YES
Input TRS:
AC symbols: plus times
      1: plus(x,0()) -> x
      2: plus(x,s(y)) -> s(plus(x,y))
      3: times(x,0()) -> 0()
      4: times(x,s(y)) -> plus(x,times(x,y))
      5: power(x,0()) -> s(0())
      6: power(x,s(y)) -> times(x,power(x,y))
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #plus(x,s(y)) -> #plus(x,y)
     #2: #power(x,s(y)) -> #times(x,power(x,y))
     #3: #power(x,s(y)) -> #power(x,y)
     #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #5: #plus(x,plus(y,z)) ->= #plus(x,y)
     #6: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #7: #times(x,times(y,z)) ->= #times(x,y)
     #8: #times(x,s(y)) -> #plus(x,times(x,y))
     #9: #times(x,s(y)) -> #times(x,y)
Number of SCCs: 3, DPs: 7
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #power	w: x2
      #plus	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      power	w: 0
      plus	w: 0
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 6
  SCC { #6 #7 #9 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #power	s: [1,2]	p: 0
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      power	s: 2
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..4 7 8 }
    Removed DPs: #7 #9
Number of SCCs: 2, DPs: 4
  SCC { #6 }
only weak rules.
Number of SCCs: 1, DPs: 3
  SCC { #1 #4 #5 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #power	w: 0
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 16575
      times	w: x1 + x2 + 23676
      power	w: 0
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1 2 7 }
    Removed DPs: #1 #5
Number of SCCs: 1, DPs: 1
  SCC { #4 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #10: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1)
     #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #12: #plus(x,plus(y,z)) ->= #plus(x,y)
     #13: #times(times(x,0()),_1) -> #times(0(),_1)
     #14: #plus(plus(x,0()),_1) -> #plus(x,_1)
     #15: #times(x,times(y,z)) ->= #times(times(x,y),z)
     #16: #times(x,times(y,z)) ->= #times(x,y)
     #17: #times(times(x,s(y)),_1) -> #times(plus(x,times(x,y)),_1)
Number of SCCs: 2, DPs: 8
  SCC { #13 #15..17 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #power	s: [1,2]	p: 0
      #plus	s: {}	p: 1
      #times	s: {1,2}	p: 2
      0 	s: []	p: 0
      times	s: {1,2}	p: 2
      power	s: 2
      plus	s: {1,2}	p: 1
    USABLE RULES: { 1..4 7 8 }
    Removed DPs: #13 #16 #17
Number of SCCs: 2, DPs: 5
  SCC { #15 }
only weak rules.
Number of SCCs: 1, DPs: 4
  SCC { #10..12 #14 }
POLO(Sum)... succeeded.
      s 	w: 1
      #power	w: 0
      #plus	w: x1 + x2
      #times	w: 0
      0 	w: 1
      times	w: x1 + x2 + 29243
      power	w: 0
      plus	w: x1 + x2 + 2
    USABLE RULES: { 1 2 7 }
    Removed DPs: #10 #12 #14
Number of SCCs: 1, DPs: 1
  SCC { #11 }
only weak rules.
Number of SCCs: 0, DPs: 0