/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__U11(tt(),N,X,XS) -> a__U12(a__splitAt(mark(N),mark(XS)),X)
    2: a__U12(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
    3: a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
    4: a__and(tt(),X) -> mark(X)
    5: a__fst(pair(X,Y)) -> mark(X)
    6: a__head(cons(N,XS)) -> mark(N)
    7: a__natsFrom(N) -> cons(mark(N),natsFrom(s(N)))
    8: a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
    9: a__snd(pair(X,Y)) -> mark(Y)
    10: a__splitAt(0(),XS) -> pair(nil(),mark(XS))
    11: a__splitAt(s(N),cons(X,XS)) -> a__U11(tt(),N,X,XS)
    12: a__tail(cons(N,XS)) -> mark(XS)
    13: a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
    14: mark(U11(X1,X2,X3,X4)) -> a__U11(mark(X1),X2,X3,X4)
    15: mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
    16: mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
    17: mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
    18: mark(snd(X)) -> a__snd(mark(X))
    19: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    20: mark(fst(X)) -> a__fst(mark(X))
    21: mark(head(X)) -> a__head(mark(X))
    22: mark(natsFrom(X)) -> a__natsFrom(mark(X))
    23: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    24: mark(tail(X)) -> a__tail(mark(X))
    25: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    26: mark(tt()) -> tt()
    27: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    28: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    29: mark(s(X)) -> s(mark(X))
    30: mark(0()) -> 0()
    31: mark(nil()) -> nil()
    32: a__U11(X1,X2,X3,X4) -> U11(X1,X2,X3,X4)
    33: a__U12(X1,X2) -> U12(X1,X2)
    34: a__splitAt(X1,X2) -> splitAt(X1,X2)
    35: a__afterNth(X1,X2) -> afterNth(X1,X2)
    36: a__snd(X) -> snd(X)
    37: a__and(X1,X2) -> and(X1,X2)
    38: a__fst(X) -> fst(X)
    39: a__head(X) -> head(X)
    40: a__natsFrom(X) -> natsFrom(X)
    41: a__sel(X1,X2) -> sel(X1,X2)
    42: a__tail(X) -> tail(X)
    43: a__take(X1,X2) -> take(X1,X2)
Number of strict rules: 43
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U12(pair(YS,ZS),X) -> #mark(X)
   #2: #a__U12(pair(YS,ZS),X) -> #mark(ZS)
   #3: #mark(s(X)) -> #mark(X)
   #4: #a__head(cons(N,XS)) -> #mark(N)
   #5: #a__take(N,XS) -> #a__fst(a__splitAt(mark(N),mark(XS)))
   #6: #a__take(N,XS) -> #a__splitAt(mark(N),mark(XS))
   #7: #a__take(N,XS) -> #mark(N)
   #8: #a__take(N,XS) -> #mark(XS)
   #9: #a__snd(pair(X,Y)) -> #mark(Y)
   #10: #a__splitAt(s(N),cons(X,XS)) -> #a__U11(tt(),N,X,XS)
   #11: #mark(tail(X)) -> #a__tail(mark(X))
   #12: #mark(tail(X)) -> #mark(X)
   #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #14: #mark(sel(X1,X2)) -> #mark(X1)
   #15: #mark(sel(X1,X2)) -> #mark(X2)
   #16: #a__tail(cons(N,XS)) -> #mark(XS)
   #17: #mark(U11(X1,X2,X3,X4)) -> #a__U11(mark(X1),X2,X3,X4)
   #18: #mark(U11(X1,X2,X3,X4)) -> #mark(X1)
   #19: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #20: #mark(take(X1,X2)) -> #mark(X1)
   #21: #mark(take(X1,X2)) -> #mark(X2)
   #22: #mark(fst(X)) -> #a__fst(mark(X))
   #23: #mark(fst(X)) -> #mark(X)
   #24: #a__natsFrom(N) -> #mark(N)
   #25: #a__splitAt(0(),XS) -> #mark(XS)
   #26: #a__fst(pair(X,Y)) -> #mark(X)
   #27: #mark(cons(X1,X2)) -> #mark(X1)
   #28: #mark(natsFrom(X)) -> #a__natsFrom(mark(X))
   #29: #mark(natsFrom(X)) -> #mark(X)
   #30: #mark(pair(X1,X2)) -> #mark(X1)
   #31: #mark(pair(X1,X2)) -> #mark(X2)
   #32: #mark(afterNth(X1,X2)) -> #a__afterNth(mark(X1),mark(X2))
   #33: #mark(afterNth(X1,X2)) -> #mark(X1)
   #34: #mark(afterNth(X1,X2)) -> #mark(X2)
   #35: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #36: #mark(and(X1,X2)) -> #mark(X1)
   #37: #mark(head(X)) -> #a__head(mark(X))
   #38: #mark(head(X)) -> #mark(X)
   #39: #mark(splitAt(X1,X2)) -> #a__splitAt(mark(X1),mark(X2))
   #40: #mark(splitAt(X1,X2)) -> #mark(X1)
   #41: #mark(splitAt(X1,X2)) -> #mark(X2)
   #42: #a__afterNth(N,XS) -> #a__snd(a__splitAt(mark(N),mark(XS)))
   #43: #a__afterNth(N,XS) -> #a__splitAt(mark(N),mark(XS))
   #44: #a__afterNth(N,XS) -> #mark(N)
   #45: #a__afterNth(N,XS) -> #mark(XS)
   #46: #a__U11(tt(),N,X,XS) -> #a__U12(a__splitAt(mark(N),mark(XS)),X)
   #47: #a__U11(tt(),N,X,XS) -> #a__splitAt(mark(N),mark(XS))
   #48: #a__U11(tt(),N,X,XS) -> #mark(N)
   #49: #a__U11(tt(),N,X,XS) -> #mark(XS)
   #50: #a__sel(N,XS) -> #a__head(a__afterNth(mark(N),mark(XS)))
   #51: #a__sel(N,XS) -> #a__afterNth(mark(N),mark(XS))
   #52: #a__sel(N,XS) -> #mark(N)
   #53: #a__sel(N,XS) -> #mark(XS)
   #54: #mark(U12(X1,X2)) -> #a__U12(mark(X1),X2)
   #55: #mark(U12(X1,X2)) -> #mark(X1)
   #56: #a__and(tt(),X) -> #mark(X)
   #57: #mark(snd(X)) -> #a__snd(mark(X))
   #58: #mark(snd(X)) -> #mark(X)
Number of SCCs: 1, DPs: 58
	SCC { #1..58 }
Sum... Max... succeeded.
  U11(x1,x2,x3,x4)		w: (max{14100 + x4, 27318 + x3, 14099 + x2, 14102 + x1})
  s(x1)		w: (x1)
  #a__head(x1)		w: (4683 + x1)
  #a__natsFrom(x1)		w: (59313 + x1)
  #a__snd(x1)		w: (17898 + x1)
  a__afterNth(x1,x2)		w: (max{27314 + x2, 27314 + x1})
  take(x1,x2)		w: (max{38873 + x2, 38875 + x1})
  and(x1,x2)		w: (max{16706 + x2, 16705 + x1})
  pair(x1,x2)		w: (max{14100 + x2, 1 + x1})
  fst(x1)		w: (24773 + x1)
  natsFrom(x1)		w: (27316 + x1)
  a__snd(x1)		w: (13214 + x1)
  splitAt(x1,x2)		w: (max{14100 + x2, 14099 + x1})
  #a__U11(x1,x2,x3,x4)		w: (max{31998 + x4, 59314 + x3, 31998 + x2, 46099 + x1})
  #a__take(x1,x2)		w: (max{46098 + x2, 70872 + x1})
  U12(x1,x2)		w: (max{27318 + x2, x1})
  #a__U12(x1,x2)		w: (max{31999 + x2, 17898 + x1})
  a__fst(x1)		w: (24773 + x1)
  a__natsFrom(x1)		w: (27316 + x1)
  tail(x1)		w: (15262 + x1)
  #mark(x1)		w: (31998 + x1)
  0()		w: (0)
  #a__and(x1,x2)		w: (max{31999 + x2, 0})
  sel(x1,x2)		w: (max{43258 + x2, 43257 + x1})
  afterNth(x1,x2)		w: (max{27314 + x2, 27314 + x1})
  nil()		w: (14098)
  a__splitAt(x1,x2)		w: (max{14100 + x2, 14099 + x1})
  #a__sel(x1,x2)		w: (max{31998 + x2, 31998 + x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3,x4)		w: (max{14100 + x4, 27318 + x3, 14099 + x2, 14102 + x1})
  a__sel(x1,x2)		w: (max{43258 + x2, 43257 + x1})
  a__U12(x1,x2)		w: (max{27318 + x2, x1})
  head(x1)		w: (15943 + x1)
  #a__afterNth(x1,x2)		w: (max{31998 + x2, 31998 + x1})
  #a__splitAt(x1,x2)		w: (max{31998 + x2, 31998 + x1})
  cons(x1,x2)		w: (max{x2, 27316 + x1})
  snd(x1)		w: (13214 + x1)
  a__take(x1,x2)		w: (max{38873 + x2, 38875 + x1})
  tt()		w: (13215)
  #a__fst(x1)		w: (31997 + x1)
  a__and(x1,x2)		w: (max{16706 + x2, 16705 + x1})
  a__tail(x1)		w: (15262 + x1)
  #a__tail(x1)		w: (31999 + x1)
  a__head(x1)		w: (15943 + x1)
    USABLE RULES: { 1..43 }
    Removed DPs: #1 #4..8 #11..24 #27..41 #50 #54 #56..58
Number of SCCs: 2, DPs: 4
	SCC { #3 #55 }
Sum... succeeded.
  U11(x1,x2,x3,x4)		w: (24394 + x1)
  s(x1)		w: (12330 + x1)
  #a__head(x1)		w: (0)
  #a__natsFrom(x1)		w: (0)
  #a__snd(x1)		w: (0)
  a__afterNth(x1,x2)		w: (1 + x2)
  take(x1,x2)		w: (22062 + x2)
  and(x1,x2)		w: (11654 + x1)
  pair(x1,x2)		w: (24395)
  fst(x1)		w: (2 + x1)
  natsFrom(x1)		w: (7181 + x1)
  a__snd(x1)		w: (2)
  splitAt(x1,x2)		w: (24393)
  #a__U11(x1,x2,x3,x4)		w: (0)
  #a__take(x1,x2)		w: (0)
  U12(x1,x2)		w: (24395 + x2 + x1)
  #a__U12(x1,x2)		w: (0)
  a__fst(x1)		w: (1 + x1)
  a__natsFrom(x1)		w: (4)
  tail(x1)		w: (2)
  #mark(x1)		w: (x1)
  0()		w: (4)
  #a__and(x1,x2)		w: (0)
  sel(x1,x2)		w: (2)
  afterNth(x1,x2)		w: (2)
  nil()		w: (4)
  a__splitAt(x1,x2)		w: (24392)
  #a__sel(x1,x2)		w: (0)
  mark(x1)		w: (3)
  a__U11(x1,x2,x3,x4)		w: (24393 + x4 + x3 + x2)
  a__sel(x1,x2)		w: (1 + x2)
  a__U12(x1,x2)		w: (24394)
  head(x1)		w: (2)
  #a__afterNth(x1,x2)		w: (0)
  #a__splitAt(x1,x2)		w: (0)
  cons(x1,x2)		w: (1 + x2 + x1)
  snd(x1)		w: (3)
  a__take(x1,x2)		w: (22061)
  tt()		w: (4)
  #a__fst(x1)		w: (0)
  a__and(x1,x2)		w: (11653 + x2)
  a__tail(x1)		w: (1 + x1)
  #a__tail(x1)		w: (0)
  a__head(x1)		w: (1 + x1)
    USABLE RULES: { }
    Removed DPs: #3 #55
Number of SCCs: 1, DPs: 2
	SCC { #10 #47 }
Sum... Max... QLPOpS... NegMaxSum... QWPOpSMaxSum... succeeded.
  U11(x1,x2,x3,x4)	1[x1,x4,x3]	w: (max{49907 + x4, 44348 + x3, 0, 49908 + x1})
  s(x1)	2[x1]	w: (x1)
  #a__head(x1)	0[]	w: (x1)
  #a__natsFrom(x1)	0[]	w: (x1)
  #a__snd(x1)	0[]	w: (1)
  a__afterNth(x1,x2)	3[x2]	w: (49908 + x2)
  take(x1,x2)	3[]	w: (49908 + x2)
  and(x1,x2)	3[x2]	w: (1 + x2)
  pair(x1,x2)	0[x1]	w: (max{14683 + x2, 14684 + x1})
  fst(x1)	3[]	w: (x1)
  natsFrom(x1)	2[x1]	w: (14964 + x1)
  a__snd(x1)	x1	w: (x1)
  splitAt(x1,x2)	1[x2]	w: (max{49907 + x2, 0})
  #a__U11(x1,x2,x3,x4)	2[x2]	w: (max{0, x2})
  #a__take(x1,x2)	0[x1]	w: (x1)
  U12(x1,x2)	1[]	w: (max{39730 + x2, x1})
  #a__U12(x1,x2)	0[x2]	w: (max{1 + x2, 0})
  a__fst(x1)	3[]	w: (x1)
  a__natsFrom(x1)	2[x1]	w: (14964 + x1)
  tail(x1)	3[]	w: (8946 + x1)
  #mark(x1)	0[]	w: (1)
  0()	4	w: (14684)
  #a__and(x1,x2)	0[x1,x2]	w: (1 + x2 + x1)
  sel(x1,x2)	4[x1,x2]	w: (52907 + x2 + x1)
  afterNth(x1,x2)	3[x2]	w: (49908 + x2)
  nil()	3	w: (14685)
  a__splitAt(x1,x2)	1[x2]	w: (max{49907 + x2, 0})
  #a__sel(x1,x2)	0[x2]	w: (x2)
  mark(x1)	x1	w: (x1)
  a__U11(x1,x2,x3,x4)	1[x1,x4,x3]	w: (max{49907 + x4, 44348 + x3, 0, 49908 + x1})
  a__sel(x1,x2)	4[x1,x2]	w: (52907 + x2 + x1)
  a__U12(x1,x2)	1[]	w: (max{39730 + x2, x1})
  head(x1)	3[]	w: (2998 + x1)
  #a__afterNth(x1,x2)	0[x2,x1]	w: (1 + x2 + x1)
  #a__splitAt(x1,x2)	x1	w: (max{0, x1})
  cons(x1,x2)	2[]	w: (max{x2, 14682 + x1})
  snd(x1)	x1	w: (x1)
  a__take(x1,x2)	3[]	w: (49908 + x2)
  tt()	4	w: (14681)
  #a__fst(x1)	0[]	w: (1)
  a__and(x1,x2)	3[x2]	w: (1 + x2)
  a__tail(x1)	3[]	w: (8946 + x1)
  #a__tail(x1)	0[]	w: (1)
  a__head(x1)	3[]	w: (2998 + x1)
    USABLE RULES: { 1..43 }
    Removed DPs: #47
Number of SCCs: 0, DPs: 0