/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: a__zeros() -> cons(0(),zeros())
    2: a__U11(tt(),L) -> s(a__length(mark(L)))
    3: a__U21(tt()) -> nil()
    4: a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
    5: a__and(tt(),X) -> mark(X)
    6: a__isNat(0()) -> tt()
    7: a__isNat(length(V1)) -> a__isNatList(V1)
    8: a__isNat(s(V1)) -> a__isNat(V1)
    9: a__isNatIList(V) -> a__isNatList(V)
    10: a__isNatIList(zeros()) -> tt()
    11: a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
    12: a__isNatList(nil()) -> tt()
    13: a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
    14: a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
    15: a__length(nil()) -> 0()
    16: a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
    17: a__take(0(),IL) -> a__U21(a__isNatIList(IL))
    18: a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N)
    19: mark(zeros()) -> a__zeros()
    20: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    21: mark(length(X)) -> a__length(mark(X))
    22: mark(U21(X)) -> a__U21(mark(X))
    23: mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4)
    24: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    25: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    26: mark(isNat(X)) -> a__isNat(X)
    27: mark(isNatList(X)) -> a__isNatList(X)
    28: mark(isNatIList(X)) -> a__isNatIList(X)
    29: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    30: mark(0()) -> 0()
    31: mark(tt()) -> tt()
    32: mark(s(X)) -> s(mark(X))
    33: mark(nil()) -> nil()
    34: a__zeros() -> zeros()
    35: a__U11(X1,X2) -> U11(X1,X2)
    36: a__length(X) -> length(X)
    37: a__U21(X) -> U21(X)
    38: a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4)
    39: a__take(X1,X2) -> take(X1,X2)
    40: a__and(X1,X2) -> and(X1,X2)
    41: a__isNat(X) -> isNat(X)
    42: a__isNatList(X) -> isNatList(X)
    43: a__isNatIList(X) -> isNatIList(X)
Number of strict rules: 43
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #a__U11(tt(),L) -> #a__length(mark(L))
   #2: #a__U11(tt(),L) -> #mark(L)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #a__isNatList(cons(V1,V2)) -> #a__and(a__isNat(V1),isNatList(V2))
   #5: #a__isNatList(cons(V1,V2)) -> #a__isNat(V1)
   #6: #a__isNatIList(V) -> #a__isNatList(V)
   #7: #a__isNatIList(cons(V1,V2)) -> #a__and(a__isNat(V1),isNatIList(V2))
   #8: #a__isNatIList(cons(V1,V2)) -> #a__isNat(V1)
   #9: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #10: #mark(take(X1,X2)) -> #mark(X1)
   #11: #mark(take(X1,X2)) -> #mark(X2)
   #12: #mark(U31(X1,X2,X3,X4)) -> #a__U31(mark(X1),X2,X3,X4)
   #13: #mark(U31(X1,X2,X3,X4)) -> #mark(X1)
   #14: #a__isNatList(take(V1,V2)) -> #a__and(a__isNat(V1),isNatIList(V2))
   #15: #a__isNatList(take(V1,V2)) -> #a__isNat(V1)
   #16: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #17: #mark(and(X1,X2)) -> #mark(X1)
   #18: #mark(U11(X1,X2)) -> #a__U11(mark(X1),X2)
   #19: #mark(U11(X1,X2)) -> #mark(X1)
   #20: #a__isNat(length(V1)) -> #a__isNatList(V1)
   #21: #a__and(tt(),X) -> #mark(X)
   #22: #mark(isNatIList(X)) -> #a__isNatIList(X)
   #23: #mark(U21(X)) -> #a__U21(mark(X))
   #24: #mark(U21(X)) -> #mark(X)
   #25: #mark(isNatList(X)) -> #a__isNatList(X)
   #26: #a__take(0(),IL) -> #a__U21(a__isNatIList(IL))
   #27: #a__take(0(),IL) -> #a__isNatIList(IL)
   #28: #mark(s(X)) -> #mark(X)
   #29: #mark(zeros()) -> #a__zeros()
   #30: #mark(isNat(X)) -> #a__isNat(X)
   #31: #mark(length(X)) -> #a__length(mark(X))
   #32: #mark(length(X)) -> #mark(X)
   #33: #a__length(cons(N,L)) -> #a__U11(a__and(a__isNatList(L),isNat(N)),L)
   #34: #a__length(cons(N,L)) -> #a__and(a__isNatList(L),isNat(N))
   #35: #a__length(cons(N,L)) -> #a__isNatList(L)
   #36: #a__isNat(s(V1)) -> #a__isNat(V1)
   #37: #a__U31(tt(),IL,M,N) -> #mark(N)
   #38: #a__take(s(M),cons(N,IL)) -> #a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N)
   #39: #a__take(s(M),cons(N,IL)) -> #a__and(a__isNatIList(IL),and(isNat(M),isNat(N)))
   #40: #a__take(s(M),cons(N,IL)) -> #a__isNatIList(IL)
Number of SCCs: 1, DPs: 37
  SCC { #1..22 #24 #25 #27 #28 #30..40 }
POLO(Sum)... succeeded.
      U21	w: x1
      isNatList	w: 0
      U11	w: x1 + x2 + 1
      s 	w: x1
      #a__U31	w: x4
      a__isNatIList	w: 0
      #a__isNat	w: 0
      take	w: x1 + x2
      and	w: x1 + x2
      isNatIList	w: 0
      #a__U11	w: x2 + 1
      zeros	w: 1
      a__U31	w: x1 + x2 + x3 + x4
      #a__take	w: x2
      a__isNatList	w: 0
      #a__U21	w: 0
      #a__isNatIList	w: 0
      #mark	w: x1
      0 	w: 0
      #a__and	w: x2
      #a__zeros	w: 0
      a__U21	w: x1
      nil	w: 0
      mark	w: x1
      a__U11	w: x1 + x2 + 1
      #a__length	w: x1 + 1
      isNat	w: 0
      U31	w: x1 + x2 + x3 + x4
      #a__isNatList	w: 0
      cons	w: x1 + x2
      a__take	w: x1 + x2
      tt	w: 0
      a__isNat	w: 0
      a__and	w: x1 + x2
      length	w: x1 + 1
      a__zeros	w: 1
      a__length	w: x1 + 1
    USABLE RULES: { 1..43 }
    Removed DPs: #2 #19 #32 #34 #35
Number of SCCs: 2, DPs: 30
  SCC { #1 #33 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.