Input TRS:
    1: a__and(tt(),T) -> mark(T)
    2: a__isNatIList(IL) -> a__isNatList(IL)
    3: a__isNat(0()) -> tt()
    4: a__isNat(s(N)) -> a__isNat(N)
    5: a__isNat(length(L)) -> a__isNatList(L)
    6: a__isNatIList(zeros()) -> tt()
    7: a__isNatIList(cons(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    8: a__isNatList(nil()) -> tt()
    9: a__isNatList(cons(N,L)) -> a__and(a__isNat(N),a__isNatList(L))
    10: a__isNatList(take(N,IL)) -> a__and(a__isNat(N),a__isNatIList(IL))
    11: a__zeros() -> cons(0(),zeros())
    12: a__take(0(),IL) -> a__uTake1(a__isNatIList(IL))
    13: a__uTake1(tt()) -> nil()
    14: a__take(s(M),cons(N,IL)) -> a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
    15: a__uTake2(tt(),M,N,IL) -> cons(mark(N),take(M,IL))
    16: a__length(cons(N,L)) -> a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
    17: a__uLength(tt(),L) -> s(a__length(mark(L)))
    18: mark(and(X1,X2)) -> a__and(mark(X1),mark(X2))
    19: mark(isNatIList(X)) -> a__isNatIList(X)
    20: mark(isNatList(X)) -> a__isNatList(X)
    21: mark(isNat(X)) -> a__isNat(X)
    22: mark(length(X)) -> a__length(mark(X))
    23: mark(zeros()) -> a__zeros()
    24: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    25: mark(uTake1(X)) -> a__uTake1(mark(X))
    26: mark(uTake2(X1,X2,X3,X4)) -> a__uTake2(mark(X1),X2,X3,X4)
    27: mark(uLength(X1,X2)) -> a__uLength(mark(X1),X2)
    28: mark(tt()) -> tt()
    29: mark(0()) -> 0()
    30: mark(s(X)) -> s(mark(X))
    31: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    32: mark(nil()) -> nil()
    33: a__and(X1,X2) -> and(X1,X2)
    34: a__isNatIList(X) -> isNatIList(X)
    35: a__isNatList(X) -> isNatList(X)
    36: a__isNat(X) -> isNat(X)
    37: a__length(X) -> length(X)
    38: a__zeros() -> zeros()
    39: a__take(X1,X2) -> take(X1,X2)
    40: a__uTake1(X) -> uTake1(X)
    41: a__uTake2(X1,X2,X3,X4) -> uTake2(X1,X2,X3,X4)
    42: a__uLength(X1,X2) -> uLength(X1,X2)
Number of strict rules: 42
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__isNatIList(IL) -> #a__isNatList(IL)
   #2: #a__isNatList(cons(N,L)) -> #a__and(a__isNat(N),a__isNatList(L))
   #3: #a__isNatList(cons(N,L)) -> #a__isNat(N)
   #4: #a__isNatList(cons(N,L)) -> #a__isNatList(L)
   #5: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #6: #mark(take(X1,X2)) -> #mark(X1)
   #7: #mark(take(X1,X2)) -> #mark(X2)
   #8: #mark(zeros()) -> #a__zeros()
   #9: #a__take(0(),IL) -> #a__uTake1(a__isNatIList(IL))
   #10: #a__take(0(),IL) -> #a__isNatIList(IL)
   #11: #mark(cons(X1,X2)) -> #mark(X1)
   #12: #a__take(s(M),cons(N,IL)) -> #a__uTake2(a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL))),M,N,IL)
   #13: #a__take(s(M),cons(N,IL)) -> #a__and(a__isNat(M),a__and(a__isNat(N),a__isNatIList(IL)))
   #14: #a__take(s(M),cons(N,IL)) -> #a__isNat(M)
   #15: #a__take(s(M),cons(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #16: #a__take(s(M),cons(N,IL)) -> #a__isNat(N)
   #17: #a__take(s(M),cons(N,IL)) -> #a__isNatIList(IL)
   #18: #mark(s(X)) -> #mark(X)
   #19: #mark(uTake1(X)) -> #a__uTake1(mark(X))
   #20: #mark(uTake1(X)) -> #mark(X)
   #21: #mark(isNatList(X)) -> #a__isNatList(X)
   #22: #a__isNatIList(cons(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #23: #a__isNatIList(cons(N,IL)) -> #a__isNat(N)
   #24: #a__isNatIList(cons(N,IL)) -> #a__isNatIList(IL)
   #25: #a__isNatList(take(N,IL)) -> #a__and(a__isNat(N),a__isNatIList(IL))
   #26: #a__isNatList(take(N,IL)) -> #a__isNat(N)
   #27: #a__isNatList(take(N,IL)) -> #a__isNatIList(IL)
   #28: #a__isNat(length(L)) -> #a__isNatList(L)
   #29: #mark(length(X)) -> #a__length(mark(X))
   #30: #mark(length(X)) -> #mark(X)
   #31: #mark(uLength(X1,X2)) -> #a__uLength(mark(X1),X2)
   #32: #mark(uLength(X1,X2)) -> #mark(X1)
   #33: #a__uLength(tt(),L) -> #a__length(mark(L))
   #34: #a__uLength(tt(),L) -> #mark(L)
   #35: #mark(isNatIList(X)) -> #a__isNatIList(X)
   #36: #mark(uTake2(X1,X2,X3,X4)) -> #a__uTake2(mark(X1),X2,X3,X4)
   #37: #mark(uTake2(X1,X2,X3,X4)) -> #mark(X1)
   #38: #mark(isNat(X)) -> #a__isNat(X)
   #39: #a__length(cons(N,L)) -> #a__uLength(a__and(a__isNat(N),a__isNatList(L)),L)
   #40: #a__length(cons(N,L)) -> #a__and(a__isNat(N),a__isNatList(L))
   #41: #a__length(cons(N,L)) -> #a__isNat(N)
   #42: #a__length(cons(N,L)) -> #a__isNatList(L)
   #43: #a__and(tt(),T) -> #mark(T)
   #44: #a__uTake2(tt(),M,N,IL) -> #mark(N)
   #45: #a__isNat(s(N)) -> #a__isNat(N)
   #46: #mark(and(X1,X2)) -> #a__and(mark(X1),mark(X2))
   #47: #mark(and(X1,X2)) -> #mark(X1)
   #48: #mark(and(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 45, edges: 328
	SCC { #1..7 #10..18 #20..48 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__uLength(x1,x2)	weight: x2
#a__uTake2(x1,x2,x3,x4)	weight: (/ 1 4) + x3 + x4
isNatList(x1)	weight: 0
     s(x1)	weight: x1
a__isNatIList(x1)	weight: 0
#a__isNat(x1)	weight: 0
  take(x1,x2)	weight: (/ 3 4) + x1 + x2
   and(x1,x2)	weight: x1 + x2
isNatIList(x1)	weight: 0
 zeros()	weight: 0
#a__take(x1,x2)	weight: (/ 1 2) + x2
uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x1 + x2 + x3 + x4
a__isNatList(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
uLength(x1,x2)	weight: x1 + x2
#mark(x1)	weight: x1
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x1 + x2 + x3 + x4
#a__and(x1,x2)	weight: x2
#a__zeros()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
#a__length(x1)	weight: x1
 isNat(x1)	weight: 0
a__uLength(x1,x2)	weight: x1 + x2
a__uTake1(x1)	weight: (/ 1 4) + x1
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: x1 + x2
a__take(x1,x2)	weight: (/ 3 4) + x1 + x2
    tt()	weight: 0
uTake1(x1)	weight: (/ 1 4) + x1
a__isNat(x1)	weight: 0
a__and(x1,x2)	weight: x1 + x2
length(x1)	weight: x1
a__zeros()	weight: 0
a__length(x1)	weight: x1
    Usable rules: { 1..42 }
    Removed DPs: #5..7 #10 #12..17 #20 #36 #37 #44
Number of SCCs: 1, DPs: 31, edges: 167
	SCC { #1..4 #11 #18 #21..35 #38..43 #45..48 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__uLength(x1,x2)	weight: (/ 1 4) + x2
#a__uTake2(x1,x2,x3,x4)	weight: (/ 1 4)
isNatList(x1)	weight: 0
     s(x1)	weight: x1
a__isNatIList(x1)	weight: 0
#a__isNat(x1)	weight: 0
  take(x1,x2)	weight: (/ 1 4) + x2
   and(x1,x2)	weight: x1 + x2
isNatIList(x1)	weight: 0
 zeros()	weight: 0
#a__take(x1,x2)	weight: (/ 1 2)
uTake2(x1,x2,x3,x4)	weight: (/ 1 4) + x1 + x3 + x4
a__isNatList(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
uLength(x1,x2)	weight: (/ 1 2) + x1 + x2
#mark(x1)	weight: x1
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: (/ 1 4) + x1 + x3 + x4
#a__and(x1,x2)	weight: x2
#a__zeros()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
#a__length(x1)	weight: (/ 1 4) + x1
 isNat(x1)	weight: 0
a__uLength(x1,x2)	weight: (/ 1 2) + x1 + x2
a__uTake1(x1)	weight: (/ 1 4) + x1
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: x1 + x2
a__take(x1,x2)	weight: (/ 1 4) + x2
    tt()	weight: 0
uTake1(x1)	weight: (/ 1 4) + x1
a__isNat(x1)	weight: 0
a__and(x1,x2)	weight: x1 + x2
length(x1)	weight: (/ 1 2) + x1
a__zeros()	weight: 0
a__length(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..42 }
    Removed DPs: #29..32 #34 #40..42
Number of SCCs: 2, DPs: 23, edges: 92
	SCC { #33 #39 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
#a__uLength(x1,x2)	weight: x2_1 + x2_2 + x1_2; 0
#a__uTake2(x1,x2,x3,x4)	weight: 0; 0
isNatList(x1)	weight: (/ 1 4); x1_2
     s(x1)	weight: (/ 1 2) + x1_1; x1_2
a__isNatIList(x1)	weight: (/ 1 4); (/ 1 2) + x1_2
#a__isNat(x1)	weight: 0; 0
  take(x1,x2)	weight: (/ 1 4) + x2_1 + x1_1; (/ 1 2) + x2_2
   and(x1,x2)	weight: x2_1; x2_2
isNatIList(x1)	weight: (/ 1 4); (/ 1 2) + x1_2
 zeros()	weight: 0; 0
#a__take(x1,x2)	weight: 0; 0
uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x4_1 + x4_2 + x2_1; (/ 1 2) + x4_2
a__isNatList(x1)	weight: (/ 1 4); x1_2
#a__isNatIList(x1)	weight: 0; 0
uLength(x1,x2)	weight: (/ 1 4) + x2_1 + x1_1 + x1_2; (/ 1 4) + x2_2
#mark(x1)	weight: 0; 0
#a__uTake1(x1)	weight: 0; 0
     0()	weight: (/ 1 4); (/ 1 4)
a__uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x4_1 + x4_2 + x2_1; (/ 1 2) + x4_2
#a__and(x1,x2)	weight: 0; 0
#a__zeros()	weight: 0; 0
   nil()	weight: 0; (/ 1 2)
  mark(x1)	weight: x1_1; x1_2
#a__length(x1)	weight: (/ 1 4) + x1_1 + x1_2; 0
 isNat(x1)	weight: x1_1; (/ 1 4) + x1_2
a__uLength(x1,x2)	weight: (/ 1 4) + x2_1 + x1_1 + x1_2; (/ 1 4) + x2_2
a__uTake1(x1)	weight: (/ 1 4); (/ 1 4) + x1_1
#a__isNatList(x1)	weight: 0; 0
  cons(x1,x2)	weight: x2_1 + x2_2; x2_2
a__take(x1,x2)	weight: (/ 1 4) + x2_1 + x1_1; (/ 1 2) + x2_2
    tt()	weight: (/ 1 4); (/ 1 2)
uTake1(x1)	weight: (/ 1 4); (/ 1 4) + x1_1
a__isNat(x1)	weight: x1_1; (/ 1 4) + x1_2
a__and(x1,x2)	weight: x2_1; x2_2
length(x1)	weight: (/ 1 2) + x1_1; (/ 1 4) + x1_2
a__zeros()	weight: 0; 0
a__length(x1)	weight: (/ 1 2) + x1_1; (/ 1 4) + x1_2
    Usable rules: { 1..42 }
    Removed DPs: #33 #39
Number of SCCs: 1, DPs: 21, edges: 90
	SCC { #1..4 #11 #18 #21..28 #35 #38 #43 #45..48 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__uLength(x1,x2)	weight: (/ 1 4)
#a__uTake2(x1,x2,x3,x4)	weight: (/ 1 4)
isNatList(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: x1
a__isNatIList(x1)	weight: (/ 1 2) + x1
#a__isNat(x1)	weight: x1
  take(x1,x2)	weight: (/ 3 4) + x1 + x2
   and(x1,x2)	weight: x1 + x2
isNatIList(x1)	weight: (/ 1 2) + x1
 zeros()	weight: 0
#a__take(x1,x2)	weight: (/ 1 2)
uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x2 + x3 + x4
a__isNatList(x1)	weight: (/ 1 4) + x1
#a__isNatIList(x1)	weight: (/ 3 4) + x1
uLength(x1,x2)	weight: (/ 3 4) + x2
#mark(x1)	weight: (/ 1 4) + x1
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: (/ 3 4) + x2 + x3 + x4
#a__and(x1,x2)	weight: (/ 1 4) + x2
#a__zeros()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: x1
#a__length(x1)	weight: (/ 1 4)
 isNat(x1)	weight: x1
a__uLength(x1,x2)	weight: (/ 3 4) + x2
a__uTake1(x1)	weight: (/ 1 4) + x1
#a__isNatList(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: x1 + x2
a__take(x1,x2)	weight: (/ 3 4) + x1 + x2
    tt()	weight: 0
uTake1(x1)	weight: (/ 1 4) + x1
a__isNat(x1)	weight: x1
a__and(x1,x2)	weight: x1 + x2
length(x1)	weight: (/ 3 4) + x1
a__zeros()	weight: 0
a__length(x1)	weight: (/ 3 4) + x1
    Usable rules: { 1..42 }
    Removed DPs: #1 #3 #23 #25..28 #38
Number of SCCs: 2, DPs: 13, edges: 47
	SCC { #45 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__uLength(x1,x2)	weight: (/ 1 16)
#a__uTake2(x1,x2,x3,x4)	weight: (/ 1 16)
isNatList(x1)	weight: (/ 1 8)
     s(x1)	weight: (/ 1 16) + x1
a__isNatIList(x1)	weight: (/ 5 16) + x1
#a__isNat(x1)	weight: x1
  take(x1,x2)	weight: (/ 1 16) + x1 + x2
   and(x1,x2)	weight: (/ 1 4)
isNatIList(x1)	weight: (/ 3 8)
 zeros()	weight: 0
#a__take(x1,x2)	weight: (/ 1 8)
uTake2(x1,x2,x3,x4)	weight: (/ 7 16) + x1 + x2 + x4
a__isNatList(x1)	weight: (/ 1 16) + x1
#a__isNatIList(x1)	weight: (/ 3 16)
uLength(x1,x2)	weight: (/ 3 8)
#mark(x1)	weight: (/ 1 16)
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: (/ 3 8)
#a__and(x1,x2)	weight: (/ 1 16)
#a__zeros()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 4)
#a__length(x1)	weight: (/ 1 16)
 isNat(x1)	weight: (/ 3 8)
a__uLength(x1,x2)	weight: (/ 5 16)
a__uTake1(x1)	weight: (/ 1 16) + x1
#a__isNatList(x1)	weight: (/ 1 8)
  cons(x1,x2)	weight: (/ 1 16)
a__take(x1,x2)	weight: (/ 5 16)
    tt()	weight: 0
uTake1(x1)	weight: (/ 1 8) + x1
a__isNat(x1)	weight: (/ 5 16) + x1
a__and(x1,x2)	weight: (/ 3 16)
length(x1)	weight: (/ 1 8)
a__zeros()	weight: 0
a__length(x1)	weight: (/ 1 16) + x1
    Usable rules: { }
    Removed DPs: #45
Number of SCCs: 1, DPs: 12, edges: 46
	SCC { #2 #4 #11 #18 #21 #22 #24 #35 #43 #46..48 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#a__uLength(x1,x2)	weight: 0
#a__uTake2(x1,x2,x3,x4)	weight: 0
isNatList(x1)	weight: (/ 1 16) + x1
     s(x1)	weight: x1
a__isNatIList(x1)	weight: (/ 1 16) + x1
#a__isNat(x1)	weight: 0
  take(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
   and(x1,x2)	weight: max{x2, (/ 1 16) + x1}
isNatIList(x1)	weight: (/ 1 16) + x1
 zeros()	weight: (/ 3 8)
#a__take(x1,x2)	weight: 0
uTake2(x1,x2,x3,x4)	weight: max{(/ 1 4) + x4, (/ 5 16) + x3, (/ 1 8) + x2, x1}
a__isNatList(x1)	weight: (/ 1 16) + x1
#a__isNatIList(x1)	weight: (/ 1 8) + x1
uLength(x1,x2)	weight: max{0, (/ 1 16) + x2}
#mark(x1)	weight: (/ 1 16) + x1
#a__uTake1(x1)	weight: 0
     0()	weight: (/ 1 16)
a__uTake2(x1,x2,x3,x4)	weight: max{(/ 1 4) + x4, (/ 5 16) + x3, (/ 1 8) + x2, x1}
#a__and(x1,x2)	weight: max{0, (/ 1 16) + x2}
#a__zeros()	weight: 0
   nil()	weight: (/ 1 16)
  mark(x1)	weight: x1
#a__length(x1)	weight: 0
 isNat(x1)	weight: (/ 1 16) + x1
a__uLength(x1,x2)	weight: max{0, (/ 1 16) + x2}
a__uTake1(x1)	weight: (/ 1 4)
#a__isNatList(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{x2, (/ 5 16) + x1}
a__take(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
    tt()	weight: (/ 1 8)
uTake1(x1)	weight: (/ 1 4)
a__isNat(x1)	weight: (/ 1 16) + x1
a__and(x1,x2)	weight: max{x2, (/ 1 16) + x1}
length(x1)	weight: (/ 1 16) + x1
a__zeros()	weight: (/ 3 8)
a__length(x1)	weight: (/ 1 16) + x1
    Usable rules: { 1..42 }
    Removed DPs: #11 #47
Number of SCCs: 1, DPs: 10, edges: 26
	SCC { #2 #4 #18 #21 #22 #24 #35 #43 #46 #48 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#a__uLength(x1,x2)	weight: 0
#a__uTake2(x1,x2,x3,x4)	weight: 0
isNatList(x1)	weight: (/ 1 16) + x1
     s(x1)	weight: x1
a__isNatIList(x1)	weight: (/ 1 16) + x1
#a__isNat(x1)	weight: 0
  take(x1,x2)	weight: max{0, (/ 5 16) + x2}
   and(x1,x2)	weight: max{0, (/ 1 8) + x2}
isNatIList(x1)	weight: (/ 1 16) + x1
 zeros()	weight: (/ 1 4)
#a__take(x1,x2)	weight: 0
uTake2(x1,x2,x3,x4)	weight: max{0, (/ 5 16) + x4, (/ 1 2) + x3, (/ 1 8) + x1}
a__isNatList(x1)	weight: (/ 1 16) + x1
#a__isNatIList(x1)	weight: (/ 1 16) + x1
uLength(x1,x2)	weight: max{0, (/ 1 16) + x2}
#mark(x1)	weight: (/ 1 16) + x1
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: max{0, (/ 7 16) + x4, (/ 1 2) + x3, (/ 1 8) + x1}
#a__and(x1,x2)	weight: max{0, (/ 1 16) + x2}
#a__zeros()	weight: 0
   nil()	weight: (/ 1 16)
  mark(x1)	weight: (/ 1 8) + x1
#a__length(x1)	weight: 0
 isNat(x1)	weight: x1
a__uLength(x1,x2)	weight: max{0, (/ 1 8) + x2}
a__uTake1(x1)	weight: (/ 1 16)
#a__isNatList(x1)	weight: (/ 1 16) + x1
  cons(x1,x2)	weight: max{(/ 1 8) + x2, (/ 3 8) + x1}
a__take(x1,x2)	weight: max{0, (/ 5 16) + x2}
    tt()	weight: 0
uTake1(x1)	weight: 0
a__isNat(x1)	weight: (/ 1 8) + x1
a__and(x1,x2)	weight: max{0, (/ 1 8) + x2}
length(x1)	weight: x1
a__zeros()	weight: (/ 3 8)
a__length(x1)	weight: x1
    Usable rules: { 1..42 }
    Removed DPs: #2 #4 #21 #22 #24 #35 #48
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #18 #43 #46 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#a__uLength(x1,x2)	weight: max{0, x1}	status: []	precedence above:
#a__uTake2(x1,x2,x3,x4)	weight: x2 + x1	status: [x2,x1]	precedence above:
isNatList(x1)	weight: (/ 1 4) + x1	status: [x1]	precedence above: take and zeros uTake2 a__isNatList #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__and a__zeros
     s(x1)	weight: x1	status: x1
a__isNatIList(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: isNatList take and isNatIList zeros uTake2 a__isNatList #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__and a__zeros
#a__isNat(x1)	weight: x1	status: []	precedence above:
  take(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 2) + x1}	status: []	precedence above:
   and(x1,x2)	weight: max{x2, x1}	status: [x2,x1]	precedence above: take zeros uTake2 #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__and a__zeros
isNatIList(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: isNatList a__isNatIList take and zeros uTake2 a__isNatList #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__and a__zeros
 zeros()	weight: (/ 1 2)	status: []	precedence above: cons tt
#a__take(x1,x2)	weight: x2 + x1	status: [x2]	precedence above:
uTake2(x1,x2,x3,x4)	weight: max{(/ 1 2) + x4, (/ 1 2) + x3, (/ 1 2) + x2, x1}	status: []	precedence above:
a__isNatList(x1)	weight: (/ 1 4) + x1	status: [x1]	precedence above: isNatList take and zeros uTake2 #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__and a__zeros
#a__isNatIList(x1)	weight: x1	status: []	precedence above:
uLength(x1,x2)	weight: max{0, x2}	status: []	precedence above: s a__uLength length a__length
#mark(x1)	weight: x1	status: [x1]	precedence above: #a__and
#a__uTake1(x1)	weight: 0	status: []	precedence above:
     0()	weight: 0	status: []	precedence above: cons tt
a__uTake2(x1,x2,x3,x4)	weight: max{(/ 1 2) + x4, (/ 1 2) + x3, (/ 1 2) + x2, x1}	status: []	precedence above: take uTake2 cons
#a__and(x1,x2)	weight: max{0, x2}	status: [x2]	precedence above: #mark
#a__zeros()	weight: 0	status: []	precedence above:
   nil()	weight: (/ 1 4)	status: []	precedence above: cons tt
  mark(x1)	weight: x1	status: [x1]	precedence above: take and zeros uTake2 #mark 0 a__uTake2 #a__and nil a__uTake1 cons a__take tt uTake1 a__and a__zeros
#a__length(x1)	weight: 0	status: []	precedence above:
 isNat(x1)	weight: (/ 1 4) + x1	status: []	precedence above: isNatList take and zeros uTake2 a__isNatList #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__isNat a__and a__zeros
a__uLength(x1,x2)	weight: max{0, x2}	status: []	precedence above: s uLength length a__length
a__uTake1(x1)	weight: (/ 1 4)	status: []	precedence above: nil cons tt uTake1
#a__isNatList(x1)	weight: x1	status: []	precedence above:
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}	status: [x2]	precedence above:
a__take(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 2) + x1}	status: []	precedence above: take uTake2 a__uTake2 nil a__uTake1 cons tt uTake1
    tt()	weight: (/ 1 4)	status: []	precedence above: cons
uTake1(x1)	weight: (/ 1 4)	status: []	precedence above:
a__isNat(x1)	weight: (/ 1 4) + x1	status: []	precedence above: isNatList take and zeros uTake2 a__isNatList #mark 0 a__uTake2 #a__and nil mark isNat a__uTake1 cons a__take tt uTake1 a__and a__zeros
a__and(x1,x2)	weight: max{x2, x1}	status: [x2,x1]	precedence above: take and zeros uTake2 #mark 0 a__uTake2 #a__and nil mark a__uTake1 cons a__take tt uTake1 a__zeros
length(x1)	weight: x1	status: []	precedence above: s uLength a__uLength a__length
a__zeros()	weight: (/ 1 2)	status: []	precedence above: zeros 0 cons tt
a__length(x1)	weight: x1	status: []	precedence above: s uLength a__uLength length
    Usable rules: { 1..42 }
    Removed DPs: #46
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__uLength(x1,x2)	weight: (/ 1 16)
#a__uTake2(x1,x2,x3,x4)	weight: (/ 1 16)
isNatList(x1)	weight: (/ 5 16)
     s(x1)	weight: (/ 1 8) + x1
a__isNatIList(x1)	weight: (/ 3 16)
#a__isNat(x1)	weight: 0
  take(x1,x2)	weight: (/ 1 16) + x2
   and(x1,x2)	weight: (/ 3 8)
isNatIList(x1)	weight: (/ 1 16)
 zeros()	weight: 0
#a__take(x1,x2)	weight: (/ 1 8)
uTake2(x1,x2,x3,x4)	weight: (/ 1 16) + x2
a__isNatList(x1)	weight: (/ 1 4)
#a__isNatIList(x1)	weight: (/ 1 16)
uLength(x1,x2)	weight: (/ 5 16) + x1 + x2
#mark(x1)	weight: (/ 1 16) + x1
#a__uTake1(x1)	weight: 0
     0()	weight: 0
a__uTake2(x1,x2,x3,x4)	weight: x1 + x2
#a__and(x1,x2)	weight: (/ 1 16)
#a__zeros()	weight: 0
   nil()	weight: 0
  mark(x1)	weight: (/ 1 16) + x1
#a__length(x1)	weight: (/ 1 16)
 isNat(x1)	weight: (/ 1 8) + x1
a__uLength(x1,x2)	weight: (/ 1 4)
a__uTake1(x1)	weight: (/ 1 4)
#a__isNatList(x1)	weight: (/ 1 16)
  cons(x1,x2)	weight: (/ 1 16) + x1
a__take(x1,x2)	weight: (/ 3 16)
    tt()	weight: 0
uTake1(x1)	weight: (/ 5 16) + x1
a__isNat(x1)	weight: (/ 1 16) + x1
a__and(x1,x2)	weight: (/ 5 16)
length(x1)	weight: (/ 1 16) + x1
a__zeros()	weight: 0
a__length(x1)	weight: (/ 3 16)
    Usable rules: { }
    Removed DPs: #18
Number of SCCs: 0, DPs: 0, edges: 0
YES