Input TRS:
    1: a__zeros() -> cons(0(),zeros())
    2: a__U11(tt()) -> tt()
    3: a__U21(tt()) -> tt()
    4: a__U31(tt()) -> tt()
    5: a__U41(tt(),V2) -> a__U42(a__isNatIList(V2))
    6: a__U42(tt()) -> tt()
    7: a__U51(tt(),V2) -> a__U52(a__isNatList(V2))
    8: a__U52(tt()) -> tt()
    9: a__U61(tt(),L,N) -> a__U62(a__isNat(N),L)
    10: a__U62(tt(),L) -> s(a__length(mark(L)))
    11: a__isNat(0()) -> tt()
    12: a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
    13: a__isNat(s(V1)) -> a__U21(a__isNat(V1))
    14: a__isNatIList(V) -> a__U31(a__isNatList(V))
    15: a__isNatIList(zeros()) -> tt()
    16: a__isNatIList(cons(V1,V2)) -> a__U41(a__isNat(V1),V2)
    17: a__isNatList(nil()) -> tt()
    18: a__isNatList(cons(V1,V2)) -> a__U51(a__isNat(V1),V2)
    19: a__length(nil()) -> 0()
    20: a__length(cons(N,L)) -> a__U61(a__isNatList(L),L,N)
    21: mark(zeros()) -> a__zeros()
    22: mark(U11(X)) -> a__U11(mark(X))
    23: mark(U21(X)) -> a__U21(mark(X))
    24: mark(U31(X)) -> a__U31(mark(X))
    25: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
    26: mark(U42(X)) -> a__U42(mark(X))
    27: mark(isNatIList(X)) -> a__isNatIList(X)
    28: mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
    29: mark(U52(X)) -> a__U52(mark(X))
    30: mark(isNatList(X)) -> a__isNatList(X)
    31: mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
    32: mark(U62(X1,X2)) -> a__U62(mark(X1),X2)
    33: mark(isNat(X)) -> a__isNat(X)
    34: mark(length(X)) -> a__length(mark(X))
    35: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    36: mark(0()) -> 0()
    37: mark(tt()) -> tt()
    38: mark(s(X)) -> s(mark(X))
    39: mark(nil()) -> nil()
    40: a__zeros() -> zeros()
    41: a__U11(X) -> U11(X)
    42: a__U21(X) -> U21(X)
    43: a__U31(X) -> U31(X)
    44: a__U41(X1,X2) -> U41(X1,X2)
    45: a__U42(X) -> U42(X)
    46: a__isNatIList(X) -> isNatIList(X)
    47: a__U51(X1,X2) -> U51(X1,X2)
    48: a__U52(X) -> U52(X)
    49: a__isNatList(X) -> isNatList(X)
    50: a__U61(X1,X2,X3) -> U61(X1,X2,X3)
    51: a__U62(X1,X2) -> U62(X1,X2)
    52: a__isNat(X) -> isNat(X)
    53: a__length(X) -> length(X)
Number of strict rules: 53
Direct Order(PosReal,>,Poly) ... removes: 4 15 19 14 12 2
   U21(x1)	weight: x1
isNatList(x1)	weight: x1
   U11(x1)	weight: (/ 1 8) + x1
     s(x1)	weight: x1
a__isNatIList(x1)	weight: (/ 1 4) + x1
   U42(x1)	weight: x1
a__U62(x1,x2)	weight: (/ 72017 4) + x1 + x2
isNatIList(x1)	weight: (/ 1 4) + x1
 zeros()	weight: 0
a__U31(x1)	weight: (/ 1 8) + x1
a__U51(x1,x2)	weight: x1 + 2 * x2
a__isNatList(x1)	weight: x1
a__U41(x1,x2)	weight: (/ 1 4) + x1 + x2
     0()	weight: 0
a__U21(x1)	weight: x1
   nil()	weight: 0
   U62(x1,x2)	weight: (/ 72017 4) + x1 + x2
  mark(x1)	weight: x1
a__U11(x1)	weight: (/ 1 8) + x1
a__U42(x1)	weight: x1
a__U52(x1)	weight: 2 * x1
 isNat(x1)	weight: x1
   U52(x1)	weight: 2 * x1
   U61(x1,x2,x3)	weight: (/ 72017 4) + x1 + x2 + 2 * x3
   U31(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: 2 * x1 + 2 * x2
a__U61(x1,x2,x3)	weight: (/ 72017 4) + x1 + x2 + 2 * x3
    tt()	weight: 0
a__isNat(x1)	weight: x1
   U51(x1,x2)	weight: x1 + 2 * x2
length(x1)	weight: (/ 72017 4) + x1
   U41(x1,x2)	weight: (/ 1 4) + x1 + x2
a__zeros()	weight: 0
a__length(x1)	weight: (/ 72017 4) + x1
Number of strict rules: 47
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(U52(X)) -> #a__U52(mark(X))
   #2: #mark(U52(X)) -> #mark(X)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #mark(s(X)) -> #mark(X)
   #5: #a__isNat(s(V1)) -> #a__U21(a__isNat(V1))
   #6: #a__isNat(s(V1)) -> #a__isNat(V1)
   #7: #a__U61(tt(),L,N) -> #a__U62(a__isNat(N),L)
   #8: #a__U61(tt(),L,N) -> #a__isNat(N)
   #9: #mark(U31(X)) -> #a__U31(mark(X))
   #10: #mark(U31(X)) -> #mark(X)
   #11: #mark(U21(X)) -> #a__U21(mark(X))
   #12: #mark(U21(X)) -> #mark(X)
   #13: #mark(U61(X1,X2,X3)) -> #a__U61(mark(X1),X2,X3)
   #14: #mark(U61(X1,X2,X3)) -> #mark(X1)
   #15: #mark(isNatList(X)) -> #a__isNatList(X)
   #16: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2)
   #17: #mark(U41(X1,X2)) -> #mark(X1)
   #18: #a__length(cons(N,L)) -> #a__U61(a__isNatList(L),L,N)
   #19: #a__length(cons(N,L)) -> #a__isNatList(L)
   #20: #a__U51(tt(),V2) -> #a__U52(a__isNatList(V2))
   #21: #a__U51(tt(),V2) -> #a__isNatList(V2)
   #22: #a__U62(tt(),L) -> #a__length(mark(L))
   #23: #a__U62(tt(),L) -> #mark(L)
   #24: #mark(isNat(X)) -> #a__isNat(X)
   #25: #a__U41(tt(),V2) -> #a__U42(a__isNatIList(V2))
   #26: #a__U41(tt(),V2) -> #a__isNatIList(V2)
   #27: #mark(U51(X1,X2)) -> #a__U51(mark(X1),X2)
   #28: #mark(U51(X1,X2)) -> #mark(X1)
   #29: #mark(U11(X)) -> #a__U11(mark(X))
   #30: #mark(U11(X)) -> #mark(X)
   #31: #mark(length(X)) -> #a__length(mark(X))
   #32: #mark(length(X)) -> #mark(X)
   #33: #mark(isNatIList(X)) -> #a__isNatIList(X)
   #34: #mark(U62(X1,X2)) -> #a__U62(mark(X1),X2)
   #35: #mark(U62(X1,X2)) -> #mark(X1)
   #36: #mark(U42(X)) -> #a__U42(mark(X))
   #37: #mark(U42(X)) -> #mark(X)
   #38: #mark(zeros()) -> #a__zeros()
   #39: #a__isNatIList(cons(V1,V2)) -> #a__U41(a__isNat(V1),V2)
   #40: #a__isNatIList(cons(V1,V2)) -> #a__isNat(V1)
   #41: #a__isNatList(cons(V1,V2)) -> #a__U51(a__isNat(V1),V2)
   #42: #a__isNatList(cons(V1,V2)) -> #a__isNat(V1)
Number of SCCs: 4, DPs: 24, edges: 208
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1)	weight: 0
isNatList(x1)	weight: 0
   U11(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#a__U31(x1)	weight: 0
a__isNatIList(x1)	weight: 0
   U42(x1)	weight: 0
#a__isNat(x1)	weight: x1
a__U62(x1,x2)	weight: 0
isNatIList(x1)	weight: 0
#a__U51(x1,x2)	weight: 0
#a__U11(x1)	weight: 0
 zeros()	weight: 0
a__U31(x1)	weight: 0
a__U51(x1,x2)	weight: 0
a__isNatList(x1)	weight: 0
#a__U62(x1,x2)	weight: 0
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: 0
#a__U21(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
#a__U61(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1)	weight: 0
   nil()	weight: 0
   U62(x1,x2)	weight: 0
#a__U52(x1)	weight: 0
  mark(x1)	weight: 0
a__U11(x1)	weight: 0
a__U42(x1)	weight: 0
a__U52(x1)	weight: 0
#a__length(x1)	weight: 0
 isNat(x1)	weight: 0
   U52(x1)	weight: 0
   U61(x1,x2,x3)	weight: 0
   U31(x1)	weight: 0
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: 0
a__U61(x1,x2,x3)	weight: 0
#a__U41(x1,x2)	weight: 0
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U51(x1,x2)	weight: 0
length(x1)	weight: 0
   U41(x1,x2)	weight: 0
a__zeros()	weight: 0
a__length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 3, DPs: 23, edges: 207
	SCC { #26 #39 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1)	weight: (/ 3 4)
isNatList(x1)	weight: 0
   U11(x1)	weight: 0
     s(x1)	weight: (/ 1 4)
#a__U31(x1)	weight: 0
a__isNatIList(x1)	weight: 0
   U42(x1)	weight: 0
#a__isNat(x1)	weight: 0
a__U62(x1,x2)	weight: 0
isNatIList(x1)	weight: 0
#a__U51(x1,x2)	weight: 0
#a__U11(x1)	weight: 0
 zeros()	weight: 0
a__U31(x1)	weight: 0
a__U51(x1,x2)	weight: 0
a__isNatList(x1)	weight: 0
#a__U62(x1,x2)	weight: 0
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: 0
#a__U21(x1)	weight: 0
#a__isNatIList(x1)	weight: x1
#a__U61(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1)	weight: (/ 1 2)
   nil()	weight: 0
   U62(x1,x2)	weight: 0
#a__U52(x1)	weight: 0
  mark(x1)	weight: 0
a__U11(x1)	weight: 0
a__U42(x1)	weight: 0
a__U52(x1)	weight: 0
#a__length(x1)	weight: 0
 isNat(x1)	weight: (/ 1 2) + x1
   U52(x1)	weight: 0
   U61(x1,x2,x3)	weight: 0
   U31(x1)	weight: 0
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x1 + x2
a__U61(x1,x2,x3)	weight: 0
#a__U41(x1,x2)	weight: (/ 1 4) + x2
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 4)
   U51(x1,x2)	weight: 0
length(x1)	weight: 0
   U41(x1,x2)	weight: 0
a__zeros()	weight: 0
a__length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #26 #39
Number of SCCs: 2, DPs: 21, edges: 205
	SCC { #21 #41 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1)	weight: (/ 3 4) + x1
isNatList(x1)	weight: 0
   U11(x1)	weight: 0
     s(x1)	weight: (/ 1 4)
#a__U31(x1)	weight: 0
a__isNatIList(x1)	weight: 0
   U42(x1)	weight: 0
#a__isNat(x1)	weight: 0
a__U62(x1,x2)	weight: 0
isNatIList(x1)	weight: 0
#a__U51(x1,x2)	weight: (/ 1 4) + x2
#a__U11(x1)	weight: 0
 zeros()	weight: 0
a__U31(x1)	weight: 0
a__U51(x1,x2)	weight: 0
a__isNatList(x1)	weight: 0
#a__U62(x1,x2)	weight: 0
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: 0
#a__U21(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
#a__U61(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1)	weight: (/ 1 2)
   nil()	weight: 0
   U62(x1,x2)	weight: 0
#a__U52(x1)	weight: 0
  mark(x1)	weight: 0
a__U11(x1)	weight: 0
a__U42(x1)	weight: 0
a__U52(x1)	weight: 0
#a__length(x1)	weight: 0
 isNat(x1)	weight: (/ 1 2)
   U52(x1)	weight: 0
   U61(x1,x2,x3)	weight: 0
   U31(x1)	weight: 0
#a__isNatList(x1)	weight: x1
  cons(x1,x2)	weight: (/ 1 2) + x2
a__U61(x1,x2,x3)	weight: 0
#a__U41(x1,x2)	weight: (/ 1 4)
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 4)
   U51(x1,x2)	weight: 0
length(x1)	weight: 0
   U41(x1,x2)	weight: 0
a__zeros()	weight: 0
a__length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #21 #41
Number of SCCs: 1, DPs: 19, edges: 203
	SCC { #2..4 #7 #10 #12..14 #17 #18 #22 #23 #28 #30..32 #34 #35 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1)	weight: x1
isNatList(x1)	weight: 0
   U11(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: x1
#a__U31(x1)	weight: 0
a__isNatIList(x1)	weight: (/ 1 4)
   U42(x1)	weight: x1
#a__isNat(x1)	weight: 0
a__U62(x1,x2)	weight: (/ 1 2) + x1 + x2
isNatIList(x1)	weight: (/ 1 4)
#a__U51(x1,x2)	weight: (/ 1 4)
#a__U11(x1)	weight: 0
 zeros()	weight: 0
a__U31(x1)	weight: (/ 1 4) + x1
a__U51(x1,x2)	weight: x1
a__isNatList(x1)	weight: 0
#a__U62(x1,x2)	weight: (/ 1 4) + x2
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: (/ 1 4) + x1
#a__U21(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
#a__U61(x1,x2,x3)	weight: (/ 1 4) + x2
#mark(x1)	weight: x1
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1)	weight: x1
   nil()	weight: 0
   U62(x1,x2)	weight: (/ 1 2) + x1 + x2
#a__U52(x1)	weight: 0
  mark(x1)	weight: x1
a__U11(x1)	weight: (/ 1 4) + x1
a__U42(x1)	weight: x1
a__U52(x1)	weight: x1
#a__length(x1)	weight: (/ 1 4) + x1
 isNat(x1)	weight: 0
   U52(x1)	weight: x1
   U61(x1,x2,x3)	weight: (/ 1 2) + x1 + x2
   U31(x1)	weight: (/ 1 4) + x1
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: x1 + x2
a__U61(x1,x2,x3)	weight: (/ 1 2) + x1 + x2
#a__U41(x1,x2)	weight: (/ 1 4)
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U51(x1,x2)	weight: x1
length(x1)	weight: (/ 1 2) + x1
   U41(x1,x2)	weight: (/ 1 4) + x1
a__zeros()	weight: 0
a__length(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1 3 5..11 13 16..18 20..53 }
    Removed DPs: #10 #13 #14 #17 #23 #30..32 #34 #35
Number of SCCs: 2, DPs: 9, edges: 39
	SCC { #7 #18 #22 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
   U21(x1)	weight: (/ 1 2); 0
isNatList(x1)	weight: (/ 1 8) + x1_2; 0
   U11(x1)	weight: (/ 1 8); 0
     s(x1)	weight: x1_1; x1_2
#a__U31(x1)	weight: 0; 0
a__isNatIList(x1)	weight: (/ 1 8) + x1_1 + x1_2; (/ 1 4) + x1_1 + x1_2
   U42(x1)	weight: x1_1; x1_2
#a__isNat(x1)	weight: 0; 0
a__U62(x1,x2)	weight: (/ 1 8); (/ 1 4)
isNatIList(x1)	weight: (/ 1 8) + x1_1 + x1_2; 0
#a__U51(x1,x2)	weight: 0; 0
#a__U11(x1)	weight: 0; 0
 zeros()	weight: (/ 1 8); (/ 1 8)
a__U31(x1)	weight: (/ 1 8) + x1_1; x1_2
a__U51(x1,x2)	weight: (/ 1 8) + x2_2; (/ 1 8)
a__isNatList(x1)	weight: (/ 1 8) + x1_2; (/ 1 8)
#a__U62(x1,x2)	weight: (/ 1 2) + x2_1; 0
#a__U42(x1)	weight: 0; 0
a__U41(x1,x2)	weight: (/ 1 8) + x2_1 + x2_2; (/ 1 4) + x2_1 + x2_2
#a__U21(x1)	weight: 0; 0
#a__isNatIList(x1)	weight: 0; 0
#a__U61(x1,x2,x3)	weight: x2_1 + x1_1; 0
#mark(x1)	weight: 0; 0
     0()	weight: (/ 1 8); (/ 1 8)
#a__zeros()	weight: 0; 0
a__U21(x1)	weight: (/ 5 8); (/ 1 8)
   nil()	weight: (/ 3 8); (/ 1 2)
   U62(x1,x2)	weight: (/ 1 8); 0
#a__U52(x1)	weight: 0; 0
  mark(x1)	weight: (/ 1 8) + x1_1 + x1_2; (/ 1 8) + x1_1
a__U11(x1)	weight: (/ 1 8); 0
a__U42(x1)	weight: x1_1; x1_2
a__U52(x1)	weight: x1_1; x1_2
#a__length(x1)	weight: (/ 1 4) + x1_2; 0
 isNat(x1)	weight: (/ 1 2); 0
   U52(x1)	weight: x1_1; x1_2
   U61(x1,x2,x3)	weight: (/ 1 8); 0
   U31(x1)	weight: (/ 1 8) + x1_1; x1_2
#a__isNatList(x1)	weight: 0; 0
  cons(x1,x2)	weight: x2_1 + x2_2; x2_1 + x2_2
a__U61(x1,x2,x3)	weight: (/ 1 8); (/ 1 4)
#a__U41(x1,x2)	weight: 0; 0
    tt()	weight: (/ 5 8); (/ 1 8)
a__isNat(x1)	weight: (/ 5 8); (/ 1 8)
   U51(x1,x2)	weight: (/ 1 8) + x2_2; 0
length(x1)	weight: (/ 1 8); 0
   U41(x1,x2)	weight: (/ 1 8) + x2_1 + x2_2; 0
a__zeros()	weight: (/ 1 4); (/ 1 4)
a__length(x1)	weight: (/ 1 8); (/ 1 4)
    Usable rules: { 1 3 5..11 13 16..18 20..53 }
    Removed DPs: #7 #18 #22
Number of SCCs: 1, DPs: 6, edges: 36
	SCC { #2..4 #12 #28 #37 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U21(x1)	weight: (/ 1 4) + x1
isNatList(x1)	weight: (/ 1 8)
   U11(x1)	weight: (/ 3 8) + x1
     s(x1)	weight: (/ 1 8) + x1
#a__U31(x1)	weight: 0
a__isNatIList(x1)	weight: (/ 1 4)
   U42(x1)	weight: (/ 3 8) + x1
#a__isNat(x1)	weight: 0
a__U62(x1,x2)	weight: (/ 1 4) + x1
isNatIList(x1)	weight: (/ 3 8) + x1
#a__U51(x1,x2)	weight: (/ 1 8)
#a__U11(x1)	weight: 0
 zeros()	weight: 0
a__U31(x1)	weight: (/ 1 4)
a__U51(x1,x2)	weight: (/ 1 8) + x1
a__isNatList(x1)	weight: 0
#a__U62(x1,x2)	weight: (/ 1 8)
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: (/ 3 8)
#a__U21(x1)	weight: 0
#a__isNatIList(x1)	weight: 0
#a__U61(x1,x2,x3)	weight: (/ 1 8)
#mark(x1)	weight: x1
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1)	weight: (/ 1 8) + x1
   nil()	weight: 0
   U62(x1,x2)	weight: (/ 3 8) + x1 + x2
#a__U52(x1)	weight: 0
  mark(x1)	weight: (/ 1 8)
a__U11(x1)	weight: (/ 1 4)
a__U42(x1)	weight: (/ 1 4) + x1
a__U52(x1)	weight: (/ 1 4) + x1
#a__length(x1)	weight: (/ 1 8)
 isNat(x1)	weight: (/ 3 8) + x1
   U52(x1)	weight: (/ 3 8) + x1
   U61(x1,x2,x3)	weight: x1 + x2 + x3
   U31(x1)	weight: x1
#a__isNatList(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 8) + x1
a__U61(x1,x2,x3)	weight: (/ 3 8) + x1 + x2
#a__U41(x1,x2)	weight: (/ 1 8)
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 4)
   U51(x1,x2)	weight: (/ 1 4) + x1 + x2
length(x1)	weight: (/ 1 4)
   U41(x1,x2)	weight: (/ 1 2) + x1 + x2
a__zeros()	weight: 0
a__length(x1)	weight: (/ 1 8) + x1
    Usable rules: { }
    Removed DPs: #2..4 #12 #28 #37
Number of SCCs: 0, DPs: 0, edges: 0
YES