/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 poly ... removes: 18 4 8 1 3 26 19 32 22 5 10 7 20 25 30 14 31 12 23 11 9 13 6 2
  isNatList(x1)		w: (1 + x1)
  U11(x1,x2)		w: (31 + x2 + x1)
  s(x1)		w: (1 + x1)
  a__isNatIList(x1)		w: (23653 + 2 * x1)
  and(x1,x2)		w: (1 + x2 + x1)
  isNatIList(x1)		w: (2 * x1)
  zeros()		w: (1)
  a__isNatList(x1)		w: (11826 + x1)
  0()		w: (11820)
  nil()		w: (11829)
  mark(x1)		w: (23654 + x1)
  a__U11(x1,x2)		w: (31 + x2 + x1)
  isNat(x1)		w: (1 + x1)
  cons(x1,x2)		w: (11831 + 2 * x2 + x1)
  tt()		w: (23654)
  a__isNat(x1)		w: (23654 + x1)
  a__and(x1,x2)		w: (1 + x2 + x1)
  length(x1)		w: (29 + x1)
  a__zeros()		w: (23654)
  a__length(x1)		w: (29 + x1)
Number of strict rules: 8
Direct poly ... removes: 15 16 21 17 27 28 29
  isNatList(x1)		w: (2 + x1)
  U11(x1,x2)		w: (26533 + x2 + x1)
  s(x1)		w: (x1)
  a__isNatIList(x1)		w: (873 + 2 * x1)
  and(x1,x2)		w: (2 + x2 + x1)
  isNatIList(x1)		w: (436 + 2 * x1)
  zeros()		w: (40972)
  a__isNatList(x1)		w: (3 + x1)
  0()		w: (20485)
  nil()		w: (11668)
  mark(x1)		w: (1 + 2 * x1)
  a__U11(x1,x2)		w: (53065 + x2 + x1)
  isNat(x1)		w: (1 + x1)
  cons(x1,x2)		w: (3 + x2 + 2 * x1)
  tt()		w: (1)
  a__isNat(x1)		w: (1 + x1)
  a__and(x1,x2)		w: (3 + x2 + x1)
  length(x1)		w: (53063 + 2 * x1)
  a__zeros()		w: (81945)
  a__length(x1)		w: (53064 + 2 * x1)
Number of strict rules: 1
Direct poly ... removes: 24
  isNatList(x1)		w: (1 + x1)
  U11(x1,x2)		w: (29298 + x2 + x1)
  s(x1)		w: (1 + x1)
  a__isNatIList(x1)		w: (3 + 2 * x1)
  and(x1,x2)		w: (1 + x2 + x1)
  isNatIList(x1)		w: (1 + 2 * x1)
  zeros()		w: (3)
  a__isNatList(x1)		w: (3 + x1)
  0()		w: (1)
  nil()		w: (1063)
  mark(x1)		w: (1 + 2 * x1)
  a__U11(x1,x2)		w: (58595 + x2 + x1)
  isNat(x1)		w: (1 + x1)
  cons(x1,x2)		w: (2 + x2 + 2 * x1)
  tt()		w: (1)
  a__isNat(x1)		w: (2 + 2 * x1)
  a__and(x1,x2)		w: (2 + x2 + x1)
  length(x1)		w: (29297 + 2 * x1)
  a__zeros()		w: (7)
  a__length(x1)		w: (58593 + 2 * x1)
Number of strict rules: 0