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 Order(PosReal,>,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, edges: 1000
	SCC { #1..52 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
   |0|()	weight: (/ 1 32)
     s(x1)	weight: x1
#a__head(x1)	weight: (/ 3 32) + x1
#a__natsFrom(x1)	weight: (/ 7 32) + x1
#a__snd(x1)	weight: (/ 1 4) + x1
a__afterNth(x1,x2)	weight: max{(/ 1 2) + x2, (/ 9 16) + x1}
     u(x1,x2,x3,x4)	weight: max{(/ 11 32) + x4, (/ 5 16) + x3, (/ 5 16) + x2, x1}
  take(x1,x2)	weight: max{(/ 3 8) + x2, (/ 7 16) + x1}
  pair(x1,x2)	weight: max{(/ 9 32) + x2, (/ 1 8) + x1}
   fst(x1)	weight: (/ 1 32) + x1
natsFrom(x1)	weight: (/ 3 16) + x1
a__snd(x1)	weight: (/ 1 8) + x1
splitAt(x1,x2)	weight: max{(/ 11 32) + x2, (/ 13 32) + x1}
#a__take(x1,x2)	weight: max{(/ 17 32) + x2, (/ 19 32) + x1}
a__natsFrom(x1)	weight: (/ 3 16) + x1
a__fst(x1)	weight: (/ 1 32) + x1
  tail(x1)	weight: (/ 1 16) + x1
#mark(x1)	weight: (/ 3 16) + x1
  a__u(x1,x2,x3,x4)	weight: max{(/ 11 32) + x4, (/ 5 16) + x3, (/ 5 16) + x2, x1}
   sel(x1,x2)	weight: max{(/ 9 16) + x2, (/ 19 32) + x1}
afterNth(x1,x2)	weight: max{(/ 1 2) + x2, (/ 9 16) + x1}
   nil()	weight: (/ 1 4)
a__splitAt(x1,x2)	weight: max{(/ 11 32) + x2, (/ 13 32) + x1}
#a__sel(x1,x2)	weight: max{(/ 5 8) + x2, (/ 11 16) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 9 16) + x2, (/ 19 32) + x1}
  head(x1)	weight: (/ 1 32) + x1
#a__afterNth(x1,x2)	weight: max{(/ 19 32) + x2, (/ 21 32) + x1}
#a__splitAt(x1,x2)	weight: max{(/ 13 32) + x2, (/ 9 16) + x1}
  cons(x1,x2)	weight: max{x2, (/ 3 16) + x1}
   snd(x1)	weight: (/ 1 8) + x1
#a__u(x1,x2,x3,x4)	weight: max{0, (/ 7 32) + x3, (/ 1 32) + x1}
a__take(x1,x2)	weight: max{(/ 3 8) + x2, (/ 7 16) + x1}
#a__fst(x1)	weight: (/ 3 32) + x1
a__tail(x1)	weight: (/ 1 16) + x1
#a__tail(x1)	weight: (/ 7 32) + x1
a__head(x1)	weight: (/ 1 32) + x1
    Usable rules: { 1..36 }
    Removed DPs: #1..9 #11..15 #17..29 #31..42 #44..52
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #30 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
   |0|()	weight: (/ 1 16)
     s(x1)	weight: max{0, (/ 3 16) + x1}
#a__head(x1)	weight: 0
#a__natsFrom(x1)	weight: 0
#a__snd(x1)	weight: 0
a__afterNth(x1,x2)	weight: max{0, (/ 5 16) + x2 + x1}
     u(x1,x2,x3,x4)	weight: max{0, x1, (/ 1 16) + x3}
  take(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
  pair(x1,x2)	weight: max{0, x1, (- (/ 1 8)) + x2}
   fst(x1)	weight: max{0, (/ 1 16) + x1}
natsFrom(x1)	weight: max{0, (/ 1 4) + x1}
a__snd(x1)	weight: max{0, (/ 1 8) + x1}
splitAt(x1,x2)	weight: max{0, (/ 3 16) + x2 + x1}
#a__take(x1,x2)	weight: 0
a__natsFrom(x1)	weight: max{0, (/ 1 4) + x1}
a__fst(x1)	weight: max{0, (/ 1 16) + x1}
  tail(x1)	weight: max{0, (/ 3 16) + x1}
#mark(x1)	weight: 0
  a__u(x1,x2,x3,x4)	weight: max{0, x1, (/ 1 16) + x3}
   sel(x1,x2)	weight: max{0, (/ 1 2) + x2 + x1}
afterNth(x1,x2)	weight: max{0, (/ 5 16) + x2 + x1}
   nil()	weight: 0
a__splitAt(x1,x2)	weight: max{0, (/ 3 16) + x2 + x1}
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: max{0, x1}
a__sel(x1,x2)	weight: max{0, (/ 1 2) + x2 + x1}
  head(x1)	weight: max{0, (/ 3 16) + x1}
#a__afterNth(x1,x2)	weight: 0
#a__splitAt(x1,x2)	weight: max{0, (- (/ 1 16)) + x1}
  cons(x1,x2)	weight: max{0, (- (/ 1 8)) + x1, (- (/ 3 16)) + x2}
   snd(x1)	weight: max{0, (/ 1 8) + x1}
#a__u(x1,x2,x3,x4)	weight: 0
a__take(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
#a__fst(x1)	weight: 0
a__tail(x1)	weight: max{0, (/ 3 16) + x1}
#a__tail(x1)	weight: 0
a__head(x1)	weight: max{0, (/ 3 16) + x1}
    Usable rules: { 1..36 }
    Removed DPs: #30
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #16 #43 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     s(x1)	weight: (/ 1 8) + x1
#a__head(x1)	weight: 0
#a__natsFrom(x1)	weight: 0
#a__snd(x1)	weight: 0
a__afterNth(x1,x2)	weight: (/ 1 8)
     u(x1,x2,x3,x4)	weight: (/ 3 4) + x1
  take(x1,x2)	weight: (/ 1 4)
  pair(x1,x2)	weight: (/ 3 4)
   fst(x1)	weight: (/ 3 8) + x1
natsFrom(x1)	weight: (/ 5 8)
a__snd(x1)	weight: (/ 1 4)
splitAt(x1,x2)	weight: (/ 5 8) + x1
#a__take(x1,x2)	weight: 0
a__natsFrom(x1)	weight: (/ 1 2)
a__fst(x1)	weight: (/ 1 4)
  tail(x1)	weight: (/ 1 4)
#mark(x1)	weight: x1
  a__u(x1,x2,x3,x4)	weight: (/ 5 8) + x2 + x3 + x4
   sel(x1,x2)	weight: (/ 5 8) + x2
afterNth(x1,x2)	weight: (/ 1 4)
   nil()	weight: 0
a__splitAt(x1,x2)	weight: (/ 1 2)
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: (/ 3 8)
a__sel(x1,x2)	weight: (/ 1 2)
  head(x1)	weight: (/ 3 4) + x1
#a__afterNth(x1,x2)	weight: 0
#a__splitAt(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 5 8)
   snd(x1)	weight: (/ 3 8) + x1
#a__u(x1,x2,x3,x4)	weight: 0
a__take(x1,x2)	weight: (/ 1 8) + x2
#a__fst(x1)	weight: 0
a__tail(x1)	weight: (/ 1 8) + x1
#a__tail(x1)	weight: 0
a__head(x1)	weight: (/ 5 8)
    Usable rules: { }
    Removed DPs: #16 #43
Number of SCCs: 0, DPs: 0, edges: 0
YES