YES
Input TRS:
      1: ack(0(),y) -> s(y)
      2: ack(s(x),0()) -> ack(x,s(0()))
      3: ack(s(x),s(y)) -> ack(x,ack(s(x),y))
      4: f(s(x),y) -> f(x,s(x))
      5: f(x,s(y)) -> f(y,x)
      6: f(x,y) -> ack(x,y)
      7: ack(s(x),y) -> f(x,x)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ack
      1: ack^1_0(y) -> s(y)
      2: ack^1_s(x,0()) -> ack(x,s(0()))
      3: ack^1_s(x,s(y)) -> ack(x,ack^1_s(x,y))
      4: f(s(x),y) -> f(x,s(x))
      5: f(x,s(y)) -> f(y,x)
      6: f(x,y) -> ack(x,y)
      7: ack^1_s(x,y) -> f(x,x)
      8: ack(0(),_1) ->= ack^1_0(_1)
      9: ack(s(_1),_2) ->= ack^1_s(_1,_2)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #ack^1_s(x,0()) -> #ack(x,s(0()))
     #2: #f(x,y) -> #ack(x,y)
     #3: #ack(s(_1),_2) ->? #ack^1_s(_1,_2)
     #4: #ack^1_s(x,y) -> #f(x,x)
     #5: #f(x,s(y)) -> #f(y,x)
     #6: #ack^1_s(x,s(y)) -> #ack(x,ack^1_s(x,y))
     #7: #ack^1_s(x,s(y)) -> #ack^1_s(x,y)
     #8: #ack(0(),_1) ->? #ack^1_0(_1)
     #9: #f(s(x),y) -> #f(x,s(x))
Number of SCCs: 1, DPs: 8
  SCC { #1..7 #9 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1 + 4
      #ack^1_s	w: max(x1 + 18819)
      #ack^1_0	w: 0
      ack	w: max(x2 + 1)
      f 	w: max(x1 + 8, x2 + 3)
      0 	w: 44083
      #f 	w: max(x1 + 18818, x2 + 18817)
      ack^1_0	w: 0
      #ack	w: max(x1 + 18816)
      ack^1_s	w: max(x2 + 2)
    USABLE RULES: { }
    Removed DPs: #1..6 #9
Number of SCCs: 1, DPs: 1
  SCC { #7 }
POLO(Sum)... succeeded.
      s 	w: x1 + 3
      #ack^1_s	w: x2
      #ack^1_0	w: 0
      ack	w: x2 + 1
      f 	w: x2 + 3
      0 	w: 1
      #f 	w: 0
      ack^1_0	w: 2
      #ack	w: 0
      ack^1_s	w: x1 + 2
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0