/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__natsFrom(N) -> cons(mark(N),natsFrom(s(N)))
    2: a__fst(pair(XS,YS)) -> mark(XS)
    3: a__snd(pair(XS,YS)) -> mark(YS)
    4: a__splitAt(0(),XS) -> pair(nil(),mark(XS))
    5: a__splitAt(s(N),cons(X,XS)) -> a__u(a__splitAt(mark(N),mark(XS)),N,X,XS)
    6: a__u(pair(YS,ZS),N,X,XS) -> pair(cons(mark(X),YS),mark(ZS))
    7: a__head(cons(N,XS)) -> mark(N)
    8: a__tail(cons(N,XS)) -> mark(XS)
    9: a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
    10: a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
    11: a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
    12: mark(natsFrom(X)) -> a__natsFrom(mark(X))
    13: mark(fst(X)) -> a__fst(mark(X))
    14: mark(snd(X)) -> a__snd(mark(X))
    15: mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
    16: mark(u(X1,X2,X3,X4)) -> a__u(mark(X1),X2,X3,X4)
    17: mark(head(X)) -> a__head(mark(X))
    18: mark(tail(X)) -> a__tail(mark(X))
    19: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    20: mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
    21: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    22: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    23: mark(s(X)) -> s(mark(X))
    24: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    25: mark(0()) -> 0()
    26: mark(nil()) -> nil()
    27: a__natsFrom(X) -> natsFrom(X)
    28: a__fst(X) -> fst(X)
    29: a__snd(X) -> snd(X)
    30: a__splitAt(X1,X2) -> splitAt(X1,X2)
    31: a__u(X1,X2,X3,X4) -> u(X1,X2,X3,X4)
    32: a__head(X) -> head(X)
    33: a__tail(X) -> tail(X)
    34: a__sel(X1,X2) -> sel(X1,X2)
    35: a__afterNth(X1,X2) -> afterNth(X1,X2)
    36: a__take(X1,X2) -> take(X1,X2)
Number of strict rules: 36
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__fst(pair(XS,YS)) -> #mark(XS)
   #2: #a__u(pair(YS,ZS),N,X,XS) -> #mark(X)
   #3: #a__u(pair(YS,ZS),N,X,XS) -> #mark(ZS)
   #4: #mark(fst(X)) -> #a__fst(mark(X))
   #5: #mark(fst(X)) -> #mark(X)
   #6: #a__sel(N,XS) -> #a__head(a__afterNth(mark(N),mark(XS)))
   #7: #a__sel(N,XS) -> #a__afterNth(mark(N),mark(XS))
   #8: #a__sel(N,XS) -> #mark(N)
   #9: #a__sel(N,XS) -> #mark(XS)
   #10: #a__afterNth(N,XS) -> #a__snd(a__splitAt(mark(N),mark(XS)))
   #11: #a__afterNth(N,XS) -> #a__splitAt(mark(N),mark(XS))
   #12: #a__afterNth(N,XS) -> #mark(N)
   #13: #a__afterNth(N,XS) -> #mark(XS)
   #14: #mark(pair(X1,X2)) -> #mark(X1)
   #15: #mark(pair(X1,X2)) -> #mark(X2)
   #16: #mark(s(X)) -> #mark(X)
   #17: #mark(natsFrom(X)) -> #a__natsFrom(mark(X))
   #18: #mark(natsFrom(X)) -> #mark(X)
   #19: #mark(snd(X)) -> #a__snd(mark(X))
   #20: #mark(snd(X)) -> #mark(X)
   #21: #mark(afterNth(X1,X2)) -> #a__afterNth(mark(X1),mark(X2))
   #22: #mark(afterNth(X1,X2)) -> #mark(X1)
   #23: #mark(afterNth(X1,X2)) -> #mark(X2)
   #24: #a__head(cons(N,XS)) -> #mark(N)
   #25: #a__take(N,XS) -> #a__fst(a__splitAt(mark(N),mark(XS)))
   #26: #a__take(N,XS) -> #a__splitAt(mark(N),mark(XS))
   #27: #a__take(N,XS) -> #mark(N)
   #28: #a__take(N,XS) -> #mark(XS)
   #29: #a__splitAt(s(N),cons(X,XS)) -> #a__u(a__splitAt(mark(N),mark(XS)),N,X,XS)
   #30: #a__splitAt(s(N),cons(X,XS)) -> #a__splitAt(mark(N),mark(XS))
   #31: #a__splitAt(s(N),cons(X,XS)) -> #mark(N)
   #32: #a__splitAt(s(N),cons(X,XS)) -> #mark(XS)
   #33: #mark(cons(X1,X2)) -> #mark(X1)
   #34: #mark(head(X)) -> #a__head(mark(X))
   #35: #mark(head(X)) -> #mark(X)
   #36: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #37: #mark(sel(X1,X2)) -> #mark(X1)
   #38: #mark(sel(X1,X2)) -> #mark(X2)
   #39: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #40: #mark(take(X1,X2)) -> #mark(X1)
   #41: #mark(take(X1,X2)) -> #mark(X2)
   #42: #mark(u(X1,X2,X3,X4)) -> #a__u(mark(X1),X2,X3,X4)
   #43: #mark(u(X1,X2,X3,X4)) -> #mark(X1)
   #44: #a__snd(pair(XS,YS)) -> #mark(YS)
   #45: #a__natsFrom(N) -> #mark(N)
   #46: #a__tail(cons(N,XS)) -> #mark(XS)
   #47: #mark(splitAt(X1,X2)) -> #a__splitAt(mark(X1),mark(X2))
   #48: #mark(splitAt(X1,X2)) -> #mark(X1)
   #49: #mark(splitAt(X1,X2)) -> #mark(X2)
   #50: #a__splitAt(0(),XS) -> #mark(XS)
   #51: #mark(tail(X)) -> #a__tail(mark(X))
   #52: #mark(tail(X)) -> #mark(X)
Number of SCCs: 1, DPs: 52
	SCC { #1..52 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__head(x1)		w: (16912 + x1)
  #a__natsFrom(x1)		w: (40527 + x1)
  #a__snd(x1)		w: (40525 + x1)
  a__afterNth(x1,x2)		w: (max{64139 + x2, 64138 + x1})
  u(x1,x2,x3,x4)		w: (max{1 + x4, 23617 + x3, x2, x1})
  take(x1,x2)		w: (max{40526 + x2, 40528 + x1})
  pair(x1,x2)		w: (max{40525 + x2, 2 + x1})
  fst(x1)		w: (1 + x1)
  natsFrom(x1)		w: (23615 + x1)
  a__snd(x1)		w: (23614 + x1)
  splitAt(x1,x2)		w: (max{40525 + x2, x1})
  #a__take(x1,x2)		w: (max{81051 + x2, 81053 + x1})
  a__natsFrom(x1)		w: (23615 + x1)
  a__fst(x1)		w: (1 + x1)
  tail(x1)		w: (21239 + x1)
  #mark(x1)		w: (40526 + x1)
  0()		w: (28068)
  a__u(x1,x2,x3,x4)		w: (max{1 + x4, 23617 + x3, x2, x1})
  sel(x1,x2)		w: (max{64141 + x2, 64140 + x1})
  afterNth(x1,x2)		w: (max{64139 + x2, 64138 + x1})
  nil()		w: (162)
  a__splitAt(x1,x2)		w: (max{40525 + x2, x1})
  #a__sel(x1,x2)		w: (max{81051 + x2, 81052 + x1})
  mark(x1)		w: (x1)
  a__sel(x1,x2)		w: (max{64141 + x2, 64140 + x1})
  head(x1)		w: (1 + x1)
  #a__afterNth(x1,x2)		w: (max{81051 + x2, 81052 + x1})
  #a__splitAt(x1,x2)		w: (max{40526 + x2, 40526 + x1})
  cons(x1,x2)		w: (max{x2, 23615 + x1})
  snd(x1)		w: (23614 + x1)
  #a__u(x1,x2,x3,x4)		w: (max{40525 + x4, 64140 + x3, 0, 1 + x1})
  a__take(x1,x2)		w: (max{40526 + x2, 40528 + x1})
  #a__fst(x1)		w: (40525 + x1)
  a__tail(x1)		w: (21239 + x1)
  #a__tail(x1)		w: (40527 + x1)
  a__head(x1)		w: (1 + x1)
    USABLE RULES: { 1..36 }
    Removed DPs: #1 #2 #4 #5 #8..15 #17..28 #33..42 #44..46 #49 #51 #52
Number of SCCs: 1, DPs: 10
	SCC { #3 #16 #29..32 #43 #47 #48 #50 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__head(x1)		w: (16912 + x1)
  #a__natsFrom(x1)		w: (40527 + x1)
  #a__snd(x1)		w: (40525 + x1)
  a__afterNth(x1,x2)		w: (max{12217 + x2, 12213 + x1})
  u(x1,x2,x3,x4)		w: (max{1 + x4, 3 + x3, x2, x1})
  take(x1,x2)		w: (max{5 + x2, 40528 + x1})
  pair(x1,x2)		w: (max{4 + x2, 2 + x1})
  fst(x1)		w: (1 + x1)
  natsFrom(x1)		w: (20585 + x1)
  a__snd(x1)		w: (12213 + x1)
  splitAt(x1,x2)		w: (max{4 + x2, x1})
  #a__take(x1,x2)		w: (max{81051 + x2, 81053 + x1})
  a__natsFrom(x1)		w: (20585 + x1)
  a__fst(x1)		w: (1 + x1)
  tail(x1)		w: (31112 + x1)
  #mark(x1)		w: (2 + x1)
  0()		w: (3)
  a__u(x1,x2,x3,x4)		w: (max{1 + x4, 3 + x3, x2, x1})
  sel(x1,x2)		w: (max{19797 + x2, 19796 + x1})
  afterNth(x1,x2)		w: (max{12217 + x2, 12213 + x1})
  nil()		w: (1)
  a__splitAt(x1,x2)		w: (max{4 + x2, x1})
  #a__sel(x1,x2)		w: (max{81051 + x2, 81052 + x1})
  mark(x1)		w: (x1)
  a__sel(x1,x2)		w: (max{19797 + x2, 19796 + x1})
  head(x1)		w: (7579 + x1)
  #a__afterNth(x1,x2)		w: (max{81051 + x2, 81052 + x1})
  #a__splitAt(x1,x2)		w: (max{6 + x2, 2 + x1})
  cons(x1,x2)		w: (max{x2, 1 + x1})
  snd(x1)		w: (12213 + x1)
  #a__u(x1,x2,x3,x4)		w: (max{5 + x4, 1 + x3, 0, 2 + x1})
  a__take(x1,x2)		w: (max{5 + x2, 40528 + x1})
  #a__fst(x1)		w: (40525 + x1)
  a__tail(x1)		w: (31112 + x1)
  #a__tail(x1)		w: (40527 + x1)
  a__head(x1)		w: (7579 + x1)
    USABLE RULES: { 1..36 }
    Removed DPs: #3 #32 #50
Number of SCCs: 1, DPs: 6
	SCC { #16 #30 #31 #43 #47 #48 }
Sum... Max... succeeded.
  s(x1)		w: (x1)
  #a__head(x1)		w: (16912)
  #a__natsFrom(x1)		w: (40527)
  #a__snd(x1)		w: (40525)
  a__afterNth(x1,x2)		w: (max{16746 + x2, 12652 + x1})
  u(x1,x2,x3,x4)		w: (max{3 + x4, 2993 + x3, 0, x1})
  take(x1,x2)		w: (max{18194 + x2, 18195 + x1})
  pair(x1,x2)		w: (max{4096 + x2, 626 + x1})
  fst(x1)		w: (14098 + x1)
  natsFrom(x1)		w: (20585 + x1)
  a__snd(x1)		w: (12650 + x1)
  splitAt(x1,x2)		w: (max{4096 + x2, 2 + x1})
  #a__take(x1,x2)		w: (0)
  a__natsFrom(x1)		w: (20585 + x1)
  a__fst(x1)		w: (14098 + x1)
  tail(x1)		w: (46425 + x1)
  #mark(x1)		w: (x1)
  0()		w: (4060)
  a__u(x1,x2,x3,x4)		w: (max{3 + x4, 2993 + x3, 0, x1})
  sel(x1,x2)		w: (max{19797 + x2, 18113 + x1})
  afterNth(x1,x2)		w: (max{16746 + x2, 12652 + x1})
  nil()		w: (72)
  a__splitAt(x1,x2)		w: (max{4096 + x2, 2 + x1})
  #a__sel(x1,x2)		w: (0)
  mark(x1)		w: (x1)
  a__sel(x1,x2)		w: (max{19797 + x2, 18113 + x1})
  head(x1)		w: (1367 + x1)
  #a__afterNth(x1,x2)		w: (0)
  #a__splitAt(x1,x2)		w: (max{0, 1 + x1})
  cons(x1,x2)		w: (max{x2, 1 + x1})
  snd(x1)		w: (12650 + x1)
  #a__u(x1,x2,x3,x4)		w: (0)
  a__take(x1,x2)		w: (max{18194 + x2, 18195 + x1})
  #a__fst(x1)		w: (40525)
  a__tail(x1)		w: (46425 + x1)
  #a__tail(x1)		w: (40527)
  a__head(x1)		w: (1367 + x1)
    USABLE RULES: { 1..36 }
    Removed DPs: #31 #47 #48
Number of SCCs: 2, DPs: 3
	SCC { #30 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 3 + x1})
  #a__head(x1)		w: (0)
  #a__natsFrom(x1)		w: (0)
  #a__snd(x1)		w: (0)
  a__afterNth(x1,x2)		w: (max{0, 3 + x2 + x1})
  u(x1,x2,x3,x4)		w: (max{0, 4 + x3, 1 + x2, x1})
  take(x1,x2)		w: (max{0, 3 + x2 + x1})
  pair(x1,x2)		w: (max{0, 21660 + x2, 2 + x1})
  fst(x1)		w: (max{0, 1 + x1})
  natsFrom(x1)		w: (max{0, 4 + x1})
  a__snd(x1)		w: (max{0, 1 + x1})
  splitAt(x1,x2)		w: (max{0, 2 + x2 + x1})
  #a__take(x1,x2)		w: (0)
  a__natsFrom(x1)		w: (max{0, 4 + x1})
  a__fst(x1)		w: (max{0, 1 + x1})
  tail(x1)		w: (max{0, 31895 + x1})
  #mark(x1)		w: (0)
  0()		w: (21658)
  a__u(x1,x2,x3,x4)		w: (max{0, 4 + x3, 1 + x2, x1})
  sel(x1,x2)		w: (max{0, 4 + x2 + x1})
  afterNth(x1,x2)		w: (max{0, 3 + x2 + x1})
  nil()		w: (1)
  a__splitAt(x1,x2)		w: (max{0, 2 + x2 + x1})
  #a__sel(x1,x2)		w: (0)
  mark(x1)		w: (max{0, x1})
  a__sel(x1,x2)		w: (max{0, 4 + x2 + x1})
  head(x1)		w: (max{0, 1 + x1})
  #a__afterNth(x1,x2)		w: (0)
  #a__splitAt(x1,x2)		w: (max{0, 25907 + x1})
  cons(x1,x2)		w: (max{0, -3 + x2, 2 + x1})
  snd(x1)		w: (max{0, 1 + x1})
  #a__u(x1,x2,x3,x4)		w: (0)
  a__take(x1,x2)		w: (max{0, 3 + x2 + x1})
  #a__fst(x1)		w: (0)
  a__tail(x1)		w: (max{0, 31895 + x1})
  #a__tail(x1)		w: (0)
  a__head(x1)		w: (max{0, 1 + x1})
    USABLE RULES: { 1..36 }
    Removed DPs: #30
Number of SCCs: 1, DPs: 2
	SCC { #16 #43 }
Sum... succeeded.
  s(x1)		w: (15047 + x1)
  #a__head(x1)		w: (2)
  #a__natsFrom(x1)		w: (2)
  #a__snd(x1)		w: (1)
  a__afterNth(x1,x2)		w: (4)
  u(x1,x2,x3,x4)		w: (9 + x1)
  take(x1,x2)		w: (2)
  pair(x1,x2)		w: (1 + x2 + x1)
  fst(x1)		w: (5)
  natsFrom(x1)		w: (6)
  a__snd(x1)		w: (1 + x1)
  splitAt(x1,x2)		w: (2 + x1)
  #a__take(x1,x2)		w: (2)
  a__natsFrom(x1)		w: (5)
  a__fst(x1)		w: (4)
  tail(x1)		w: (1)
  #mark(x1)		w: (x1)
  0()		w: (4)
  a__u(x1,x2,x3,x4)		w: (8 + x4 + x3 + x2)
  sel(x1,x2)		w: (5 + x2)
  afterNth(x1,x2)		w: (5)
  nil()		w: (4)
  a__splitAt(x1,x2)		w: (1 + x2)
  #a__sel(x1,x2)		w: (3)
  mark(x1)		w: (3)
  a__sel(x1,x2)		w: (4)
  head(x1)		w: (3583)
  #a__afterNth(x1,x2)		w: (2)
  #a__splitAt(x1,x2)		w: (0)
  cons(x1,x2)		w: (6)
  snd(x1)		w: (2)
  #a__u(x1,x2,x3,x4)		w: (1)
  a__take(x1,x2)		w: (1 + x2 + x1)
  #a__fst(x1)		w: (0)
  a__tail(x1)		w: (0)
  #a__tail(x1)		w: (2)
  a__head(x1)		w: (3582 + x1)
    USABLE RULES: { }
    Removed DPs: #16 #43
Number of SCCs: 0, DPs: 0