/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: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    2: active(sel(0(),cons(X,Z))) -> mark(X)
    3: active(first(0(),Z)) -> mark(nil())
    4: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
    5: active(from(X)) -> mark(cons(X,from(s(X))))
    6: active(sel1(s(X),cons(Y,Z))) -> mark(sel1(X,Z))
    7: active(sel1(0(),cons(X,Z))) -> mark(quote(X))
    8: active(first1(0(),Z)) -> mark(nil1())
    9: active(first1(s(X),cons(Y,Z))) -> mark(cons1(quote(Y),first1(X,Z)))
    10: active(quote(0())) -> mark(01())
    11: active(quote1(cons(X,Z))) -> mark(cons1(quote(X),quote1(Z)))
    12: active(quote1(nil())) -> mark(nil1())
    13: active(quote(s(X))) -> mark(s1(quote(X)))
    14: active(quote(sel(X,Z))) -> mark(sel1(X,Z))
    15: active(quote1(first(X,Z))) -> mark(first1(X,Z))
    16: active(unquote(01())) -> mark(0())
    17: active(unquote(s1(X))) -> mark(s(unquote(X)))
    18: active(unquote1(nil1())) -> mark(nil())
    19: active(unquote1(cons1(X,Z))) -> mark(fcons(unquote(X),unquote1(Z)))
    20: active(fcons(X,Z)) -> mark(cons(X,Z))
    21: active(sel(X1,X2)) -> sel(active(X1),X2)
    22: active(sel(X1,X2)) -> sel(X1,active(X2))
    23: active(s(X)) -> s(active(X))
    24: active(cons(X1,X2)) -> cons(active(X1),X2)
    25: active(first(X1,X2)) -> first(active(X1),X2)
    26: active(first(X1,X2)) -> first(X1,active(X2))
    27: active(from(X)) -> from(active(X))
    28: active(sel1(X1,X2)) -> sel1(active(X1),X2)
    29: active(sel1(X1,X2)) -> sel1(X1,active(X2))
    30: active(first1(X1,X2)) -> first1(active(X1),X2)
    31: active(first1(X1,X2)) -> first1(X1,active(X2))
    32: active(cons1(X1,X2)) -> cons1(active(X1),X2)
    33: active(cons1(X1,X2)) -> cons1(X1,active(X2))
    34: active(s1(X)) -> s1(active(X))
    35: active(unquote(X)) -> unquote(active(X))
    36: active(unquote1(X)) -> unquote1(active(X))
    37: active(fcons(X1,X2)) -> fcons(active(X1),X2)
    38: active(fcons(X1,X2)) -> fcons(X1,active(X2))
    39: sel(mark(X1),X2) -> mark(sel(X1,X2))
    40: sel(X1,mark(X2)) -> mark(sel(X1,X2))
    41: s(mark(X)) -> mark(s(X))
    42: cons(mark(X1),X2) -> mark(cons(X1,X2))
    43: first(mark(X1),X2) -> mark(first(X1,X2))
    44: first(X1,mark(X2)) -> mark(first(X1,X2))
    45: from(mark(X)) -> mark(from(X))
    46: sel1(mark(X1),X2) -> mark(sel1(X1,X2))
    47: sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
    48: first1(mark(X1),X2) -> mark(first1(X1,X2))
    49: first1(X1,mark(X2)) -> mark(first1(X1,X2))
    50: cons1(mark(X1),X2) -> mark(cons1(X1,X2))
    51: cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
    52: s1(mark(X)) -> mark(s1(X))
    53: unquote(mark(X)) -> mark(unquote(X))
    54: unquote1(mark(X)) -> mark(unquote1(X))
    55: fcons(mark(X1),X2) -> mark(fcons(X1,X2))
    56: fcons(X1,mark(X2)) -> mark(fcons(X1,X2))
    57: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
    58: proper(s(X)) -> s(proper(X))
    59: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    60: proper(0()) -> ok(0())
    61: proper(first(X1,X2)) -> first(proper(X1),proper(X2))
    62: proper(nil()) -> ok(nil())
    63: proper(from(X)) -> from(proper(X))
    64: proper(sel1(X1,X2)) -> sel1(proper(X1),proper(X2))
    65: proper(quote(X)) -> quote(proper(X))
    66: proper(first1(X1,X2)) -> first1(proper(X1),proper(X2))
    67: proper(nil1()) -> ok(nil1())
    68: proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
    69: proper(01()) -> ok(01())
    70: proper(quote1(X)) -> quote1(proper(X))
    71: proper(s1(X)) -> s1(proper(X))
    72: proper(unquote(X)) -> unquote(proper(X))
    73: proper(unquote1(X)) -> unquote1(proper(X))
    74: proper(fcons(X1,X2)) -> fcons(proper(X1),proper(X2))
    75: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
    76: s(ok(X)) -> ok(s(X))
    77: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    78: first(ok(X1),ok(X2)) -> ok(first(X1,X2))
    79: from(ok(X)) -> ok(from(X))
    80: sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
    81: quote(ok(X)) -> ok(quote(X))
    82: first1(ok(X1),ok(X2)) -> ok(first1(X1,X2))
    83: cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
    84: quote1(ok(X)) -> ok(quote1(X))
    85: s1(ok(X)) -> ok(s1(X))
    86: unquote(ok(X)) -> ok(unquote(X))
    87: unquote1(ok(X)) -> ok(unquote1(X))
    88: fcons(ok(X1),ok(X2)) -> ok(fcons(X1,X2))
    89: top(mark(X)) -> top(proper(X))
    90: top(ok(X)) -> top(active(X))
Number of strict rules: 90
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #unquote(ok(X)) -> #unquote(X)
   #2: #first(mark(X1),X2) -> #first(X1,X2)
   #3: #active(sel1(X1,X2)) -> #sel1(X1,active(X2))
   #4: #active(sel1(X1,X2)) -> #active(X2)
   #5: #active(unquote(X)) -> #unquote(active(X))
   #6: #active(unquote(X)) -> #active(X)
   #7: #cons1(ok(X1),ok(X2)) -> #cons1(X1,X2)
   #8: #proper(first1(X1,X2)) -> #first1(proper(X1),proper(X2))
   #9: #proper(first1(X1,X2)) -> #proper(X1)
   #10: #proper(first1(X1,X2)) -> #proper(X2)
   #11: #sel1(mark(X1),X2) -> #sel1(X1,X2)
   #12: #cons(mark(X1),X2) -> #cons(X1,X2)
   #13: #s(mark(X)) -> #s(X)
   #14: #active(fcons(X1,X2)) -> #fcons(active(X1),X2)
   #15: #active(fcons(X1,X2)) -> #active(X1)
   #16: #proper(unquote1(X)) -> #unquote1(proper(X))
   #17: #proper(unquote1(X)) -> #proper(X)
   #18: #sel1(X1,mark(X2)) -> #sel1(X1,X2)
   #19: #unquote(mark(X)) -> #unquote(X)
   #20: #proper(s1(X)) -> #s1(proper(X))
   #21: #proper(s1(X)) -> #proper(X)
   #22: #first1(mark(X1),X2) -> #first1(X1,X2)
   #23: #sel(ok(X1),ok(X2)) -> #sel(X1,X2)
   #24: #proper(fcons(X1,X2)) -> #fcons(proper(X1),proper(X2))
   #25: #proper(fcons(X1,X2)) -> #proper(X1)
   #26: #proper(fcons(X1,X2)) -> #proper(X2)
   #27: #proper(s(X)) -> #s(proper(X))
   #28: #proper(s(X)) -> #proper(X)
   #29: #proper(first(X1,X2)) -> #first(proper(X1),proper(X2))
   #30: #proper(first(X1,X2)) -> #proper(X1)
   #31: #proper(first(X1,X2)) -> #proper(X2)
   #32: #active(fcons(X1,X2)) -> #fcons(X1,active(X2))
   #33: #active(fcons(X1,X2)) -> #active(X2)
   #34: #active(sel1(s(X),cons(Y,Z))) -> #sel1(X,Z)
   #35: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #36: #proper(cons(X1,X2)) -> #proper(X1)
   #37: #proper(cons(X1,X2)) -> #proper(X2)
   #38: #fcons(mark(X1),X2) -> #fcons(X1,X2)
   #39: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #40: #top(ok(X)) -> #top(active(X))
   #41: #top(ok(X)) -> #active(X)
   #42: #cons1(X1,mark(X2)) -> #cons1(X1,X2)
   #43: #active(quote(s(X))) -> #s1(quote(X))
   #44: #active(quote(s(X))) -> #quote(X)
   #45: #active(first1(s(X),cons(Y,Z))) -> #cons1(quote(Y),first1(X,Z))
   #46: #active(first1(s(X),cons(Y,Z))) -> #quote(Y)
   #47: #active(first1(s(X),cons(Y,Z))) -> #first1(X,Z)
   #48: #active(quote1(cons(X,Z))) -> #cons1(quote(X),quote1(Z))
   #49: #active(quote1(cons(X,Z))) -> #quote(X)
   #50: #active(quote1(cons(X,Z))) -> #quote1(Z)
   #51: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2))
   #52: #proper(sel(X1,X2)) -> #proper(X1)
   #53: #proper(sel(X1,X2)) -> #proper(X2)
   #54: #s(ok(X)) -> #s(X)
   #55: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #56: #active(cons(X1,X2)) -> #active(X1)
   #57: #proper(quote1(X)) -> #quote1(proper(X))
   #58: #proper(quote1(X)) -> #proper(X)
   #59: #active(s(X)) -> #s(active(X))
   #60: #active(s(X)) -> #active(X)
   #61: #quote(ok(X)) -> #quote(X)
   #62: #first(ok(X1),ok(X2)) -> #first(X1,X2)
   #63: #from(mark(X)) -> #from(X)
   #64: #active(first1(X1,X2)) -> #first1(X1,active(X2))
   #65: #active(first1(X1,X2)) -> #active(X2)
   #66: #from(ok(X)) -> #from(X)
   #67: #fcons(X1,mark(X2)) -> #fcons(X1,X2)
   #68: #top(mark(X)) -> #top(proper(X))
   #69: #top(mark(X)) -> #proper(X)
   #70: #first1(ok(X1),ok(X2)) -> #first1(X1,X2)
   #71: #active(quote(sel(X,Z))) -> #sel1(X,Z)
   #72: #active(first1(X1,X2)) -> #first1(active(X1),X2)
   #73: #active(first1(X1,X2)) -> #active(X1)
   #74: #s1(mark(X)) -> #s1(X)
   #75: #first1(X1,mark(X2)) -> #first1(X1,X2)
   #76: #active(first(X1,X2)) -> #first(active(X1),X2)
   #77: #active(first(X1,X2)) -> #active(X1)
   #78: #active(fcons(X,Z)) -> #cons(X,Z)
   #79: #fcons(ok(X1),ok(X2)) -> #fcons(X1,X2)
   #80: #active(sel1(0(),cons(X,Z))) -> #quote(X)
   #81: #sel(mark(X1),X2) -> #sel(X1,X2)
   #82: #proper(sel1(X1,X2)) -> #sel1(proper(X1),proper(X2))
   #83: #proper(sel1(X1,X2)) -> #proper(X1)
   #84: #proper(sel1(X1,X2)) -> #proper(X2)
   #85: #active(cons1(X1,X2)) -> #cons1(X1,active(X2))
   #86: #active(cons1(X1,X2)) -> #active(X2)
   #87: #proper(unquote(X)) -> #unquote(proper(X))
   #88: #proper(unquote(X)) -> #proper(X)
   #89: #active(from(X)) -> #cons(X,from(s(X)))
   #90: #active(from(X)) -> #from(s(X))
   #91: #active(from(X)) -> #s(X)
   #92: #first(X1,mark(X2)) -> #first(X1,X2)
   #93: #proper(quote(X)) -> #quote(proper(X))
   #94: #proper(quote(X)) -> #proper(X)
   #95: #active(sel1(X1,X2)) -> #sel1(active(X1),X2)
   #96: #active(sel1(X1,X2)) -> #active(X1)
   #97: #active(sel(X1,X2)) -> #sel(X1,active(X2))
   #98: #active(sel(X1,X2)) -> #active(X2)
   #99: #active(s1(X)) -> #s1(active(X))
   #100: #active(s1(X)) -> #active(X)
   #101: #quote1(ok(X)) -> #quote1(X)
   #102: #unquote1(ok(X)) -> #unquote1(X)
   #103: #active(from(X)) -> #from(active(X))
   #104: #active(from(X)) -> #active(X)
   #105: #active(unquote(s1(X))) -> #s(unquote(X))
   #106: #active(unquote(s1(X))) -> #unquote(X)
   #107: #active(cons1(X1,X2)) -> #cons1(active(X1),X2)
   #108: #active(cons1(X1,X2)) -> #active(X1)
   #109: #active(unquote1(cons1(X,Z))) -> #fcons(unquote(X),unquote1(Z))
   #110: #active(unquote1(cons1(X,Z))) -> #unquote(X)
   #111: #active(unquote1(cons1(X,Z))) -> #unquote1(Z)
   #112: #proper(from(X)) -> #from(proper(X))
   #113: #proper(from(X)) -> #proper(X)
   #114: #active(first(X1,X2)) -> #first(X1,active(X2))
   #115: #active(first(X1,X2)) -> #active(X2)
   #116: #s1(ok(X)) -> #s1(X)
   #117: #proper(cons1(X1,X2)) -> #cons1(proper(X1),proper(X2))
   #118: #proper(cons1(X1,X2)) -> #proper(X1)
   #119: #proper(cons1(X1,X2)) -> #proper(X2)
   #120: #active(unquote1(X)) -> #unquote1(active(X))
   #121: #active(unquote1(X)) -> #active(X)
   #122: #active(sel(X1,X2)) -> #sel(active(X1),X2)
   #123: #active(sel(X1,X2)) -> #active(X1)
   #124: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #125: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
   #126: #unquote1(mark(X)) -> #unquote1(X)
   #127: #active(quote1(first(X,Z))) -> #first1(X,Z)
   #128: #active(first(s(X),cons(Y,Z))) -> #cons(Y,first(X,Z))
   #129: #active(first(s(X),cons(Y,Z))) -> #first(X,Z)
   #130: #sel1(ok(X1),ok(X2)) -> #sel1(X1,X2)
   #131: #cons1(mark(X1),X2) -> #cons1(X1,X2)
Number of SCCs: 17, DPs: 73
  SCC { #101 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: x1
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: 0
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #101
Number of SCCs: 16, DPs: 72
  SCC { #61 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: 0
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: x1
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #61
Number of SCCs: 15, DPs: 71
  SCC { #63 #66 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: x1 + 1
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: x1
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #63 #66
Number of SCCs: 14, DPs: 69
  SCC { #13 #54 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: x1
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: x1 + 1
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #13 #54
Number of SCCs: 13, DPs: 67
  SCC { #1 #19 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: x1 + 1
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: x1
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #1 #19
Number of SCCs: 12, DPs: 65
  SCC { #102 #126 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: x1
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: x1 + 1
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: 0
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #102 #126
Number of SCCs: 11, DPs: 63
  SCC { #74 #116 }
POLO(Sum)... succeeded.
      01	w: 0
      #cons	w: 0
      s 	w: 0
      unquote1	w: 0
      #quote1	w: 0
      #cons1	w: 0
      top	w: 0
      #unquote1	w: 0
      #top	w: 0
      #fcons	w: 0
      #first1	w: 0
      cons1	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      from	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      #sel1	w: 0
      quote1	w: 0
      mark	w: x1 + 1
      nil1	w: 0
      first	w: 0
      first1	w: 0
      #proper	w: 0
      #unquote	w: 0
      #from	w: 0
      active	w: 0
      quote	w: 0
      cons	w: 0
      #active	w: 0
      #quote	w: 0
      #s1	w: x1
      sel1	w: 0
      s1	w: 0
      unquote	w: 0
      fcons	w: 0
    USABLE RULES: { }
    Removed DPs: #74 #116
Number of SCCs: 10, DPs: 61
  SCC { #40 #68 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.