/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__U101(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
    2: a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
    3: a__U21(tt(),X) -> mark(X)
    4: a__U31(tt(),N) -> mark(N)
    5: a__U41(tt(),N) -> cons(mark(N),natsFrom(s(N)))
    6: a__U51(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
    7: a__U61(tt(),Y) -> mark(Y)
    8: a__U71(tt(),XS) -> pair(nil(),mark(XS))
    9: a__U81(tt(),N,X,XS) -> a__U82(a__splitAt(mark(N),mark(XS)),X)
    10: a__U82(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
    11: a__U91(tt(),XS) -> mark(XS)
    12: a__afterNth(N,XS) -> a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS)
    13: a__and(tt(),X) -> mark(X)
    14: a__fst(pair(X,Y)) -> a__U21(a__and(a__isLNat(X),isLNat(Y)),X)
    15: a__head(cons(N,XS)) -> a__U31(a__and(a__isNatural(N),isLNat(XS)),N)
    16: a__isLNat(nil()) -> tt()
    17: a__isLNat(afterNth(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
    18: a__isLNat(cons(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
    19: a__isLNat(fst(V1)) -> a__isPLNat(V1)
    20: a__isLNat(natsFrom(V1)) -> a__isNatural(V1)
    21: a__isLNat(snd(V1)) -> a__isPLNat(V1)
    22: a__isLNat(tail(V1)) -> a__isLNat(V1)
    23: a__isLNat(take(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
    24: a__isNatural(0()) -> tt()
    25: a__isNatural(head(V1)) -> a__isLNat(V1)
    26: a__isNatural(s(V1)) -> a__isNatural(V1)
    27: a__isNatural(sel(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
    28: a__isPLNat(pair(V1,V2)) -> a__and(a__isLNat(V1),isLNat(V2))
    29: a__isPLNat(splitAt(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
    30: a__natsFrom(N) -> a__U41(a__isNatural(N),N)
    31: a__sel(N,XS) -> a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS)
    32: a__snd(pair(X,Y)) -> a__U61(a__and(a__isLNat(X),isLNat(Y)),Y)
    33: a__splitAt(0(),XS) -> a__U71(a__isLNat(XS),XS)
    34: a__splitAt(s(N),cons(X,XS)) -> a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
    35: a__tail(cons(N,XS)) -> a__U91(a__and(a__isNatural(N),isLNat(XS)),XS)
    36: a__take(N,XS) -> a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS)
    37: mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
    38: mark(fst(X)) -> a__fst(mark(X))
    39: mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
    40: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    41: mark(snd(X)) -> a__snd(mark(X))
    42: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    43: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
    44: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
    45: mark(natsFrom(X)) -> a__natsFrom(mark(X))
    46: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
    47: mark(head(X)) -> a__head(mark(X))
    48: mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
    49: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
    50: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
    51: mark(U81(X1,X2,X3,X4)) -> a__U81(mark(X1),X2,X3,X4)
    52: mark(U82(X1,X2)) -> a__U82(mark(X1),X2)
    53: mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
    54: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    55: mark(isNatural(X)) -> a__isNatural(X)
    56: mark(isLNat(X)) -> a__isLNat(X)
    57: mark(isPLNat(X)) -> a__isPLNat(X)
    58: mark(tail(X)) -> a__tail(mark(X))
    59: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    60: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    61: mark(tt()) -> tt()
    62: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    63: mark(s(X)) -> s(mark(X))
    64: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    65: mark(nil()) -> nil()
    66: mark(0()) -> 0()
    67: a__U101(X1,X2,X3) -> U101(X1,X2,X3)
    68: a__fst(X) -> fst(X)
    69: a__splitAt(X1,X2) -> splitAt(X1,X2)
    70: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    71: a__snd(X) -> snd(X)
    72: a__U21(X1,X2) -> U21(X1,X2)
    73: a__U31(X1,X2) -> U31(X1,X2)
    74: a__U41(X1,X2) -> U41(X1,X2)
    75: a__natsFrom(X) -> natsFrom(X)
    76: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
    77: a__head(X) -> head(X)
    78: a__afterNth(X1,X2) -> afterNth(X1,X2)
    79: a__U61(X1,X2) -> U61(X1,X2)
    80: a__U71(X1,X2) -> U71(X1,X2)
    81: a__U81(X1,X2,X3,X4) -> U81(X1,X2,X3,X4)
    82: a__U82(X1,X2) -> U82(X1,X2)
    83: a__U91(X1,X2) -> U91(X1,X2)
    84: a__and(X1,X2) -> and(X1,X2)
    85: a__isNatural(X) -> isNatural(X)
    86: a__isLNat(X) -> isLNat(X)
    87: a__isPLNat(X) -> isPLNat(X)
    88: a__tail(X) -> tail(X)
    89: a__take(X1,X2) -> take(X1,X2)
    90: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 90
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U11(tt(),N,XS) -> #a__snd(a__splitAt(mark(N),mark(XS)))
   #2: #a__U11(tt(),N,XS) -> #a__splitAt(mark(N),mark(XS))
   #3: #a__U11(tt(),N,XS) -> #mark(N)
   #4: #a__U11(tt(),N,XS) -> #mark(XS)
   #5: #mark(U31(X1,X2)) -> #a__U31(mark(X1),X2)
   #6: #mark(U31(X1,X2)) -> #mark(X1)
   #7: #a__isPLNat(splitAt(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2))
   #8: #a__isPLNat(splitAt(V1,V2)) -> #a__isNatural(V1)
   #9: #a__tail(cons(N,XS)) -> #a__U91(a__and(a__isNatural(N),isLNat(XS)),XS)
   #10: #a__tail(cons(N,XS)) -> #a__and(a__isNatural(N),isLNat(XS))
   #11: #a__tail(cons(N,XS)) -> #a__isNatural(N)
   #12: #mark(U51(X1,X2,X3)) -> #a__U51(mark(X1),X2,X3)
   #13: #mark(U51(X1,X2,X3)) -> #mark(X1)
   #14: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2)
   #15: #mark(U21(X1,X2)) -> #mark(X1)
   #16: #mark(snd(X)) -> #a__snd(mark(X))
   #17: #mark(snd(X)) -> #mark(X)
   #18: #mark(U101(X1,X2,X3)) -> #a__U101(mark(X1),X2,X3)
   #19: #mark(U101(X1,X2,X3)) -> #mark(X1)
   #20: #mark(head(X)) -> #a__head(mark(X))
   #21: #mark(head(X)) -> #mark(X)
   #22: #mark(U91(X1,X2)) -> #a__U91(mark(X1),X2)
   #23: #mark(U91(X1,X2)) -> #mark(X1)
   #24: #mark(afterNth(X1,X2)) -> #a__afterNth(mark(X1),mark(X2))
   #25: #mark(afterNth(X1,X2)) -> #mark(X1)
   #26: #mark(afterNth(X1,X2)) -> #mark(X2)
   #27: #mark(tail(X)) -> #a__tail(mark(X))
   #28: #mark(tail(X)) -> #mark(X)
   #29: #mark(fst(X)) -> #a__fst(mark(X))
   #30: #mark(fst(X)) -> #mark(X)
   #31: #a__U51(tt(),N,XS) -> #a__head(a__afterNth(mark(N),mark(XS)))
   #32: #a__U51(tt(),N,XS) -> #a__afterNth(mark(N),mark(XS))
   #33: #a__U51(tt(),N,XS) -> #mark(N)
   #34: #a__U51(tt(),N,XS) -> #mark(XS)
   #35: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #36: #mark(take(X1,X2)) -> #mark(X1)
   #37: #mark(take(X1,X2)) -> #mark(X2)
   #38: #mark(isNatural(X)) -> #a__isNatural(X)
   #39: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3)
   #40: #mark(U11(X1,X2,X3)) -> #mark(X1)
   #41: #mark(U81(X1,X2,X3,X4)) -> #a__U81(mark(X1),X2,X3,X4)
   #42: #mark(U81(X1,X2,X3,X4)) -> #mark(X1)
   #43: #a__and(tt(),X) -> #mark(X)
   #44: #a__U81(tt(),N,X,XS) -> #a__U82(a__splitAt(mark(N),mark(XS)),X)
   #45: #a__U81(tt(),N,X,XS) -> #a__splitAt(mark(N),mark(XS))
   #46: #a__U81(tt(),N,X,XS) -> #mark(N)
   #47: #a__U81(tt(),N,X,XS) -> #mark(XS)
   #48: #a__U91(tt(),XS) -> #mark(XS)
   #49: #mark(isPLNat(X)) -> #a__isPLNat(X)
   #50: #a__isLNat(take(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2))
   #51: #a__isLNat(take(V1,V2)) -> #a__isNatural(V1)
   #52: #mark(natsFrom(X)) -> #a__natsFrom(mark(X))
   #53: #mark(natsFrom(X)) -> #mark(X)
   #54: #a__afterNth(N,XS) -> #a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS)
   #55: #a__afterNth(N,XS) -> #a__and(a__isNatural(N),isLNat(XS))
   #56: #a__afterNth(N,XS) -> #a__isNatural(N)
   #57: #a__sel(N,XS) -> #a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS)
   #58: #a__sel(N,XS) -> #a__and(a__isNatural(N),isLNat(XS))
   #59: #a__sel(N,XS) -> #a__isNatural(N)
   #60: #mark(isLNat(X)) -> #a__isLNat(X)
   #61: #a__fst(pair(X,Y)) -> #a__U21(a__and(a__isLNat(X),isLNat(Y)),X)
   #62: #a__fst(pair(X,Y)) -> #a__and(a__isLNat(X),isLNat(Y))
   #63: #a__fst(pair(X,Y)) -> #a__isLNat(X)
   #64: #mark(cons(X1,X2)) -> #mark(X1)
   #65: #a__natsFrom(N) -> #a__U41(a__isNatural(N),N)
   #66: #a__natsFrom(N) -> #a__isNatural(N)
   #67: #mark(U82(X1,X2)) -> #a__U82(mark(X1),X2)
   #68: #mark(U82(X1,X2)) -> #mark(X1)
   #69: #mark(U61(X1,X2)) -> #a__U61(mark(X1),X2)
   #70: #mark(U61(X1,X2)) -> #mark(X1)
   #71: #a__isNatural(head(V1)) -> #a__isLNat(V1)
   #72: #a__isLNat(natsFrom(V1)) -> #a__isNatural(V1)
   #73: #a__U61(tt(),Y) -> #mark(Y)
   #74: #mark(splitAt(X1,X2)) -> #a__splitAt(mark(X1),mark(X2))
   #75: #mark(splitAt(X1,X2)) -> #mark(X1)
   #76: #mark(splitAt(X1,X2)) -> #mark(X2)
   #77: #a__U82(pair(YS,ZS),X) -> #mark(X)
   #78: #a__U82(pair(YS,ZS),X) -> #mark(ZS)
   #79: #mark(pair(X1,X2)) -> #mark(X1)
   #80: #mark(pair(X1,X2)) -> #mark(X2)
   #81: #a__splitAt(0(),XS) -> #a__U71(a__isLNat(XS),XS)
   #82: #a__splitAt(0(),XS) -> #a__isLNat(XS)
   #83: #a__U41(tt(),N) -> #mark(N)
   #84: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2)
   #85: #mark(U41(X1,X2)) -> #mark(X1)
   #86: #a__isPLNat(pair(V1,V2)) -> #a__and(a__isLNat(V1),isLNat(V2))
   #87: #a__isPLNat(pair(V1,V2)) -> #a__isLNat(V1)
   #88: #a__isLNat(tail(V1)) -> #a__isLNat(V1)
   #89: #a__splitAt(s(N),cons(X,XS)) -> #a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
   #90: #a__splitAt(s(N),cons(X,XS)) -> #a__and(a__isNatural(N),and(isNatural(X),isLNat(XS)))
   #91: #a__splitAt(s(N),cons(X,XS)) -> #a__isNatural(N)
   #92: #a__isNatural(sel(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2))
   #93: #a__isNatural(sel(V1,V2)) -> #a__isNatural(V1)
   #94: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #95: #mark(sel(X1,X2)) -> #mark(X1)
   #96: #mark(sel(X1,X2)) -> #mark(X2)
   #97: #a__isLNat(afterNth(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2))
   #98: #a__isLNat(afterNth(V1,V2)) -> #a__isNatural(V1)
   #99: #a__snd(pair(X,Y)) -> #a__U61(a__and(a__isLNat(X),isLNat(Y)),Y)
   #100: #a__snd(pair(X,Y)) -> #a__and(a__isLNat(X),isLNat(Y))
   #101: #a__snd(pair(X,Y)) -> #a__isLNat(X)
   #102: #a__isLNat(fst(V1)) -> #a__isPLNat(V1)
   #103: #mark(s(X)) -> #mark(X)
   #104: #a__isNatural(s(V1)) -> #a__isNatural(V1)
   #105: #a__take(N,XS) -> #a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS)
   #106: #a__take(N,XS) -> #a__and(a__isNatural(N),isLNat(XS))
   #107: #a__take(N,XS) -> #a__isNatural(N)
   #108: #a__isLNat(snd(V1)) -> #a__isPLNat(V1)
   #109: #a__U21(tt(),X) -> #mark(X)
   #110: #a__U101(tt(),N,XS) -> #a__fst(a__splitAt(mark(N),mark(XS)))
   #111: #a__U101(tt(),N,XS) -> #a__splitAt(mark(N),mark(XS))
   #112: #a__U101(tt(),N,XS) -> #mark(N)
   #113: #a__U101(tt(),N,XS) -> #mark(XS)
   #114: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #115: #mark(and(X1,X2)) -> #mark(X1)
   #116: #a__U71(tt(),XS) -> #mark(XS)
   #117: #a__head(cons(N,XS)) -> #a__U31(a__and(a__isNatural(N),isLNat(XS)),N)
   #118: #a__head(cons(N,XS)) -> #a__and(a__isNatural(N),isLNat(XS))
   #119: #a__head(cons(N,XS)) -> #a__isNatural(N)
   #120: #a__U31(tt(),N) -> #mark(N)
   #121: #mark(U71(X1,X2)) -> #a__U71(mark(X1),X2)
   #122: #mark(U71(X1,X2)) -> #mark(X1)
   #123: #a__isLNat(cons(V1,V2)) -> #a__and(a__isNatural(V1),isLNat(V2))
   #124: #a__isLNat(cons(V1,V2)) -> #a__isNatural(V1)
Number of SCCs: 1, DPs: 124
	SCC { #1..124 }
Sum... Max... succeeded.
  U21(x1,x2)		w: (max{x2, x1})
  #a__U82(x1,x2)		w: (max{5 + x2, 4 + x1})
  #a__U71(x1,x2)		w: (max{4 + x2, 4 + x1})
  U11(x1,x2,x3)		w: (max{x3, 10 + x2, x1})
  s(x1)		w: (x1)
  #a__U31(x1,x2)		w: (max{4 + x2, 0})
  #a__head(x1)		w: (4 + x1)
  #a__natsFrom(x1)		w: (8 + x1)
  isPLNat(x1)		w: (x1)
  #a__snd(x1)		w: (4 + x1)
  a__afterNth(x1,x2)		w: (max{x2, 11 + x1})
  U91(x1,x2)		w: (max{1 + x2, 2 + x1})
  a__U82(x1,x2)		w: (max{8 + x2, x1})
  take(x1,x2)		w: (max{24407 + x2, 18 + x1})
  U71(x1,x2)		w: (max{x2, x1})
  and(x1,x2)		w: (max{x2, x1})
  U101(x1,x2,x3)		w: (max{19 + x3, 10 + x2, 11 + x1})
  pair(x1,x2)		w: (max{x2, x1})
  fst(x1)		w: (x1)
  natsFrom(x1)		w: (8 + x1)
  a__snd(x1)		w: (x1)
  #a__U51(x1,x2,x3)		w: (max{4 + x3, 15 + x2, 4 + x1})
  splitAt(x1,x2)		w: (max{x2, 9 + x1})
  #a__U11(x1,x2,x3)		w: (max{4 + x3, 13 + x2, 3 + x1})
  a__U31(x1,x2)		w: (max{x2, x1})
  a__U51(x1,x2,x3)		w: (max{x3, 11 + x2, x1})
  a__U81(x1,x2,x3,x4)		w: (max{x4, 8 + x3, 9 + x2, x1})
  #a__take(x1,x2)		w: (max{6 + x2, 15 + x1})
  isNatural(x1)		w: (7 + x1)
  a__U41(x1,x2)		w: (max{8 + x2, 1 + x1})
  #a__U21(x1,x2)		w: (max{4 + x2, 0})
  #a__U81(x1,x2,x3,x4)		w: (max{4 + x4, 12 + x3, 13 + x2, 4 + x1})
  #a__U61(x1,x2)		w: (max{4 + x2, 0})
  a__fst(x1)		w: (x1)
  tail(x1)		w: (9 + x1)
  a__natsFrom(x1)		w: (8 + x1)
  #mark(x1)		w: (4 + x1)
  0()		w: (0)
  #a__and(x1,x2)		w: (max{4 + x2, 1 + x1})
  a__isLNat(x1)		w: (x1)
  a__U21(x1,x2)		w: (max{x2, x1})
  a__U91(x1,x2)		w: (max{1 + x2, 2 + x1})
  sel(x1,x2)		w: (max{x2, 11 + x1})
  afterNth(x1,x2)		w: (max{x2, 11 + x1})
  nil()		w: (2)
  a__splitAt(x1,x2)		w: (max{x2, 9 + x1})
  isLNat(x1)		w: (x1)
  #a__sel(x1,x2)		w: (max{4 + x2, 15 + x1})
  mark(x1)		w: (x1)
  #a__isLNat(x1)		w: (4 + x1)
  #a__U101(x1,x2,x3)		w: (max{5 + x3, 14 + x2, 0})
  a__U11(x1,x2,x3)		w: (max{x3, 10 + x2, x1})
  a__sel(x1,x2)		w: (max{x2, 11 + x1})
  a__isPLNat(x1)		w: (x1)
  U61(x1,x2)		w: (max{x2, x1})
  U31(x1,x2)		w: (max{x2, x1})
  a__U71(x1,x2)		w: (max{x2, x1})
  #a__isPLNat(x1)		w: (4 + x1)
  head(x1)		w: (x1)
  #a__afterNth(x1,x2)		w: (max{4 + x2, 14 + x1})
  #a__splitAt(x1,x2)		w: (max{4 + x2, 13 + x1})
  cons(x1,x2)		w: (max{x2, 8 + x1})
  a__U61(x1,x2)		w: (max{x2, x1})
  snd(x1)		w: (x1)
  a__take(x1,x2)		w: (max{24407 + x2, 18 + x1})
  U81(x1,x2,x3,x4)		w: (max{x4, 8 + x3, 9 + x2, x1})
  #a__U41(x1,x2)		w: (max{4 + x2, 0})
  U82(x1,x2)		w: (max{8 + x2, x1})
  tt()		w: (2)
  a__isNatural(x1)		w: (7 + x1)
  #a__isNatural(x1)		w: (7 + x1)
  #a__fst(x1)		w: (4 + x1)
  U51(x1,x2,x3)		w: (max{x3, 11 + x2, x1})
  a__and(x1,x2)		w: (max{x2, x1})
  a__tail(x1)		w: (9 + x1)
  U41(x1,x2)		w: (max{8 + x2, 1 + x1})
  #a__tail(x1)		w: (12 + x1)
  a__U101(x1,x2,x3)		w: (max{19 + x3, 10 + x2, 11 + x1})
  #a__U91(x1,x2)		w: (max{4 + x2, 0})
  a__head(x1)		w: (x1)
    USABLE RULES: { 1..90 }
    Removed DPs: #3 #8..11 #19 #22 #23 #25 #27 #28 #33 #35..38 #46 #50..53 #56 #59 #64..66 #71 #72 #75 #77 #84 #85 #88 #91..93 #95 #98 #105..107 #110..113 #117 #119 #124
Number of SCCs: 2, DPs: 73
	SCC { #104 }
Sum... succeeded.
  U21(x1,x2)		w: (9124 + x1)
  #a__U82(x1,x2)		w: (0)
  #a__U71(x1,x2)		w: (0)
  U11(x1,x2,x3)		w: (9127 + x3)
  s(x1)		w: (1 + x1)
  #a__U31(x1,x2)		w: (0)
  #a__head(x1)		w: (0)
  #a__natsFrom(x1)		w: (0)
  isPLNat(x1)		w: (14870 + x1)
  #a__snd(x1)		w: (0)
  a__afterNth(x1,x2)		w: (9125)
  U91(x1,x2)		w: (9124)
  a__U82(x1,x2)		w: (9127 + x2)
  take(x1,x2)		w: (9126)
  U71(x1,x2)		w: (9127 + x2)
  and(x1,x2)		w: (14871)
  U101(x1,x2,x3)		w: (9127 + x2 + x1)
  pair(x1,x2)		w: (9128)
  fst(x1)		w: (9128 + x1)
  natsFrom(x1)		w: (19407)
  a__snd(x1)		w: (9122)
  #a__U51(x1,x2,x3)		w: (1)
  splitAt(x1,x2)		w: (9126)
  #a__U11(x1,x2,x3)		w: (1)
  a__U31(x1,x2)		w: (9128)
  a__U51(x1,x2,x3)		w: (9126 + x3)
  a__U81(x1,x2,x3,x4)		w: (9126 + x4 + x3)
  #a__take(x1,x2)		w: (0)
  isNatural(x1)		w: (14870)
  a__U41(x1,x2)		w: (19407)
  #a__U21(x1,x2)		w: (0)
  #a__U81(x1,x2,x3,x4)		w: (0)
  #a__U61(x1,x2)		w: (0)
  a__fst(x1)		w: (9127)
  tail(x1)		w: (9126)
  a__natsFrom(x1)		w: (19406)
  #mark(x1)		w: (1)
  0()		w: (9125)
  #a__and(x1,x2)		w: (1)
  a__isLNat(x1)		w: (14868)
  a__U21(x1,x2)		w: (9123)
  a__U91(x1,x2)		w: (9123)
  sel(x1,x2)		w: (9126 + x2)
  afterNth(x1,x2)		w: (9126)
  nil()		w: (9125)
  a__splitAt(x1,x2)		w: (9125)
  isLNat(x1)		w: (14869)
  #a__sel(x1,x2)		w: (1)
  mark(x1)		w: (9124)
  #a__isLNat(x1)		w: (0)
  #a__U101(x1,x2,x3)		w: (0)
  a__U11(x1,x2,x3)		w: (9126 + x2)
  a__sel(x1,x2)		w: (9125)
  a__isPLNat(x1)		w: (14869)
  U61(x1,x2)		w: (9124)
  U31(x1,x2)		w: (9129 + x1)
  a__U71(x1,x2)		w: (9126)
  #a__isPLNat(x1)		w: (0)
  head(x1)		w: (9128 + x1)
  #a__afterNth(x1,x2)		w: (0)
  #a__splitAt(x1,x2)		w: (0)
  cons(x1,x2)		w: (19408)
  a__U61(x1,x2)		w: (9123)
  snd(x1)		w: (9123)
  a__take(x1,x2)		w: (9125)
  U81(x1,x2,x3,x4)		w: (9127 + x2)
  #a__U41(x1,x2)		w: (1)
  U82(x1,x2)		w: (9128 + x1)
  tt()		w: (14870)
  a__isNatural(x1)		w: (14869)
  #a__isNatural(x1)		w: (x1)
  #a__fst(x1)		w: (0)
  U51(x1,x2,x3)		w: (9127 + x2)
  a__and(x1,x2)		w: (14870)
  a__tail(x1)		w: (9125)
  U41(x1,x2)		w: (19408)
  #a__tail(x1)		w: (0)
  a__U101(x1,x2,x3)		w: (9126 + x3)
  #a__U91(x1,x2)		w: (1)
  a__head(x1)		w: (9127)
    USABLE RULES: { }
    Removed DPs: #104
Number of SCCs: 1, DPs: 72
	SCC { #1 #2 #4..7 #12..17 #20 #21 #24 #26 #29..32 #34 #39..45 #47 #49 #54 #55 #57 #58 #60..63 #67..70 #73 #74 #76 #78..82 #86 #87 #89 #90 #94 #96 #97 #99..103 #108 #109 #114..116 #118 #120..123 }
Sum... Max... succeeded.
  U21(x1,x2)		w: (max{1515 + x2, 1515 + x1})
  #a__U82(x1,x2)		w: (max{95526 + x2, 11677 + x1})
  #a__U71(x1,x2)		w: (max{47188 + x2, 9335 + x1})
  U11(x1,x2,x3)		w: (max{50994 + x3, 50996 + x2, 50995 + x1})
  s(x1)		w: (x1)
  #a__U31(x1,x2)		w: (max{63209 + x2, 17209 + x1})
  #a__head(x1)		w: (82695 + x1)
  #a__natsFrom(x1)		w: (8)
  isPLNat(x1)		w: (7141 + x1)
  #a__snd(x1)		w: (34352 + x1)
  a__afterNth(x1,x2)		w: (max{86503 + x2, 86503 + x1})
  U91(x1,x2)		w: (max{52954 + x2, 52954 + x1})
  a__U82(x1,x2)		w: (max{83851 + x2, x1})
  take(x1,x2)		w: (max{110633 + x2, 110632 + x1})
  U71(x1,x2)		w: (max{38479 + x2, 38479 + x1})
  and(x1,x2)		w: (max{x2, 12826 + x1})
  U101(x1,x2,x3)		w: (max{110633 + x3, 75123 + x2, 75124 + x1})
  pair(x1,x2)		w: (max{35511 + x2, 48337 + x1})
  fst(x1)		w: (26784 + x1)
  natsFrom(x1)		w: (35514 + x1)
  a__snd(x1)		w: (2656 + x1)
  #a__U51(x1,x2,x3)		w: (max{169199 + x3, 169199 + x2, 0})
  splitAt(x1,x2)		w: (max{48337 + x2, 48339 + x1})
  #a__U11(x1,x2,x3)		w: (max{82692 + x3, 98180 + x2, 72834 + x1})
  a__U31(x1,x2)		w: (max{35511 + x2, 16021 + x1})
  a__U51(x1,x2,x3)		w: (max{122013 + x3, 131873 + x2, 122014 + x1})
  a__U81(x1,x2,x3,x4)		w: (max{48337 + x4, 83851 + x3, 48339 + x2, 12831 + x1})
  #a__take(x1,x2)		w: (0)
  isNatural(x1)		w: (22682 + x1)
  a__U41(x1,x2)		w: (max{35514 + x2, 0})
  #a__U21(x1,x2)		w: (max{48701 + x2, 0})
  #a__U81(x1,x2,x3,x4)		w: (max{60017 + x4, 95531 + x3, 95525 + x2, 24508 + x1})
  #a__U61(x1,x2)		w: (max{60002 + x2, 60004 + x1})
  a__fst(x1)		w: (26784 + x1)
  tail(x1)		w: (88462 + x1)
  a__natsFrom(x1)		w: (35514 + x1)
  #mark(x1)		w: (47187 + x1)
  0()		w: (48337)
  #a__and(x1,x2)		w: (max{47187 + x2, 60012 + x1})
  a__isLNat(x1)		w: (9858 + x1)
  a__U21(x1,x2)		w: (max{1515 + x2, 1515 + x1})
  a__U91(x1,x2)		w: (max{52954 + x2, 52954 + x1})
  sel(x1,x2)		w: (max{131872 + x2, 157522 + x1})
  afterNth(x1,x2)		w: (max{86503 + x2, 86503 + x1})
  nil()		w: (61161)
  a__splitAt(x1,x2)		w: (max{48337 + x2, 48339 + x1})
  isLNat(x1)		w: (9858 + x1)
  #a__sel(x1,x2)		w: (max{169200 + x2, 179060 + x1})
  mark(x1)		w: (x1)
  #a__isLNat(x1)		w: (57045 + x1)
  #a__U101(x1,x2,x3)		w: (0)
  a__U11(x1,x2,x3)		w: (max{50994 + x3, 50996 + x2, 50995 + x1})
  a__sel(x1,x2)		w: (max{131872 + x2, 157522 + x1})
  a__isPLNat(x1)		w: (7141 + x1)
  U61(x1,x2)		w: (max{12816 + x2, 12818 + x1})
  U31(x1,x2)		w: (max{35511 + x2, 16021 + x1})
  a__U71(x1,x2)		w: (max{38479 + x2, 38479 + x1})
  #a__isPLNat(x1)		w: (34358 + x1)
  head(x1)		w: (35510 + x1)
  #a__afterNth(x1,x2)		w: (max{82693 + x2, 133689 + x1})
  #a__splitAt(x1,x2)		w: (max{60017 + x2, 95525 + x1})
  cons(x1,x2)		w: (max{x2, 35514 + x1})
  a__U61(x1,x2)		w: (max{12816 + x2, 12818 + x1})
  snd(x1)		w: (2656 + x1)
  a__take(x1,x2)		w: (max{110633 + x2, 110632 + x1})
  U81(x1,x2,x3,x4)		w: (max{48337 + x4, 83851 + x3, 48339 + x2, 12831 + x1})
  #a__U41(x1,x2)		w: (0)
  U82(x1,x2)		w: (max{83851 + x2, x1})
  tt()		w: (71019)
  a__isNatural(x1)		w: (22682 + x1)
  #a__isNatural(x1)		w: (7)
  #a__fst(x1)		w: (73970 + x1)
  U51(x1,x2,x3)		w: (max{122013 + x3, 131873 + x2, 122014 + x1})
  a__and(x1,x2)		w: (max{x2, 12826 + x1})
  a__tail(x1)		w: (88462 + x1)
  U41(x1,x2)		w: (max{35514 + x2, 0})
  #a__tail(x1)		w: (12)
  a__U101(x1,x2,x3)		w: (max{110633 + x3, 75123 + x2, 75124 + x1})
  #a__U91(x1,x2)		w: (0)
  a__head(x1)		w: (35510 + x1)
    USABLE RULES: { 1..90 }
    Removed DPs: #1 #2 #4..7 #12..17 #20 #21 #24 #26 #29..32 #34 #39..42 #44 #47 #49 #54 #55 #57 #58 #61..63 #67 #69 #70 #73 #74 #76 #78..82 #86 #87 #90 #94 #96 #97 #99..102 #108 #109 #115 #116 #118 #120..122
Number of SCCs: 2, DPs: 8
	SCC { #45 #89 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... succeeded.
  U21(x1,x2)	4[]	w: (max{1 + x2, 2 + x1})
  #a__U82(x1,x2)	0[]	w: (x2)
  #a__U71(x1,x2)	0[x2,x1]	w: (1 + x2 + x1)
  U11(x1,x2,x3)	13[]	w: (max{35 + x3, 16 + x2, 19 + x1})
  s(x1)	11[x1]	w: (x1)
  #a__U31(x1,x2)	0[]	w: (x1)
  #a__head(x1)	0[]	w: (1)
  #a__natsFrom(x1)	0[]	w: (x1)
  isPLNat(x1)	8[x1]	w: (9 + x1)
  #a__snd(x1)	0[]	w: (1)
  a__afterNth(x1,x2)	14[]	w: (max{44 + x2, 36 + x1})
  U91(x1,x2)	9[]	w: (max{1 + x2, 0})
  a__U82(x1,x2)	11[]	w: (max{17 + x2, x1})
  take(x1,x2)	13[x2,x1]	w: (38 + x2 + x1)
  U71(x1,x2)	12[]	w: (max{28 + x2, 0})
  and(x1,x2)	x2	w: (max{x2, 0})
  U101(x1,x2,x3)	13[]	w: (max{37 + x3, 29 + x2, 0})
  pair(x1,x2)	1[x2]	w: (max{8 + x2, 5 + x1})
  fst(x1)	9[x1]	w: (7 + x1)
  natsFrom(x1)	7[]	w: (10 + x1)
  a__snd(x1)	8[]	w: (5 + x1)
  #a__U51(x1,x2,x3)	0[]	w: (x1)
  splitAt(x1,x2)	12[]	w: (max{29 + x2, 10 + x1})
  #a__U11(x1,x2,x3)	0[x1,x3]	w: (1 + x3 + x1)
  a__U31(x1,x2)	0[x1]	w: (max{10 + x2, x1})
  a__U51(x1,x2,x3)	1[x2]	w: (max{51 + x3, 43 + x2, 51 + x1})
  a__U81(x1,x2,x3,x4)	12[]	w: (max{29 + x4, 28 + x3, 10 + x2, 0})
  #a__take(x1,x2)	0[x1]	w: (1 + x2 + x1)
  isNatural(x1)	x1	w: (x1)
  a__U41(x1,x2)	6[]	w: (max{10 + x2, 7 + x1})
  #a__U21(x1,x2)	0[x2]	w: (x2 + x1)
  #a__U81(x1,x2,x3,x4)	12[x2,x3]	w: (max{6 + x4, 7 + x3, 17 + x2, 0})
  #a__U61(x1,x2)	0[x2,x1]	w: (1 + x2 + x1)
  a__fst(x1)	9[x1]	w: (7 + x1)
  tail(x1)	9[x1]	w: (2 + x1)
  a__natsFrom(x1)	7[]	w: (10 + x1)
  #mark(x1)	0[]	w: (x1)
  0()	12	w: (17)
  #a__and(x1,x2)	0[x2,x1]	w: (max{1 + x2, 1 + x1})
  a__isLNat(x1)	4[]	w: (5 + x1)
  a__U21(x1,x2)	4[]	w: (max{1 + x2, 2 + x1})
  a__U91(x1,x2)	9[]	w: (max{1 + x2, 0})
  sel(x1,x2)	5[x1,x2]	w: (57 + x2 + x1)
  afterNth(x1,x2)	14[]	w: (max{44 + x2, 36 + x1})
  nil()	4	w: (17)
  a__splitAt(x1,x2)	12[]	w: (max{29 + x2, 10 + x1})
  isLNat(x1)	4[]	w: (5 + x1)
  #a__sel(x1,x2)	0[]	w: (1)
  mark(x1)	x1	w: (x1)
  #a__isLNat(x1)	0[]	w: (1)
  #a__U101(x1,x2,x3)	0[x1]	w: (max{0, x1})
  a__U11(x1,x2,x3)	13[]	w: (max{35 + x3, 16 + x2, 19 + x1})
  a__sel(x1,x2)	5[x1,x2]	w: (57 + x2 + x1)
  a__isPLNat(x1)	8[x1]	w: (9 + x1)
  U61(x1,x2)	3[]	w: (max{9 + x2, 0})
  U31(x1,x2)	0[x1]	w: (max{10 + x2, x1})
  a__U71(x1,x2)	12[]	w: (max{28 + x2, 0})
  #a__isPLNat(x1)	0[]	w: (x1)
  head(x1)	1[x1]	w: (6 + x1)
  #a__afterNth(x1,x2)	0[x2,x1]	w: (1 + x2 + x1)
  #a__splitAt(x1,x2)	12[x1]	w: (max{6 + x2, 17 + x1})
  cons(x1,x2)	5[]	w: (max{x2, 9 + x1})
  a__U61(x1,x2)	3[]	w: (max{9 + x2, 0})
  snd(x1)	8[]	w: (5 + x1)
  a__take(x1,x2)	13[x2,x1]	w: (38 + x2 + x1)
  U81(x1,x2,x3,x4)	12[]	w: (max{29 + x4, 28 + x3, 10 + x2, 0})
  #a__U41(x1,x2)	0[x1]	w: (1 + x1)
  U82(x1,x2)	11[]	w: (max{17 + x2, x1})
  tt()	10	w: (16)
  a__isNatural(x1)	x1	w: (x1)
  #a__isNatural(x1)	0[]	w: (1)
  #a__fst(x1)	0[]	w: (x1)
  U51(x1,x2,x3)	1[x2]	w: (max{51 + x3, 43 + x2, 51 + x1})
  a__and(x1,x2)	x2	w: (max{x2, 0})
  a__tail(x1)	9[x1]	w: (2 + x1)
  U41(x1,x2)	6[]	w: (max{10 + x2, 7 + x1})
  #a__tail(x1)	0[]	w: (x1)
  a__U101(x1,x2,x3)	13[]	w: (max{37 + x3, 29 + x2, 0})
  #a__U91(x1,x2)	0[]	w: (1)
  a__head(x1)	1[x1]	w: (6 + x1)
    USABLE RULES: { 1..90 }
    Removed DPs: #45 #89
Number of SCCs: 1, DPs: 6
	SCC { #43 #60 #68 #103 #114 #123 }
Sum... succeeded.
  U21(x1,x2)		w: (59029 + x1)
  #a__U82(x1,x2)		w: (18246)
  #a__U71(x1,x2)		w: (18247)
  U11(x1,x2,x3)		w: (26008 + x1)
  s(x1)		w: (1 + x1)
  #a__U31(x1,x2)		w: (18246)
  #a__head(x1)		w: (18247)
  #a__natsFrom(x1)		w: (0)
  isPLNat(x1)		w: (1)
  #a__snd(x1)		w: (18247)
  a__afterNth(x1,x2)		w: (1 + x1)
  U91(x1,x2)		w: (59025 + x1)
  a__U82(x1,x2)		w: (59028 + x2)
  take(x1,x2)		w: (59027)
  U71(x1,x2)		w: (59028 + x1)
  and(x1,x2)		w: (2 + x2 + x1)
  U101(x1,x2,x3)		w: (59028 + x1)
  pair(x1,x2)		w: (59029)
  fst(x1)		w: (59029 + x1)
  natsFrom(x1)		w: (59027 + x1)
  a__snd(x1)		w: (40180)
  #a__U51(x1,x2,x3)		w: (18247)
  splitAt(x1,x2)		w: (59027)
  #a__U11(x1,x2,x3)		w: (18247)
  a__U31(x1,x2)		w: (59024)
  a__U51(x1,x2,x3)		w: (59027 + x3 + x2)
  a__U81(x1,x2,x3,x4)		w: (59027 + x3 + x2)
  #a__take(x1,x2)		w: (0)
  isNatural(x1)		w: (59027)
  a__U41(x1,x2)		w: (59027 + x2)
  #a__U21(x1,x2)		w: (18247)
  #a__U81(x1,x2,x3,x4)		w: (18247)
  #a__U61(x1,x2)		w: (18247)
  a__fst(x1)		w: (59028)
  tail(x1)		w: (2)
  a__natsFrom(x1)		w: (59026)
  #mark(x1)		w: (2 + x1)
  0()		w: (59026)
  #a__and(x1,x2)		w: (3 + x2)
  a__isLNat(x1)		w: (90086)
  a__U21(x1,x2)		w: (59028 + x1)
  a__U91(x1,x2)		w: (59024)
  sel(x1,x2)		w: (59027 + x2)
  afterNth(x1,x2)		w: (11)
  nil()		w: (59026)
  a__splitAt(x1,x2)		w: (59026)
  isLNat(x1)		w: (90087 + x1)
  #a__sel(x1,x2)		w: (18247)
  mark(x1)		w: (59025)
  #a__isLNat(x1)		w: (90088 + x1)
  #a__U101(x1,x2,x3)		w: (0)
  a__U11(x1,x2,x3)		w: (26007 + x2)
  a__sel(x1,x2)		w: (59026)
  a__isPLNat(x1)		w: (0)
  U61(x1,x2)		w: (59025 + x2)
  U31(x1,x2)		w: (59025 + x1)
  a__U71(x1,x2)		w: (59027)
  #a__isPLNat(x1)		w: (18247)
  head(x1)		w: (3)
  #a__afterNth(x1,x2)		w: (18247)
  #a__splitAt(x1,x2)		w: (18246)
  cons(x1,x2)		w: (59021 + x2)
  a__U61(x1,x2)		w: (59024)
  snd(x1)		w: (40181)
  a__take(x1,x2)		w: (59026)
  U81(x1,x2,x3,x4)		w: (59028 + x4)
  #a__U41(x1,x2)		w: (1)
  U82(x1,x2)		w: (59029 + x1)
  tt()		w: (90087)
  a__isNatural(x1)		w: (59026)
  #a__isNatural(x1)		w: (0)
  #a__fst(x1)		w: (18247)
  U51(x1,x2,x3)		w: (59028 + x1)
  a__and(x1,x2)		w: (1)
  a__tail(x1)		w: (1 + x1)
  U41(x1,x2)		w: (59028 + x1)
  #a__tail(x1)		w: (0)
  a__U101(x1,x2,x3)		w: (59027 + x3)
  #a__U91(x1,x2)		w: (1)
  a__head(x1)		w: (2 + x1)
    USABLE RULES: { }
    Removed DPs: #43 #60 #68 #103 #114 #123
Number of SCCs: 0, DPs: 0