YES
Input TRS:
      1: plus(s(s(x)),y) -> s(plus(x,s(y)))
      2: plus(x,s(s(y))) -> s(plus(s(x),y))
      3: plus(s(0()),y) -> s(y)
      4: plus(0(),y) -> y
      5: ack(0(),y) -> s(y)
      6: ack(s(x),0()) -> ack(x,s(0()))
      7: ack(s(x),s(y)) -> ack(x,plus(y,ack(s(x),y)))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ack
      1: plus(s(s(x)),y) -> s(plus(x,s(y)))
      2: plus(x,s(s(y))) -> s(plus(s(x),y))
      3: plus(s(0()),y) -> s(y)
      4: plus(0(),y) -> y
      5: ack^1_0(y) -> s(y)
      6: ack^1_s(x,0()) -> ack(x,s(0()))
      7: ack^1_s(x,s(y)) -> ack(x,plus(y,ack^1_s(x,y)))
      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: #plus(x,s(s(y))) -> #plus(s(x),y)
     #2: #ack^1_s(x,0()) -> #ack(x,s(0()))
     #3: #ack(s(_1),_2) ->? #ack^1_s(_1,_2)
     #4: #ack^1_s(x,s(y)) -> #ack(x,plus(y,ack^1_s(x,y)))
     #5: #ack^1_s(x,s(y)) -> #plus(y,ack^1_s(x,y))
     #6: #ack^1_s(x,s(y)) -> #ack^1_s(x,y)
     #7: #plus(s(s(x)),y) -> #plus(x,s(y))
     #8: #ack(0(),_1) ->? #ack^1_0(_1)
Number of SCCs: 2, DPs: 6
  SCC { #1 #7 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #ack^1_s	w: 0
      #ack^1_0	w: 0
      ack	w: 0
      #plus	w: x1 + x2
      0 	w: 0
      ack^1_0	w: 0
      plus	w: 0
      #ack	w: 0
      ack^1_s	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #7
Number of SCCs: 1, DPs: 4
  SCC { #2..4 #6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 21241
      #ack^1_s	w: x1 + 1
      #ack^1_0	w: 0
      ack	w: x1 + x2
      #plus	w: 0
      0 	w: 21239
      ack^1_0	w: 21240
      plus	w: x1 + x2 + 21242
      #ack	w: x1
      ack^1_s	w: x2 + 2
    USABLE RULES: { }
    Removed DPs: #2..4
Number of SCCs: 1, DPs: 1
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 21241
      #ack^1_s	w: x2 + 1
      #ack^1_0	w: 0
      ack	w: x1 + x2
      #plus	w: 0
      0 	w: 21239
      ack^1_0	w: 21240
      plus	w: x1 + x2 + 29607
      #ack	w: 0
      ack^1_s	w: x2 + 2
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0