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


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