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


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YES
Input TRS:
    1: 0(\#()) -> \#()
    2: +(\#(),x) -> x
    3: +(x,\#()) -> x
    4: +(0(x),0(y)) -> 0(+(x,y))
    5: +(0(x),1(y)) -> 1(+(x,y))
    6: +(1(x),0(y)) -> 1(+(x,y))
    7: +(0(x),j(y)) -> j(+(x,y))
    8: +(j(x),0(y)) -> j(+(x,y))
    9: +(1(x),1(y)) -> j(+(+(x,y),1(\#())))
    10: +(j(x),j(y)) -> 1(+(+(x,y),j(\#())))
    11: +(1(x),j(y)) -> 0(+(x,y))
    12: +(j(x),1(y)) -> 0(+(x,y))
    13: +(+(x,y),z) -> +(x,+(y,z))
    14: opp(\#()) -> \#()
    15: opp(0(x)) -> 0(opp(x))
    16: opp(1(x)) -> j(opp(x))
    17: opp(j(x)) -> 1(opp(x))
    18: -(x,y) -> +(x,opp(y))
    19: *(\#(),x) -> \#()
    20: *(0(x),y) -> 0(*(x,y))
    21: *(1(x),y) -> +(0(*(x,y)),y)
    22: *(j(x),y) -> -(0(*(x,y)),y)
    23: *(*(x,y),z) -> *(x,*(y,z))
Number of strict rules: 23
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #+(1(x),0(y)) -> #+(x,y)
   #2: #+(+(x,y),z) -> #+(x,+(y,z))
   #3: #+(+(x,y),z) -> #+(y,z)
   #4: #+(1(x),1(y)) -> #+(+(x,y),1(\#()))
   #5: #+(1(x),1(y)) -> #+(x,y)
   #6: #+(1(x),j(y)) -> #0(+(x,y))
   #7: #+(1(x),j(y)) -> #+(x,y)
   #8: #*(*(x,y),z) -> #*(x,*(y,z))
   #9: #*(*(x,y),z) -> #*(y,z)
   #10: #+(j(x),1(y)) -> #0(+(x,y))
   #11: #+(j(x),1(y)) -> #+(x,y)
   #12: #*(0(x),y) -> #0(*(x,y))
   #13: #*(0(x),y) -> #*(x,y)
   #14: #+(0(x),j(y)) -> #+(x,y)
   #15: #+(j(x),j(y)) -> #+(+(x,y),j(\#()))
   #16: #+(j(x),j(y)) -> #+(x,y)
   #17: #+(0(x),1(y)) -> #+(x,y)
   #18: #*(j(x),y) -> #-(0(*(x,y)),y)
   #19: #*(j(x),y) -> #0(*(x,y))
   #20: #*(j(x),y) -> #*(x,y)
   #21: #opp(j(x)) -> #opp(x)
   #22: #*(1(x),y) -> #+(0(*(x,y)),y)
   #23: #*(1(x),y) -> #0(*(x,y))
   #24: #*(1(x),y) -> #*(x,y)
   #25: #opp(1(x)) -> #opp(x)
   #26: #+(j(x),0(y)) -> #+(x,y)
   #27: #opp(0(x)) -> #0(opp(x))
   #28: #opp(0(x)) -> #opp(x)
   #29: #+(0(x),0(y)) -> #0(+(x,y))
   #30: #+(0(x),0(y)) -> #+(x,y)
   #31: #-(x,y) -> #+(x,opp(y))
   #32: #-(x,y) -> #opp(y)
Number of SCCs: 3, DPs: 21
  SCC { #21 #25 #28 }
POLO(Sum)... succeeded.
      #0 	w: 0
      1 	w: x1 + 1
      #* 	w: 0
      \#	w: 0
      #opp	w: x1
      0 	w: x1 + 1
      - 	w: 0
      j 	w: x1 + 1
      opp	w: 0
      #- 	w: 0
      + 	w: 0
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #21 #25 #28
Number of SCCs: 2, DPs: 18
  SCC { #8 #9 #13 #20 #24 }
POLO(Sum)... succeeded.
      #0 	w: 0
      1 	w: x1 + 1
      #* 	w: x1
      \#	w: 2
      #opp	w: 0
      0 	w: x1 + 1
      - 	w: x1 + 2
      j 	w: x1 + 3
      opp	w: 1
      #- 	w: 0
      + 	w: x1 + x2 + 1
      #+ 	w: 0
      * 	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #8 #9 #13 #20 #24
Number of SCCs: 1, DPs: 13
  SCC { #1..5 #7 #11 #14..17 #26 #30 }
POLO(Sum)... succeeded.
      #0 	w: 0
      1 	w: x1 + 1
      #* 	w: 0
      \#	w: 0
      #opp	w: 0
      0 	w: x1 + 1
      - 	w: 1
      j 	w: x1 + 1
      opp	w: x1 + 1
      #- 	w: 0
      + 	w: x1 + x2
      #+ 	w: x1 + x2
      * 	w: x2 + 1
    USABLE RULES: { 1..17 }
    Removed DPs: #1 #4 #5 #7 #11 #14..17 #26 #30
Number of SCCs: 1, DPs: 2
  SCC { #2 #3 }
POLO(Sum)... succeeded.
      #0 	w: 0
      1 	w: 1
      #* 	w: 0
      \#	w: 0
      #opp	w: 0
      0 	w: 3
      - 	w: 2
      j 	w: 1
      opp	w: x1 + 1
      #- 	w: 0
      + 	w: x1 + x2 + 1
      #+ 	w: x1 + x2
      * 	w: x2 + 2
    USABLE RULES: { 1..17 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      #0 	w: 0
      1 	w: 1
      #* 	w: 0
      \#	w: 0
      #opp	w: 0
      0 	w: 3
      - 	w: 2
      j 	w: 1
      opp	w: x1 + 1
      #- 	w: 0
      + 	w: x1 + x2 + 1
      #+ 	w: x1
      * 	w: x2 + 2
    USABLE RULES: { 1..17 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0