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


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


YES
Input TRS:
    1: half(0()) -> 0()
    2: half(s(0())) -> 0()
    3: half(s(s(x))) -> s(half(x))
    4: le(0(),y) -> true()
    5: le(s(x),0()) -> false()
    6: le(s(x),s(y)) -> le(x,y)
    7: inc(s(x)) -> s(inc(x))
    8: inc(0()) -> s(0())
    9: logarithm(x) -> logIter(x,0())
    10: logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
    11: if(false(),b,x,y) -> logZeroError()
    12: if(true(),false(),x,s(y)) -> y
    13: if(true(),true(),x,y) -> logIter(x,y)
    14: f() -> g()
    15: f() -> h()
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying le
1: half(0()) -> 0()
2: half(s(0())) -> 0()
3: half(s(s(x))) -> s(half(x))
4: le^1_0(y) -> true()
5: le^1_s(x,0()) -> false()
6: le^1_s(x,s(y)) -> le(x,y)
7: inc(s(x)) -> s(inc(x))
8: inc(0()) -> s(0())
9: logarithm(x) -> logIter(x,0())
10: logIter(x,y) -> if(le^1_s(0(),x),le^1_s(s(0()),x),half(x),inc(y))
11: if(false(),b,x,y) -> logZeroError()
12: if(true(),false(),x,s(y)) -> y
13: if(true(),true(),x,y) -> logIter(x,y)
14: f() -> g()
15: f() -> h()
16: le(0(),_1) ->= le^1_0(_1)
17: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #le^1_s(x,s(y)) -> #le(x,y)
   #2: #if(true(),true(),x,y) -> #logIter(x,y)
   #3: #logarithm(x) -> #logIter(x,0())
   #4: #inc(s(x)) -> #inc(x)
   #5: #logIter(x,y) -> #if(le^1_s(0(),x),le^1_s(s(0()),x),half(x),inc(y))
   #6: #logIter(x,y) -> #le^1_s(0(),x)
   #7: #logIter(x,y) -> #le^1_s(s(0()),x)
   #8: #logIter(x,y) -> #half(x)
   #9: #logIter(x,y) -> #inc(y)
   #10: #le(s(_1),_2) ->? #le^1_s(_1,_2)
   #11: #le(0(),_1) ->? #le^1_0(_1)
   #12: #half(s(s(x))) -> #half(x)
Number of SCCs: 4, DPs: 6
  SCC { #4 }
POLO(Sum)... succeeded.
      h 	w: 0
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      s 	w: x1 + 1
      #le	w: 0
      #le^1_0	w: 0
      false	w: 0
      logZeroError	w: 0
      #half	w: 0
      #inc	w: x1
      inc	w: 0
      true	w: 0
      f 	w: 0
      half	w: 0
      0 	w: 0
      if	w: 0
      #f 	w: 0
      logIter	w: 0
      logarithm	w: 0
      #logIter	w: 0
      le^1_0	w: 0
      #if	w: 0
      #logarithm	w: 0
      g 	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 5
  SCC { #12 }
POLO(Sum)... succeeded.
      h 	w: 0
      #le^1_s	w: 0
      le	w: 0
      le^1_s	w: 0
      s 	w: x1 + 1
      #le	w: 0
      #le^1_0	w: 0
      false	w: 0
      logZeroError	w: 0
      #half	w: x1
      #inc	w: 0
      inc	w: 0
      true	w: 0
      f 	w: 0
      half	w: 0
      0 	w: 0
      if	w: 0
      #f 	w: 0
      logIter	w: 0
      logarithm	w: 0
      #logIter	w: 0
      le^1_0	w: 0
      #if	w: 0
      #logarithm	w: 0
      g 	w: 0
    USABLE RULES: { }
    Removed DPs: #12
Number of SCCs: 2, DPs: 4
  SCC { #1 #10 }
POLO(Sum)... succeeded.
      h 	w: 0
      #le^1_s	w: x2
      le	w: 0
      le^1_s	w: 0
      s 	w: x1 + 2
      #le	w: x2 + 1
      #le^1_0	w: 0
      false	w: 0
      logZeroError	w: 0
      #half	w: 0
      #inc	w: 0
      inc	w: 0
      true	w: 0
      f 	w: 0
      half	w: 0
      0 	w: 0
      if	w: 0
      #f 	w: 0
      logIter	w: 0
      logarithm	w: 0
      #logIter	w: 0
      le^1_0	w: 0
      #if	w: 0
      #logarithm	w: 0
      g 	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #10
Number of SCCs: 1, DPs: 2
  SCC { #2 #5 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      h 	w: 0
      #le^1_s	w: max(x1 - 1, 0)
      le	w: max(x2 + 2, 0)
      le^1_s	w: max(x2 - 2, 0)
      s 	w: max(x1 + 4, 0)
      #le	w: max(x1 - 1, 0)
      #le^1_0	w: max(x1 - 1, 0)
      false	w: 0
      logZeroError	w: 0
      #half	w: max(x1 - 1, 0)
      #inc	w: 0
      inc	w: max(x1 - 3, 0)
      true	w: 2
      f 	w: 0
      half	w: max(x1 - 1, 0)
      0 	w: 0
      if	w: max(x3 - 1, 0)
      #f 	w: 0
      logIter	w: 0
      logarithm	w: 0
      #logIter	w: max(x1 - 2, 0)
      le^1_0	w: 2
      #if	w: max(x1 - 1, x2 - 1, x3 - 1, 0)
      #logarithm	w: max(x1 - 1, 0)
      g 	w: 0
    USABLE RULES: { 1..6 16 17 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0