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