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


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YES
Input TRS:
    1: even(0()) -> true()
    2: even(s(0())) -> false()
    3: even(s(s(x))) -> even(x)
    4: half(0()) -> 0()
    5: half(s(s(x))) -> s(half(x))
    6: plus(0(),y) -> y
    7: plus(s(x),y) -> s(plus(x,y))
    8: times(0(),y) -> 0()
    9: times(s(x),y) -> if_times(even(s(x)),s(x),y)
    10: if_times(true(),s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y))
    11: if_times(false(),s(x),y) -> plus(y,times(x,y))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying even half
1: even^1_0() -> true()
2: even^1_s(0()) -> false()
3: even^1_s(s(x)) -> even(x)
4: half^1_0() -> 0()
5: half^1_s(s(x)) -> s(half(x))
6: plus(0(),y) -> y
7: plus(s(x),y) -> s(plus(x,y))
8: times(0(),y) -> 0()
9: times(s(x),y) -> if_times(even^1_s(x),s(x),y)
10: if_times(true(),s(x),y) -> plus(times(half^1_s(x),y),times(half^1_s(x),y))
11: if_times(false(),s(x),y) -> plus(y,times(x,y))
12: half(0()) ->= half^1_0()
13: half(s(_1)) ->= half^1_s(_1)
14: even(0()) ->= even^1_0()
15: even(s(_1)) ->= even^1_s(_1)
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #half(s(_1)) ->? #half^1_s(_1)
   #2: #times(s(x),y) -> #if_times(even^1_s(x),s(x),y)
   #3: #times(s(x),y) -> #even^1_s(x)
   #4: #if_times(false(),s(x),y) -> #plus(y,times(x,y))
   #5: #if_times(false(),s(x),y) -> #times(x,y)
   #6: #half(0()) ->? #half^1_0()
   #7: #even(0()) ->? #even^1_0()
   #8: #plus(s(x),y) -> #plus(x,y)
   #9: #if_times(true(),s(x),y) -> #plus(times(half^1_s(x),y),times(half^1_s(x),y))
   #10: #if_times(true(),s(x),y) -> #times(half^1_s(x),y)
   #11: #if_times(true(),s(x),y) -> #half^1_s(x)
   #12: #if_times(true(),s(x),y) -> #times(half^1_s(x),y)
   #13: #if_times(true(),s(x),y) -> #half^1_s(x)
   #14: #half^1_s(s(x)) -> #half(x)
   #15: #even^1_s(s(x)) -> #even(x)
   #16: #even(s(_1)) ->? #even^1_s(_1)
Number of SCCs: 4, DPs: 9
  SCC { #8 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #if_times	w: 0
      #even^1_s	w: 0
      even	w: 0
      #plus	w: x1
      false	w: 0
      #half	w: 0
      #even^1_0	w: 0
      half^1_s	w: 0
      true	w: 0
      half	w: 0
      #even	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      #half^1_s	w: 0
      half^1_0	w: 0
      if_times	w: 0
      plus	w: 0
      #half^1_0	w: 0
      even^1_s	w: 0
      even^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 3, DPs: 8
  SCC { #15 #16 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #if_times	w: 0
      #even^1_s	w: x1
      even	w: 0
      #plus	w: 0
      false	w: 0
      #half	w: 0
      #even^1_0	w: 0
      half^1_s	w: 0
      true	w: 0
      half	w: 0
      #even	w: x1
      #times	w: 0
      0 	w: 0
      times	w: 0
      #half^1_s	w: 0
      half^1_0	w: 0
      if_times	w: 0
      plus	w: 0
      #half^1_0	w: 0
      even^1_s	w: 0
      even^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #15 #16
Number of SCCs: 2, DPs: 6
  SCC { #1 #14 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #if_times	w: 0
      #even^1_s	w: 0
      even	w: 0
      #plus	w: 0
      false	w: 0
      #half	w: x1
      #even^1_0	w: 0
      half^1_s	w: 0
      true	w: 0
      half	w: 0
      #even	w: 0
      #times	w: 0
      0 	w: 0
      times	w: 0
      #half^1_s	w: x1
      half^1_0	w: 0
      if_times	w: 0
      plus	w: 0
      #half^1_0	w: 0
      even^1_s	w: 0
      even^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #14
Number of SCCs: 1, DPs: 4
  SCC { #2 #5 #10 #12 }
POLO(Sum)... succeeded.
      s 	w: x1 + 4
      #if_times	w: x2
      #even^1_s	w: 0
      even	w: x1 + 2
      #plus	w: 0
      false	w: 2
      #half	w: 0
      #even^1_0	w: 0
      half^1_s	w: x1 + 2
      true	w: 5
      half	w: x1 + 1
      #even	w: 0
      #times	w: x1 + 1
      0 	w: 1
      times	w: 0
      #half^1_s	w: 0
      half^1_0	w: 1
      if_times	w: 0
      plus	w: 0
      #half^1_0	w: 0
      even^1_s	w: 1
      even^1_0	w: 4
    USABLE RULES: { 4 5 12 13 }
    Removed DPs: #2 #5 #10 #12
Number of SCCs: 0, DPs: 0