/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


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