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


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MAYBE
Input TRS:
    1: ge(0(),0()) -> true()
    2: ge(s(x),0()) -> ge(x,0())
    3: ge(0(),s(0())) -> false()
    4: ge(0(),s(s(x))) -> ge(0(),s(x))
    5: ge(s(x),s(y)) -> ge(x,y)
    6: minus(0(),0()) -> 0()
    7: minus(0(),s(x)) -> minus(0(),x)
    8: minus(s(x),0()) -> s(minus(x,0()))
    9: minus(s(x),s(y)) -> minus(x,y)
    10: plus(0(),0()) -> 0()
    11: plus(0(),s(x)) -> s(plus(0(),x))
    12: plus(s(x),y) -> s(plus(x,y))
    13: div(x,y) -> ify(ge(y,s(0())),x,y)
    14: ify(false(),x,y) -> divByZeroError()
    15: ify(true(),x,y) -> if(ge(x,y),x,y)
    16: if(false(),x,y) -> 0()
    17: if(true(),x,y) -> s(div(minus(x,y),y))
Number of strict rules: 17
Direct POLO(bPol) ... failed.
Uncurrying minus ge^1_0 ge plus
1: ge^1_0^1_0() -> true()
2: ge^1_s(x,0()) -> ge(x,0())
3: ge^1_0^1_s(0()) -> false()
4: ge^1_0^1_s(s(x)) -> ge^1_0^1_s(x)
5: ge^1_s(x,s(y)) -> ge(x,y)
6: minus^1_0(0()) -> 0()
7: minus^1_0(s(x)) -> minus^1_0(x)
8: minus^1_s(x,0()) -> s(minus(x,0()))
9: minus^1_s(x,s(y)) -> minus(x,y)
10: plus^1_0(0()) -> 0()
11: plus^1_0(s(x)) -> s(plus^1_0(x))
12: plus^1_s(x,y) -> s(plus(x,y))
13: div(x,y) -> ify(ge(y,s(0())),x,y)
14: ify(false(),x,y) -> divByZeroError()
15: ify(true(),x,y) -> if(ge(x,y),x,y)
16: if(false(),x,y) -> 0()
17: if(true(),x,y) -> s(div(minus(x,y),y))
18: plus(0(),_1) ->= plus^1_0(_1)
19: plus(s(_1),_2) ->= plus^1_s(_1,_2)
20: ge(0(),_1) ->= ge^1_0(_1)
21: ge(s(_1),_2) ->= ge^1_s(_1,_2)
22: ge^1_0(0()) ->= ge^1_0^1_0()
23: ge^1_0(s(_1)) ->= ge^1_0^1_s(_1)
24: minus(0(),_1) ->= minus^1_0(_1)
25: minus(s(_1),_2) ->= minus^1_s(_1,_2)
Number of strict rules: 17
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #ge^1_s(x,0()) -> #ge(x,0())
   #2: #div(x,y) -> #ify(ge(y,s(0())),x,y)
   #3: #div(x,y) -> #ge(y,s(0()))
   #4: #minus^1_s(x,s(y)) -> #minus(x,y)
   #5: #plus^1_0(s(x)) -> #plus^1_0(x)
   #6: #minus(0(),_1) ->? #minus^1_0(_1)
   #7: #ge^1_0(s(_1)) ->? #ge^1_0^1_s(_1)
   #8: #plus^1_s(x,y) -> #plus(x,y)
   #9: #minus(s(_1),_2) ->? #minus^1_s(_1,_2)
   #10: #ge(0(),_1) ->? #ge^1_0(_1)
   #11: #minus^1_0(s(x)) -> #minus^1_0(x)
   #12: #ge^1_s(x,s(y)) -> #ge(x,y)
   #13: #ge^1_0(0()) ->? #ge^1_0^1_0()
   #14: #if(true(),x,y) -> #div(minus(x,y),y)
   #15: #if(true(),x,y) -> #minus(x,y)
   #16: #plus(s(_1),_2) ->? #plus^1_s(_1,_2)
   #17: #ge(s(_1),_2) ->? #ge^1_s(_1,_2)
   #18: #minus^1_s(x,0()) -> #minus(x,0())
   #19: #ify(true(),x,y) -> #if(ge(x,y),x,y)
   #20: #ify(true(),x,y) -> #ge(x,y)
   #21: #ge^1_0^1_s(s(x)) -> #ge^1_0^1_s(x)
   #22: #plus(0(),_1) ->? #plus^1_0(_1)
Number of SCCs: 7, DPs: 14
  SCC { #5 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 1
      #plus^1_0	w: x1
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 0
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 0
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 0
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 6, DPs: 13
  SCC { #11 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 1
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 0
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 0
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: x1
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 0
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 5, DPs: 12
  SCC { #21 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 1
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 0
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 0
      #ge^1_0^1_s	w: x1
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 0
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #21
Number of SCCs: 4, DPs: 11
  SCC { #8 #16 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 2
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: x1
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 0
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 0
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: x1 + 1
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #8 #16
Number of SCCs: 3, DPs: 9
  SCC { #4 #9 #18 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 1
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 1
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: x2
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: x2
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 1
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 8
  SCC { #9 #18 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 2
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: 0
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: 0
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 1
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: x1 + x2 + 1
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: x1 + x2
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 1
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #9 #18
Number of SCCs: 2, DPs: 6
  SCC { #1 #12 #17 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 1
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: x2
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: x2
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 1
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 1
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 1
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #12
Number of SCCs: 2, DPs: 5
  SCC { #1 #17 }
POLO(Sum)... succeeded.
      plus^1_s	w: 0
      plus^1_0	w: 0
      #div	w: 0
      s 	w: x1 + 2
      #plus^1_0	w: 0
      divByZeroError	w: 0
      #ge^1_s	w: x1 + x2 + 1
      #ge^1_0^1_0	w: 0
      minus	w: 0
      #ify	w: 0
      ge^1_s	w: 0
      #plus	w: 0
      false	w: 0
      div	w: 0
      #ge^1_0	w: 0
      #ge	w: x1 + x2
      minus^1_0	w: 0
      true	w: 0
      ge^1_0^1_0	w: 0
      0 	w: 1
      if	w: 0
      minus^1_s	w: 0
      ge	w: 0
      #minus^1_s	w: 1
      #ge^1_0^1_s	w: 0
      ify	w: 0
      #minus^1_0	w: 0
      #minus	w: 0
      plus	w: 0
      ge^1_0^1_s	w: 0
      #if	w: 0
      #plus^1_s	w: 1
      ge^1_0	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #17
Number of SCCs: 1, DPs: 3
  SCC { #2 #14 #19 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.