/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: a__zeros() -> cons(0(),zeros())
    2: a__U11(tt(),L) -> s(a__length(mark(L)))
    3: a__and(tt(),X) -> mark(X)
    4: a__isNat(0()) -> tt()
    5: a__isNat(length(V1)) -> a__isNatList(V1)
    6: a__isNat(s(V1)) -> a__isNat(V1)
    7: a__isNatIList(V) -> a__isNatList(V)
    8: a__isNatIList(zeros()) -> tt()
    9: a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2))
    10: a__isNatList(nil()) -> tt()
    11: a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2))
    12: a__length(nil()) -> 0()
    13: a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L)
    14: mark(zeros()) -> a__zeros()
    15: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    16: mark(length(X)) -> a__length(mark(X))
    17: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    18: mark(isNat(X)) -> a__isNat(X)
    19: mark(isNatList(X)) -> a__isNatList(X)
    20: mark(isNatIList(X)) -> a__isNatIList(X)
    21: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    22: mark(0()) -> 0()
    23: mark(tt()) -> tt()
    24: mark(s(X)) -> s(mark(X))
    25: mark(nil()) -> nil()
    26: a__zeros() -> zeros()
    27: a__U11(X1,X2) -> U11(X1,X2)
    28: a__length(X) -> length(X)
    29: a__and(X1,X2) -> and(X1,X2)
    30: a__isNat(X) -> isNat(X)
    31: a__isNatList(X) -> isNatList(X)
    32: a__isNatIList(X) -> isNatIList(X)
Number of strict rules: 32
Direct POLO(bPol) ... removes: 8 5 10 7 12
      isNatList	w: x1
      U11	w: x1 + 2 * x2 + 1
      s 	w: x1
      a__isNatIList	w: 2 * x1 + 1
      and	w: x1 + x2
      isNatIList	w: 2 * x1 + 1
      zeros	w: 0
      a__isNatList	w: x1
      0 	w: 0
      nil	w: 3
      mark	w: x1
      a__U11	w: x1 + 2 * x2 + 1
      isNat	w: x1
      cons	w: x1 + 2 * x2
      tt	w: 0
      a__isNat	w: x1
      a__and	w: x1 + x2
      length	w: 2 * x1 + 1
      a__zeros	w: 0
      a__length	w: 2 * x1 + 1
Number of strict rules: 27
Direct POLO(bPol) ... removes: 18 4 1 3 26 19 32 22 20 25 30 14 31 23 11 9 13 2
      isNatList	w: x1 + 1
      U11	w: x1 + x2 + 2
      s 	w: x1
      a__isNatIList	w: 2 * x1 + 13
      and	w: x1 + x2 + 1
      isNatIList	w: 2 * x1 + 1
      zeros	w: 8
      a__isNatList	w: x1 + 14
      0 	w: 1
      nil	w: 15
      mark	w: x1 + 29
      a__U11	w: x1 + x2 + 2
      isNat	w: x1 + 1
      cons	w: x1 + 2 * x2 + 18
      tt	w: 29
      a__isNat	w: x1 + 29
      a__and	w: x1 + x2 + 1
      length	w: x1 + 1
      a__zeros	w: 36
      a__length	w: x1 + 1
Number of strict rules: 9
Direct POLO(bPol) ... removes: 6
      isNatList	w: x1 + 1
      U11	w: x1 + x2 + 2
      s 	w: x1 + 1
      a__isNatIList	w: 2 * x1 + 13
      and	w: x1 + x2 + 1
      isNatIList	w: 2 * x1 + 1
      zeros	w: 8
      a__isNatList	w: x1 + 14
      0 	w: 1
      nil	w: 15
      mark	w: x1 + 29
      a__U11	w: x1 + x2 + 2
      isNat	w: x1 + 1
      cons	w: x1 + 2 * x2 + 18
      tt	w: 29
      a__isNat	w: x1 + 29
      a__and	w: x1 + x2 + 1
      length	w: x1 + 1
      a__zeros	w: 36
      a__length	w: x1 + 1
Number of strict rules: 8
Direct POLO(bPol) ... removes: 15 16 21 17 27 28 24 29
      isNatList	w: x1 + 1
      U11	w: x1 + x2 + 2
      s 	w: x1 + 2
      a__isNatIList	w: 2 * x1 + 14
      and	w: x1 + x2 + 3
      isNatIList	w: 2 * x1 + 1
      zeros	w: 9
      a__isNatList	w: x1 + 15
      0 	w: 2
      nil	w: 17
      mark	w: 2 * x1 + 30
      a__U11	w: x1 + x2 + 3
      isNat	w: x1 + 1
      cons	w: x1 + 2 * x2 + 20
      tt	w: 32
      a__isNat	w: x1 + 30
      a__and	w: x1 + x2 + 4
      length	w: x1 + 2
      a__zeros	w: 48
      a__length	w: x1 + 3
Number of strict rules: 0