/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: active(and(tt(),T)) -> mark(T)
    2: active(isNatIList(IL)) -> mark(isNatList(IL))
    3: active(isNat(0())) -> mark(tt())
    4: active(isNat(s(N))) -> mark(isNat(N))
    5: active(isNat(length(L))) -> mark(isNatList(L))
    6: active(isNatIList(zeros())) -> mark(tt())
    7: active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
    8: active(isNatList(nil())) -> mark(tt())
    9: active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
    10: active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
    11: active(zeros()) -> mark(cons(0(),zeros()))
    12: active(take(0(),IL)) -> mark(uTake1(isNatIList(IL)))
    13: active(uTake1(tt())) -> mark(nil())
    14: active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
    15: active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL)))
    16: active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
    17: active(uLength(tt(),L)) -> mark(s(length(L)))
    18: active(and(X1,X2)) -> and(active(X1),X2)
    19: active(and(X1,X2)) -> and(X1,active(X2))
    20: active(s(X)) -> s(active(X))
    21: active(length(X)) -> length(active(X))
    22: active(cons(X1,X2)) -> cons(active(X1),X2)
    23: active(take(X1,X2)) -> take(active(X1),X2)
    24: active(take(X1,X2)) -> take(X1,active(X2))
    25: active(uTake1(X)) -> uTake1(active(X))
    26: active(uTake2(X1,X2,X3,X4)) -> uTake2(active(X1),X2,X3,X4)
    27: active(uLength(X1,X2)) -> uLength(active(X1),X2)
    28: and(mark(X1),X2) -> mark(and(X1,X2))
    29: and(X1,mark(X2)) -> mark(and(X1,X2))
    30: s(mark(X)) -> mark(s(X))
    31: length(mark(X)) -> mark(length(X))
    32: cons(mark(X1),X2) -> mark(cons(X1,X2))
    33: take(mark(X1),X2) -> mark(take(X1,X2))
    34: take(X1,mark(X2)) -> mark(take(X1,X2))
    35: uTake1(mark(X)) -> mark(uTake1(X))
    36: uTake2(mark(X1),X2,X3,X4) -> mark(uTake2(X1,X2,X3,X4))
    37: uLength(mark(X1),X2) -> mark(uLength(X1,X2))
    38: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    39: proper(tt()) -> ok(tt())
    40: proper(isNatIList(X)) -> isNatIList(proper(X))
    41: proper(isNatList(X)) -> isNatList(proper(X))
    42: proper(isNat(X)) -> isNat(proper(X))
    43: proper(0()) -> ok(0())
    44: proper(s(X)) -> s(proper(X))
    45: proper(length(X)) -> length(proper(X))
    46: proper(zeros()) -> ok(zeros())
    47: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    48: proper(nil()) -> ok(nil())
    49: proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    50: proper(uTake1(X)) -> uTake1(proper(X))
    51: proper(uTake2(X1,X2,X3,X4)) -> uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
    52: proper(uLength(X1,X2)) -> uLength(proper(X1),proper(X2))
    53: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    54: isNatIList(ok(X)) -> ok(isNatIList(X))
    55: isNatList(ok(X)) -> ok(isNatList(X))
    56: isNat(ok(X)) -> ok(isNat(X))
    57: s(ok(X)) -> ok(s(X))
    58: length(ok(X)) -> ok(length(X))
    59: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    60: take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    61: uTake1(ok(X)) -> ok(uTake1(X))
    62: uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(uTake2(X1,X2,X3,X4))
    63: uLength(ok(X1),ok(X2)) -> ok(uLength(X1,X2))
    64: top(mark(X)) -> top(proper(X))
    65: top(ok(X)) -> top(active(X))
Number of strict rules: 65
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #active(isNatIList(IL)) -> #isNatList(IL)
   #2: #and(X1,mark(X2)) -> #and(X1,X2)
   #3: #uTake1(mark(X)) -> #uTake1(X)
   #4: #proper(isNat(X)) -> #isNat(proper(X))
   #5: #proper(isNat(X)) -> #proper(X)
   #6: #proper(isNatList(X)) -> #isNatList(proper(X))
   #7: #proper(isNatList(X)) -> #proper(X)
   #8: #uLength(mark(X1),X2) -> #uLength(X1,X2)
   #9: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #10: #proper(cons(X1,X2)) -> #proper(X1)
   #11: #proper(cons(X1,X2)) -> #proper(X2)
   #12: #and(ok(X1),ok(X2)) -> #and(X1,X2)
   #13: #length(ok(X)) -> #length(X)
   #14: #uTake1(ok(X)) -> #uTake1(X)
   #15: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2))
   #16: #proper(and(X1,X2)) -> #proper(X1)
   #17: #proper(and(X1,X2)) -> #proper(X2)
   #18: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #19: #isNatList(ok(X)) -> #isNatList(X)
   #20: #proper(isNatIList(X)) -> #isNatIList(proper(X))
   #21: #proper(isNatIList(X)) -> #proper(X)
   #22: #proper(uTake2(X1,X2,X3,X4)) -> #uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
   #23: #proper(uTake2(X1,X2,X3,X4)) -> #proper(X1)
   #24: #proper(uTake2(X1,X2,X3,X4)) -> #proper(X2)
   #25: #proper(uTake2(X1,X2,X3,X4)) -> #proper(X3)
   #26: #proper(uTake2(X1,X2,X3,X4)) -> #proper(X4)
   #27: #active(isNatList(cons(N,L))) -> #and(isNat(N),isNatList(L))
   #28: #active(isNatList(cons(N,L))) -> #isNat(N)
   #29: #active(isNatList(cons(N,L))) -> #isNatList(L)
   #30: #active(zeros()) -> #cons(0(),zeros())
   #31: #s(ok(X)) -> #s(X)
   #32: #active(take(X1,X2)) -> #take(X1,active(X2))
   #33: #active(take(X1,X2)) -> #active(X2)
   #34: #active(take(X1,X2)) -> #take(active(X1),X2)
   #35: #active(take(X1,X2)) -> #active(X1)
   #36: #proper(length(X)) -> #length(proper(X))
   #37: #proper(length(X)) -> #proper(X)
   #38: #active(take(0(),IL)) -> #uTake1(isNatIList(IL))
   #39: #active(take(0(),IL)) -> #isNatIList(IL)
   #40: #length(mark(X)) -> #length(X)
   #41: #isNat(ok(X)) -> #isNat(X)
   #42: #active(take(s(M),cons(N,IL))) -> #uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)
   #43: #active(take(s(M),cons(N,IL))) -> #and(isNat(M),and(isNat(N),isNatIList(IL)))
   #44: #active(take(s(M),cons(N,IL))) -> #isNat(M)
   #45: #active(take(s(M),cons(N,IL))) -> #and(isNat(N),isNatIList(IL))
   #46: #active(take(s(M),cons(N,IL))) -> #isNat(N)
   #47: #active(take(s(M),cons(N,IL))) -> #isNatIList(IL)
   #48: #uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> #uTake2(X1,X2,X3,X4)
   #49: #s(mark(X)) -> #s(X)
   #50: #proper(uLength(X1,X2)) -> #uLength(proper(X1),proper(X2))
   #51: #proper(uLength(X1,X2)) -> #proper(X1)
   #52: #proper(uLength(X1,X2)) -> #proper(X2)
   #53: #proper(take(X1,X2)) -> #take(proper(X1),proper(X2))
   #54: #proper(take(X1,X2)) -> #proper(X1)
   #55: #proper(take(X1,X2)) -> #proper(X2)
   #56: #active(uTake1(X)) -> #uTake1(active(X))
   #57: #active(uTake1(X)) -> #active(X)
   #58: #active(s(X)) -> #s(active(X))
   #59: #active(s(X)) -> #active(X)
   #60: #active(isNatIList(cons(N,IL))) -> #and(isNat(N),isNatIList(IL))
   #61: #active(isNatIList(cons(N,IL))) -> #isNat(N)
   #62: #active(isNatIList(cons(N,IL))) -> #isNatIList(IL)
   #63: #active(isNatList(take(N,IL))) -> #and(isNat(N),isNatIList(IL))
   #64: #active(isNatList(take(N,IL))) -> #isNat(N)
   #65: #active(isNatList(take(N,IL))) -> #isNatIList(IL)
   #66: #top(mark(X)) -> #top(proper(X))
   #67: #top(mark(X)) -> #proper(X)
   #68: #take(mark(X1),X2) -> #take(X1,X2)
   #69: #active(isNat(length(L))) -> #isNatList(L)
   #70: #proper(s(X)) -> #s(proper(X))
   #71: #proper(s(X)) -> #proper(X)
   #72: #top(ok(X)) -> #top(active(X))
   #73: #top(ok(X)) -> #active(X)
   #74: #and(mark(X1),X2) -> #and(X1,X2)
   #75: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #76: #active(cons(X1,X2)) -> #active(X1)
   #77: #take(X1,mark(X2)) -> #take(X1,X2)
   #78: #active(uLength(X1,X2)) -> #uLength(active(X1),X2)
   #79: #active(uLength(X1,X2)) -> #active(X1)
   #80: #take(ok(X1),ok(X2)) -> #take(X1,X2)
   #81: #active(uLength(tt(),L)) -> #s(length(L))
   #82: #active(uLength(tt(),L)) -> #length(L)
   #83: #cons(mark(X1),X2) -> #cons(X1,X2)
   #84: #active(and(X1,X2)) -> #and(X1,active(X2))
   #85: #active(and(X1,X2)) -> #active(X2)
   #86: #uLength(ok(X1),ok(X2)) -> #uLength(X1,X2)
   #87: #active(uTake2(X1,X2,X3,X4)) -> #uTake2(active(X1),X2,X3,X4)
   #88: #active(uTake2(X1,X2,X3,X4)) -> #active(X1)
   #89: #uTake2(mark(X1),X2,X3,X4) -> #uTake2(X1,X2,X3,X4)
   #90: #active(length(X)) -> #length(active(X))
   #91: #active(length(X)) -> #active(X)
   #92: #active(length(cons(N,L))) -> #uLength(and(isNat(N),isNatList(L)),L)
   #93: #active(length(cons(N,L))) -> #and(isNat(N),isNatList(L))
   #94: #active(length(cons(N,L))) -> #isNat(N)
   #95: #active(length(cons(N,L))) -> #isNatList(L)
   #96: #isNatIList(ok(X)) -> #isNatIList(X)
   #97: #active(uTake2(tt(),M,N,IL)) -> #cons(N,take(M,IL))
   #98: #active(uTake2(tt(),M,N,IL)) -> #take(M,IL)
   #99: #active(isNat(s(N))) -> #isNat(N)
   #100: #proper(uTake1(X)) -> #uTake1(proper(X))
   #101: #proper(uTake1(X)) -> #proper(X)
   #102: #active(and(X1,X2)) -> #and(active(X1),X2)
   #103: #active(and(X1,X2)) -> #active(X1)
Number of SCCs: 14, DPs: 51
  SCC { #41 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: x1
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: 0
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: 0
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: 0
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #41
Number of SCCs: 13, DPs: 50
  SCC { #19 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: 0
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: x1
      #s 	w: 0
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: 0
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: 0
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #19
Number of SCCs: 12, DPs: 49
  SCC { #96 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: 0
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: 0
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: x1
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: 0
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #96
Number of SCCs: 11, DPs: 48
  SCC { #3 #14 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: x1
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: 0
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: 0
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #3 #14
Number of SCCs: 10, DPs: 46
  SCC { #31 #49 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: 0
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: 0
      #s 	w: x1
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: 0
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: 0
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #31 #49
Number of SCCs: 9, DPs: 44
  SCC { #13 #40 }
POLO(Sum)... succeeded.
      #uTake2	w: 0
      isNatList	w: 0
      #cons	w: 0
      s 	w: 0
      #isNat	w: 0
      #take	w: 0
      take	w: 0
      top	w: 0
      #uTake1	w: 0
      and	w: 0
      isNatIList	w: 0
      #top	w: 0
      zeros	w: 0
      uTake2	w: 0
      uLength	w: 0
      proper	w: 0
      ok	w: x1 + 1
      0 	w: 0
      #isNatList	w: 0
      #s 	w: 0
      nil	w: 0
      mark	w: x1 + 1
      #proper	w: 0
      isNat	w: 0
      active	w: 0
      cons	w: 0
      #active	w: 0
      #isNatIList	w: 0
      tt	w: 0
      uTake1	w: 0
      length	w: 0
      #length	w: x1
      #and	w: 0
      #uLength	w: 0
    USABLE RULES: { }
    Removed DPs: #13 #40
Number of SCCs: 8, DPs: 42
  SCC { #66 #72 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.