)
      3: a__if(false(),X,Y) -> mark(Y)
      4: mark(f(X)) -> a__f(mark(X))
      5: mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
      6: mark(c()) -> c()
      7: mark(true()) -> true()
      8: mark(false()) -> false()
      9: a__f(X) -> f(X)
      10: a__if(X1,X2,X3) -> if(X1,X2,X3)
Number of strict rules: 10
Direct POLO(bPol) ... removes: 3
      a__f	w: 2 * x1
      false	w: 31892
      c 	w: 0
      true	w: 0
      f 	w: 2 * x1
      if	w: x1 + 2 * x2 + 2 * x3
      mark	w: x1
      a__if	w: x1 + 2 * x2 + 2 * x3
Number of strict rules: 9
Direct POLO(bPol) ... removes: 8
      a__f	w: 2 * x1
      false	w: 1
      c 	w: 0
      true	w: 0
      f 	w: 2 * x1
      if	w: x1 + 2 * x2 + 2 * x3
      mark	w: 2 * x1
      a__if	w: x1 + 2 * x2 + 2 * x3
Number of strict rules: 8
Direct POLO(bPol) ... removes: 9
      a__f	w: 2 * x1 + 33408
      false	w: 0
      c 	w: 0
      true	w: 0
      f 	w: 2 * x1 + 16704
      if	w: x1 + 2 * x2 + 2 * x3
      mark	w: 2 * x1
      a__if	w: x1 + 2 * x2 + 2 * x3
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__if(true(),X,Y) -> #mark(X)
     #2: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),mark(X2),X3)
     #3: #mark(if(X1,X2,X3)) -> #mark(X1)
     #4: #mark(if(X1,X2,X3)) -> #mark(X2)
     #5: #a__f(X) -> #a__if(mark(X),c(),f(true()))
     #6: #a__f(X) -> #mark(X)
     #7: #mark(f(X)) -> #a__f(mark(X))
     #8: #mark(f(X)) -> #mark(X)
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      a__f	w: x1 + 2
      false	w: 0
      c 	w: 1
      true	w: 2
      f 	w: x1 + 2
      #mark	w: x1 + 1
      if	w: x1 + x2 + 1
      mark	w: x1
      #a__if	w: x1 + x2
      #a__f	w: x1 + 2
      a__if	w: x1 + x2 + 1
    USABLE RULES: { 1 2 4..7 10 }
    Removed DPs: #1..8
Number of SCCs: 0, DPs: 0