YES
Input TRS:
AC symbols: ac1 ac2
      1: ac1(a(),ac2(b(),c())) -> ac1(b(),f(ac2(a(),c())))
      2: ac2(a(),ac1(b(),c())) -> ac2(b(),f(ac1(a(),c())))
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #ac2(a(),ac1(b(),c())) -> #ac2(b(),f(ac1(a(),c())))
     #2: #ac2(a(),ac1(b(),c())) -> #ac1(a(),c())
     #3: #ac1(x,ac1(y,z)) ->= #ac1(ac1(x,y),z)
     #4: #ac1(x,ac1(y,z)) ->= #ac1(x,y)
     #5: #ac1(a(),ac2(b(),c())) -> #ac1(b(),f(ac2(a(),c())))
     #6: #ac1(a(),ac2(b(),c())) -> #ac2(a(),c())
     #7: #ac2(x,ac2(y,z)) ->= #ac2(ac2(x,y),z)
     #8: #ac2(x,ac2(y,z)) ->= #ac2(x,y)
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      a 	w: 8857
      #ac1	w: x1 + x2
      b 	w: 1
      c 	w: 0
      f 	w: x1 + 8855
      ac1	w: x1 + x2 + 1
      ac2	w: 2439
      #ac2	w: 11295
    USABLE RULES: { 1..4 }
    Removed DPs: #2 #4..6
Number of SCCs: 2, DPs: 4
  SCC { #3 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #1 #7 #8 }
POLO(Sum)... succeeded.
      a 	w: 0
      #ac1	w: x1 + x2
      b 	w: 2
      c 	w: 1
      f 	w: 2
      ac1	w: x1 + x2 + 2
      ac2	w: x1 + x2 + 1
      #ac2	w: x1 + x2 + 11295
    USABLE RULES: { 1..4 }
    Removed DPs: #1 #8
Number of SCCs: 1, DPs: 1
  SCC { #7 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #9: #ac2(ac2(a(),ac1(b(),c())),_1) -> #ac2(ac2(b(),f(ac1(a(),c()))),_1)
     #10: #ac1(x,ac1(y,z)) ->= #ac1(ac1(x,y),z)
     #11: #ac1(x,ac1(y,z)) ->= #ac1(x,y)
     #12: #ac1(ac1(a(),ac2(b(),c())),_1) -> #ac1(ac1(b(),f(ac2(a(),c()))),_1)
     #13: #ac2(x,ac2(y,z)) ->= #ac2(ac2(x,y),z)
     #14: #ac2(x,ac2(y,z)) ->= #ac2(x,y)
Number of SCCs: 2, DPs: 6
  SCC { #9 #13 #14 }
POLO(Sum)... succeeded.
      a 	w: 1
      #ac1	w: x1 + x2
      b 	w: 1
      c 	w: 0
      f 	w: 1
      ac1	w: x1 + x2 + 1
      ac2	w: x1 + x2 + 4
      #ac2	w: x1 + x2 + 11295
    USABLE RULES: { 1..4 }
    Removed DPs: #9 #14
Number of SCCs: 2, DPs: 4
  SCC { #13 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #10..12 }
POLO(Sum)... succeeded.
      a 	w: 0
      #ac1	w: x1 + x2
      b 	w: 2
      c 	w: 1
      f 	w: 0
      ac1	w: x1 + x2 + 32279
      ac2	w: x1 + x2 + 9725
      #ac2	w: x1 + x2 + 11295
    USABLE RULES: { 1..4 }
    Removed DPs: #11 #12
Number of SCCs: 1, DPs: 1
  SCC { #10 }
only weak rules.
Number of SCCs: 0, DPs: 0