Input TRS:
    1: active(zeros()) -> mark(cons(0(),zeros()))
    2: active(and(tt(),X)) -> mark(X)
    3: active(length(nil())) -> mark(0())
    4: active(length(cons(N,L))) -> mark(s(length(L)))
    5: active(take(0(),IL)) -> mark(nil())
    6: active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
    7: mark(zeros()) -> active(zeros())
    8: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    9: mark(0()) -> active(0())
    10: mark(and(X1,X2)) -> active(and(mark(X1),X2))
    11: mark(tt()) -> active(tt())
    12: mark(length(X)) -> active(length(mark(X)))
    13: mark(nil()) -> active(nil())
    14: mark(s(X)) -> active(s(mark(X)))
    15: mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
    16: cons(mark(X1),X2) -> cons(X1,X2)
    17: cons(X1,mark(X2)) -> cons(X1,X2)
    18: cons(active(X1),X2) -> cons(X1,X2)
    19: cons(X1,active(X2)) -> cons(X1,X2)
    20: and(mark(X1),X2) -> and(X1,X2)
    21: and(X1,mark(X2)) -> and(X1,X2)
    22: and(active(X1),X2) -> and(X1,X2)
    23: and(X1,active(X2)) -> and(X1,X2)
    24: length(mark(X)) -> length(X)
    25: length(active(X)) -> length(X)
    26: s(mark(X)) -> s(X)
    27: s(active(X)) -> s(X)
    28: take(mark(X1),X2) -> take(X1,X2)
    29: take(X1,mark(X2)) -> take(X1,X2)
    30: take(active(X1),X2) -> take(X1,X2)
    31: take(X1,active(X2)) -> take(X1,X2)
Number of strict rules: 31
Direct Order(PosReal,>,Poly) ... removes: 3 5 2
     s(x1)	weight: x1
  take(x1,x2)	weight: (/ 195105 8) + x1 + x2
   and(x1,x2)	weight: (/ 108041 8) + x1 + x2
 zeros()	weight: 0
     0()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
active(x1)	weight: x1
  cons(x1,x2)	weight: x1 + x2
    tt()	weight: 0
length(x1)	weight: (/ 1 8) + x1
Number of strict rules: 28
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #take(X1,mark(X2)) -> #take(X1,X2)
   #2: #active(take(s(M),cons(N,IL))) -> #mark(cons(N,take(M,IL)))
   #3: #active(take(s(M),cons(N,IL))) -> #cons(N,take(M,IL))
   #4: #active(take(s(M),cons(N,IL))) -> #take(M,IL)
   #5: #mark(nil()) -> #active(nil())
   #6: #mark(0()) -> #active(0())
   #7: #mark(tt()) -> #active(tt())
   #8: #length(mark(X)) -> #length(X)
   #9: #and(X1,active(X2)) -> #and(X1,X2)
   #10: #mark(length(X)) -> #active(length(mark(X)))
   #11: #mark(length(X)) -> #length(mark(X))
   #12: #mark(length(X)) -> #mark(X)
   #13: #take(X1,active(X2)) -> #take(X1,X2)
   #14: #mark(s(X)) -> #active(s(mark(X)))
   #15: #mark(s(X)) -> #s(mark(X))
   #16: #mark(s(X)) -> #mark(X)
   #17: #take(active(X1),X2) -> #take(X1,X2)
   #18: #length(active(X)) -> #length(X)
   #19: #and(mark(X1),X2) -> #and(X1,X2)
   #20: #mark(zeros()) -> #active(zeros())
   #21: #mark(and(X1,X2)) -> #active(and(mark(X1),X2))
   #22: #mark(and(X1,X2)) -> #and(mark(X1),X2)
   #23: #mark(and(X1,X2)) -> #mark(X1)
   #24: #take(mark(X1),X2) -> #take(X1,X2)
   #25: #and(active(X1),X2) -> #and(X1,X2)
   #26: #s(active(X)) -> #s(X)
   #27: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #28: #cons(X1,active(X2)) -> #cons(X1,X2)
   #29: #s(mark(X)) -> #s(X)
   #30: #and(X1,mark(X2)) -> #and(X1,X2)
   #31: #cons(mark(X1),X2) -> #cons(X1,X2)
   #32: #active(zeros()) -> #mark(cons(0(),zeros()))
   #33: #active(zeros()) -> #cons(0(),zeros())
   #34: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #35: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #36: #mark(cons(X1,X2)) -> #mark(X1)
   #37: #mark(take(X1,X2)) -> #active(take(mark(X1),mark(X2)))
   #38: #mark(take(X1,X2)) -> #take(mark(X1),mark(X2))
   #39: #mark(take(X1,X2)) -> #mark(X1)
   #40: #mark(take(X1,X2)) -> #mark(X2)
   #41: #active(length(cons(N,L))) -> #mark(s(length(L)))
   #42: #active(length(cons(N,L))) -> #s(length(L))
   #43: #active(length(cons(N,L))) -> #length(L)
   #44: #cons(active(X1),X2) -> #cons(X1,X2)
Number of SCCs: 6, DPs: 28, edges: 116
	SCC { #26 #29 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: x1
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #26 #29
Number of SCCs: 5, DPs: 26, edges: 112
	SCC { #8 #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: x1
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8 #18
Number of SCCs: 4, DPs: 24, edges: 108
	SCC { #1 #13 #17 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x2
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #13
Number of SCCs: 4, DPs: 22, edges: 96
	SCC { #17 #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x1
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #17 #24
Number of SCCs: 3, DPs: 20, edges: 92
	SCC { #27 #28 #31 #44 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #27 #28
Number of SCCs: 4, DPs: 18, edges: 80
	SCC { #31 #44 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #31 #44
Number of SCCs: 3, DPs: 16, edges: 76
	SCC { #9 #19 #25 #30 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #9 #30
Number of SCCs: 4, DPs: 14, edges: 64
	SCC { #19 #25 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    tt()	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
 #and(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #19 #25
Number of SCCs: 3, DPs: 12, edges: 60
	SCC { #2 #10 #12 #16 #20 #23 #32 #36 #37 #39..41 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: (/ 1 2) + x1 + x2
   and(x1,x2)	weight: (/ 1 2) + x1
 zeros()	weight: 0
#mark(x1)	weight: x1
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
active(x1)	weight: x1
  cons(x1,x2)	weight: x1 + x2
#active(x1)	weight: x1
    tt()	weight: 0
length(x1)	weight: (/ 1 2) + x1
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 1 4 6..31 }
    Removed DPs: #12 #23 #39 #40
Number of SCCs: 4, DPs: 8, edges: 16
	SCC { #2 #10 #16 #20 #32 #36 #37 #41 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: (/ 1 2) + x1 + x2
   and(x1,x2)	weight: (/ 1 2) + x1
 zeros()	weight: 0
#mark(x1)	weight: x1
     0()	weight: 0
   #s(x1)	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
active(x1)	weight: x1
  cons(x1,x2)	weight: x1
#active(x1)	weight: x1
    tt()	weight: 0
length(x1)	weight: (/ 1 2)
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 1 4 6..31 }
    Removed DPs: #2
Number of SCCs: 4, DPs: 6, edges: 12
	SCC { #10 #16 #20 #32 #36 #41 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   and(x1,x2)	weight: 0
 zeros()	weight: (/ 1 2)
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
   #s(x1)	weight: 0
   nil()	weight: (/ 1 8)
  mark(x1)	weight: (/ 1 8)
active(x1)	weight: 0
  cons(x1,x2)	weight: max{0, (/ 1 8) + x1}
#active(x1)	weight: (/ 3 8)
    tt()	weight: (/ 1 8)
length(x1)	weight: (/ 3 8)
#length(x1)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 24 25 }
    Removed DPs: #20 #32 #36
Number of SCCs: 4, DPs: 3, edges: 4
	SCC { #10 #16 #41 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE