YES
Input TRS:
      1: ack_in(0(),n) -> ack_out(s(n))
      2: ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
      3: u11(ack_out(n)) -> ack_out(n)
      4: ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
      5: u21(ack_out(n),m) -> u22(ack_in(m,n))
      6: u22(ack_out(n)) -> ack_out(n)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ack_in
      1: ack_in^1_0(n) -> ack_out(s(n))
      2: ack_in^1_s(m,0()) -> u11(ack_in(m,s(0())))
      3: u11(ack_out(n)) -> ack_out(n)
      4: ack_in^1_s(m,s(n)) -> u21(ack_in^1_s(m,n),m)
      5: u21(ack_out(n),m) -> u22(ack_in(m,n))
      6: u22(ack_out(n)) -> ack_out(n)
      7: ack_in(0(),_1) ->= ack_in^1_0(_1)
      8: ack_in(s(_1),_2) ->= ack_in^1_s(_1,_2)
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #ack_in^1_s(m,0()) -> #u11(ack_in(m,s(0())))
     #2: #ack_in^1_s(m,0()) -> #ack_in(m,s(0()))
     #3: #ack_in(0(),_1) ->? #ack_in^1_0(_1)
     #4: #u21(ack_out(n),m) -> #u22(ack_in(m,n))
     #5: #u21(ack_out(n),m) -> #ack_in(m,n)
     #6: #ack_in(s(_1),_2) ->? #ack_in^1_s(_1,_2)
     #7: #ack_in^1_s(m,s(n)) -> #u21(ack_in^1_s(m,n),m)
     #8: #ack_in^1_s(m,s(n)) -> #ack_in^1_s(m,n)
Number of SCCs: 1, DPs: 5
  SCC { #2 #5..8 }
POLO(Sum)... succeeded.
      #u22	w: 0
      #ack_in^1_s	w: x1 + 2
      #ack_in	w: x1
      s 	w: x1 + 3
      ack_in^1_0	w: x1 + 3
      #u21	w: x2 + 1
      ack_in^1_s	w: x2 + 5
      #u11	w: 0
      0 	w: 1
      ack_out	w: x1 + 1
      u11	w: x1 + 6
      u21	w: x1 + x2 + 4
      #ack_in^1_0	w: 0
      u22	w: 0
      ack_in	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #2 #5..7
Number of SCCs: 1, DPs: 1
  SCC { #8 }
POLO(Sum)... succeeded.
      #u22	w: 0
      #ack_in^1_s	w: x2 + 2
      #ack_in	w: 0
      s 	w: x1 + 3
      ack_in^1_0	w: x1 + 3
      #u21	w: 1
      ack_in^1_s	w: x2 + 5
      #u11	w: 0
      0 	w: 1
      ack_out	w: x1 + 1
      u11	w: x1 + 6
      u21	w: x1 + x2 + 4
      #ack_in^1_0	w: 0
      u22	w: 0
      ack_in	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0