Input TRS:
    1: a__zeros() -> cons(0(),zeros())
    2: a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1)
    3: a__U12(tt(),V1) -> a__U13(a__isNatList(V1))
    4: a__U13(tt()) -> tt()
    5: a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
    6: a__U22(tt(),V1) -> a__U23(a__isNat(V1))
    7: a__U23(tt()) -> tt()
    8: a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V)
    9: a__U32(tt(),V) -> a__U33(a__isNatList(V))
    10: a__U33(tt()) -> tt()
    11: a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2)
    12: a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2)
    13: a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2)
    14: a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2)
    15: a__U45(tt(),V2) -> a__U46(a__isNatIList(V2))
    16: a__U46(tt()) -> tt()
    17: a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2))
    18: a__U52(tt()) -> tt()
    19: a__U61(tt()) -> tt()
    20: a__U71(tt()) -> tt()
    21: a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2)
    22: a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2)
    23: a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2)
    24: a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2)
    25: a__U85(tt(),V2) -> a__U86(a__isNatList(V2))
    26: a__U86(tt()) -> tt()
    27: a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N)
    28: a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N)
    29: a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L)
    30: a__U94(tt(),L) -> s(a__length(mark(L)))
    31: a__isNat(0()) -> tt()
    32: a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1)
    33: a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
    34: a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V)
    35: a__isNatIList(zeros()) -> tt()
    36: a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2)
    37: a__isNatIListKind(nil()) -> tt()
    38: a__isNatIListKind(zeros()) -> tt()
    39: a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2)
    40: a__isNatKind(0()) -> tt()
    41: a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1))
    42: a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1))
    43: a__isNatList(nil()) -> tt()
    44: a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2)
    45: a__length(nil()) -> 0()
    46: a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N)
    47: mark(zeros()) -> a__zeros()
    48: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
    49: mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
    50: mark(isNatIListKind(X)) -> a__isNatIListKind(X)
    51: mark(U13(X)) -> a__U13(mark(X))
    52: mark(isNatList(X)) -> a__isNatList(X)
    53: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    54: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
    55: mark(isNatKind(X)) -> a__isNatKind(X)
    56: mark(U23(X)) -> a__U23(mark(X))
    57: mark(isNat(X)) -> a__isNat(X)
    58: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
    59: mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
    60: mark(U33(X)) -> a__U33(mark(X))
    61: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
    62: mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
    63: mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3)
    64: mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3)
    65: mark(U45(X1,X2)) -> a__U45(mark(X1),X2)
    66: mark(U46(X)) -> a__U46(mark(X))
    67: mark(isNatIList(X)) -> a__isNatIList(X)
    68: mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
    69: mark(U52(X)) -> a__U52(mark(X))
    70: mark(U61(X)) -> a__U61(mark(X))
    71: mark(U71(X)) -> a__U71(mark(X))
    72: mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
    73: mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
    74: mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3)
    75: mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3)
    76: mark(U85(X1,X2)) -> a__U85(mark(X1),X2)
    77: mark(U86(X)) -> a__U86(mark(X))
    78: mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3)
    79: mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3)
    80: mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3)
    81: mark(U94(X1,X2)) -> a__U94(mark(X1),X2)
    82: mark(length(X)) -> a__length(mark(X))
    83: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    84: mark(0()) -> 0()
    85: mark(tt()) -> tt()
    86: mark(s(X)) -> s(mark(X))
    87: mark(nil()) -> nil()
    88: a__zeros() -> zeros()
    89: a__U11(X1,X2) -> U11(X1,X2)
    90: a__U12(X1,X2) -> U12(X1,X2)
    91: a__isNatIListKind(X) -> isNatIListKind(X)
    92: a__U13(X) -> U13(X)
    93: a__isNatList(X) -> isNatList(X)
    94: a__U21(X1,X2) -> U21(X1,X2)
    95: a__U22(X1,X2) -> U22(X1,X2)
    96: a__isNatKind(X) -> isNatKind(X)
    97: a__U23(X) -> U23(X)
    98: a__isNat(X) -> isNat(X)
    99: a__U31(X1,X2) -> U31(X1,X2)
    100: a__U32(X1,X2) -> U32(X1,X2)
    101: a__U33(X) -> U33(X)
    102: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
    103: a__U42(X1,X2,X3) -> U42(X1,X2,X3)
    104: a__U43(X1,X2,X3) -> U43(X1,X2,X3)
    105: a__U44(X1,X2,X3) -> U44(X1,X2,X3)
    106: a__U45(X1,X2) -> U45(X1,X2)
    107: a__U46(X) -> U46(X)
    108: a__isNatIList(X) -> isNatIList(X)
    109: a__U51(X1,X2) -> U51(X1,X2)
    110: a__U52(X) -> U52(X)
    111: a__U61(X) -> U61(X)
    112: a__U71(X) -> U71(X)
    113: a__U81(X1,X2,X3) -> U81(X1,X2,X3)
    114: a__U82(X1,X2,X3) -> U82(X1,X2,X3)
    115: a__U83(X1,X2,X3) -> U83(X1,X2,X3)
    116: a__U84(X1,X2,X3) -> U84(X1,X2,X3)
    117: a__U85(X1,X2) -> U85(X1,X2)
    118: a__U86(X) -> U86(X)
    119: a__U91(X1,X2,X3) -> U91(X1,X2,X3)
    120: a__U92(X1,X2,X3) -> U92(X1,X2,X3)
    121: a__U93(X1,X2,X3) -> U93(X1,X2,X3)
    122: a__U94(X1,X2) -> U94(X1,X2)
    123: a__length(X) -> length(X)
Number of strict rules: 123
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U11(tt(),V1) -> #a__U12(a__isNatIListKind(V1),V1)
   #2: #a__U11(tt(),V1) -> #a__isNatIListKind(V1)
   #3: #mark(s(X)) -> #mark(X)
   #4: #a__U93(tt(),L,N) -> #a__U94(a__isNatKind(N),L)
   #5: #a__U93(tt(),L,N) -> #a__isNatKind(N)
   #6: #mark(cons(X1,X2)) -> #mark(X1)
   #7: #mark(U46(X)) -> #a__U46(mark(X))
   #8: #mark(U46(X)) -> #mark(X)
   #9: #a__length(cons(N,L)) -> #a__U91(a__isNatList(L),L,N)
   #10: #a__length(cons(N,L)) -> #a__isNatList(L)
   #11: #a__isNatKind(s(V1)) -> #a__U71(a__isNatKind(V1))
   #12: #a__isNatKind(s(V1)) -> #a__isNatKind(V1)
   #13: #a__isNatKind(length(V1)) -> #a__U61(a__isNatIListKind(V1))
   #14: #a__isNatKind(length(V1)) -> #a__isNatIListKind(V1)
   #15: #mark(U82(X1,X2,X3)) -> #a__U82(mark(X1),X2,X3)
   #16: #mark(U82(X1,X2,X3)) -> #mark(X1)
   #17: #mark(zeros()) -> #a__zeros()
   #18: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2)
   #19: #mark(U21(X1,X2)) -> #mark(X1)
   #20: #mark(U71(X)) -> #a__U71(mark(X))
   #21: #mark(U71(X)) -> #mark(X)
   #22: #mark(U11(X1,X2)) -> #a__U11(mark(X1),X2)
   #23: #mark(U11(X1,X2)) -> #mark(X1)
   #24: #mark(U84(X1,X2,X3)) -> #a__U84(mark(X1),X2,X3)
   #25: #mark(U84(X1,X2,X3)) -> #mark(X1)
   #26: #mark(U83(X1,X2,X3)) -> #a__U83(mark(X1),X2,X3)
   #27: #mark(U83(X1,X2,X3)) -> #mark(X1)
   #28: #mark(U31(X1,X2)) -> #a__U31(mark(X1),X2)
   #29: #mark(U31(X1,X2)) -> #mark(X1)
   #30: #mark(U41(X1,X2,X3)) -> #a__U41(mark(X1),X2,X3)
   #31: #mark(U41(X1,X2,X3)) -> #mark(X1)
   #32: #a__U22(tt(),V1) -> #a__U23(a__isNat(V1))
   #33: #a__U22(tt(),V1) -> #a__isNat(V1)
   #34: #mark(U32(X1,X2)) -> #a__U32(mark(X1),X2)
   #35: #mark(U32(X1,X2)) -> #mark(X1)
   #36: #mark(isNatKind(X)) -> #a__isNatKind(X)
   #37: #mark(isNatIList(X)) -> #a__isNatIList(X)
   #38: #mark(U13(X)) -> #a__U13(mark(X))
   #39: #mark(U13(X)) -> #mark(X)
   #40: #a__U43(tt(),V1,V2) -> #a__U44(a__isNatIListKind(V2),V1,V2)
   #41: #a__U43(tt(),V1,V2) -> #a__isNatIListKind(V2)
   #42: #a__U32(tt(),V) -> #a__U33(a__isNatList(V))
   #43: #a__U32(tt(),V) -> #a__isNatList(V)
   #44: #a__U41(tt(),V1,V2) -> #a__U42(a__isNatKind(V1),V1,V2)
   #45: #a__U41(tt(),V1,V2) -> #a__isNatKind(V1)
   #46: #mark(isNat(X)) -> #a__isNat(X)
   #47: #mark(U85(X1,X2)) -> #a__U85(mark(X1),X2)
   #48: #mark(U85(X1,X2)) -> #mark(X1)
   #49: #a__U84(tt(),V1,V2) -> #a__U85(a__isNat(V1),V2)
   #50: #a__U84(tt(),V1,V2) -> #a__isNat(V1)
   #51: #mark(U61(X)) -> #a__U61(mark(X))
   #52: #mark(U61(X)) -> #mark(X)
   #53: #a__U83(tt(),V1,V2) -> #a__U84(a__isNatIListKind(V2),V1,V2)
   #54: #a__U83(tt(),V1,V2) -> #a__isNatIListKind(V2)
   #55: #mark(U94(X1,X2)) -> #a__U94(mark(X1),X2)
   #56: #mark(U94(X1,X2)) -> #mark(X1)
   #57: #mark(U91(X1,X2,X3)) -> #a__U91(mark(X1),X2,X3)
   #58: #mark(U91(X1,X2,X3)) -> #mark(X1)
   #59: #mark(U52(X)) -> #a__U52(mark(X))
   #60: #mark(U52(X)) -> #mark(X)
   #61: #a__U42(tt(),V1,V2) -> #a__U43(a__isNatIListKind(V2),V1,V2)
   #62: #a__U42(tt(),V1,V2) -> #a__isNatIListKind(V2)
   #63: #mark(U92(X1,X2,X3)) -> #a__U92(mark(X1),X2,X3)
   #64: #mark(U92(X1,X2,X3)) -> #mark(X1)
   #65: #mark(U23(X)) -> #a__U23(mark(X))
   #66: #mark(U23(X)) -> #mark(X)
   #67: #mark(length(X)) -> #a__length(mark(X))
   #68: #mark(length(X)) -> #mark(X)
   #69: #a__U44(tt(),V1,V2) -> #a__U45(a__isNat(V1),V2)
   #70: #a__U44(tt(),V1,V2) -> #a__isNat(V1)
   #71: #mark(U42(X1,X2,X3)) -> #a__U42(mark(X1),X2,X3)
   #72: #mark(U42(X1,X2,X3)) -> #mark(X1)
   #73: #a__U94(tt(),L) -> #a__length(mark(L))
   #74: #a__U94(tt(),L) -> #mark(L)
   #75: #mark(isNatList(X)) -> #a__isNatList(X)
   #76: #mark(U12(X1,X2)) -> #a__U12(mark(X1),X2)
   #77: #mark(U12(X1,X2)) -> #mark(X1)
   #78: #a__U85(tt(),V2) -> #a__U86(a__isNatList(V2))
   #79: #a__U85(tt(),V2) -> #a__isNatList(V2)
   #80: #a__isNatIListKind(cons(V1,V2)) -> #a__U51(a__isNatKind(V1),V2)
   #81: #a__isNatIListKind(cons(V1,V2)) -> #a__isNatKind(V1)
   #82: #mark(U44(X1,X2,X3)) -> #a__U44(mark(X1),X2,X3)
   #83: #mark(U44(X1,X2,X3)) -> #mark(X1)
   #84: #a__isNat(s(V1)) -> #a__U21(a__isNatKind(V1),V1)
   #85: #a__isNat(s(V1)) -> #a__isNatKind(V1)
   #86: #mark(U81(X1,X2,X3)) -> #a__U81(mark(X1),X2,X3)
   #87: #mark(U81(X1,X2,X3)) -> #mark(X1)
   #88: #a__U21(tt(),V1) -> #a__U22(a__isNatKind(V1),V1)
   #89: #a__U21(tt(),V1) -> #a__isNatKind(V1)
   #90: #a__isNatList(cons(V1,V2)) -> #a__U81(a__isNatKind(V1),V1,V2)
   #91: #a__isNatList(cons(V1,V2)) -> #a__isNatKind(V1)
   #92: #mark(U45(X1,X2)) -> #a__U45(mark(X1),X2)
   #93: #mark(U45(X1,X2)) -> #mark(X1)
   #94: #a__U92(tt(),L,N) -> #a__U93(a__isNat(N),L,N)
   #95: #a__U92(tt(),L,N) -> #a__isNat(N)
   #96: #a__U82(tt(),V1,V2) -> #a__U83(a__isNatIListKind(V2),V1,V2)
   #97: #a__U82(tt(),V1,V2) -> #a__isNatIListKind(V2)
   #98: #a__isNatIList(V) -> #a__U31(a__isNatIListKind(V),V)
   #99: #a__isNatIList(V) -> #a__isNatIListKind(V)
   #100: #a__U91(tt(),L,N) -> #a__U92(a__isNatIListKind(L),L,N)
   #101: #a__U91(tt(),L,N) -> #a__isNatIListKind(L)
   #102: #mark(U33(X)) -> #a__U33(mark(X))
   #103: #mark(U33(X)) -> #mark(X)
   #104: #a__U51(tt(),V2) -> #a__U52(a__isNatIListKind(V2))
   #105: #a__U51(tt(),V2) -> #a__isNatIListKind(V2)
   #106: #a__isNat(length(V1)) -> #a__U11(a__isNatIListKind(V1),V1)
   #107: #a__isNat(length(V1)) -> #a__isNatIListKind(V1)
   #108: #mark(U43(X1,X2,X3)) -> #a__U43(mark(X1),X2,X3)
   #109: #mark(U43(X1,X2,X3)) -> #mark(X1)
   #110: #mark(U51(X1,X2)) -> #a__U51(mark(X1),X2)
   #111: #mark(U51(X1,X2)) -> #mark(X1)
   #112: #a__isNatIList(cons(V1,V2)) -> #a__U41(a__isNatKind(V1),V1,V2)
   #113: #a__isNatIList(cons(V1,V2)) -> #a__isNatKind(V1)
   #114: #a__U81(tt(),V1,V2) -> #a__U82(a__isNatKind(V1),V1,V2)
   #115: #a__U81(tt(),V1,V2) -> #a__isNatKind(V1)
   #116: #a__U12(tt(),V1) -> #a__U13(a__isNatList(V1))
   #117: #a__U12(tt(),V1) -> #a__isNatList(V1)
   #118: #mark(U86(X)) -> #a__U86(mark(X))
   #119: #mark(U86(X)) -> #mark(X)
   #120: #mark(U22(X1,X2)) -> #a__U22(mark(X1),X2)
   #121: #mark(U22(X1,X2)) -> #mark(X1)
   #122: #a__U31(tt(),V) -> #a__U32(a__isNatIListKind(V),V)
   #123: #a__U31(tt(),V) -> #a__isNatIListKind(V)
   #124: #a__U45(tt(),V2) -> #a__U46(a__isNatIList(V2))
   #125: #a__U45(tt(),V2) -> #a__isNatIList(V2)
   #126: #mark(U93(X1,X2,X3)) -> #a__U93(mark(X1),X2,X3)
   #127: #mark(U93(X1,X2,X3)) -> #mark(X1)
   #128: #mark(isNatIListKind(X)) -> #a__isNatIListKind(X)
Number of SCCs: 4, DPs: 67, edges: 1264
	SCC { #12 #14 #80 #81 #105 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: 0
a__U83(x1,x2,x3)	weight: 0
#a__isNatKind(x1)	weight: (/ 1 8) + x1
isNatKind(x1)	weight: 0
   U21(x1,x2)	weight: 0
#a__U82(x1,x2,x3)	weight: 0
a__U45(x1,x2)	weight: 0
isNatList(x1)	weight: 0
a__U85(x1,x2)	weight: 0
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: 0
#a__U92(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: 0
a__isNatIList(x1)	weight: 0
a__U33(x1)	weight: 0
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: x1
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: 0
   U91(x1,x2,x3)	weight: 0
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: 0
   U71(x1)	weight: (/ 3 8) + x1
a__U84(x1,x2,x3)	weight: 0
a__U86(x1)	weight: 0
a__U44(x1,x2,x3)	weight: 0
isNatIList(x1)	weight: 0
#a__U43(x1,x2,x3)	weight: 0
   U43(x1,x2,x3)	weight: 0
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: 0
   U86(x1)	weight: 0
   U44(x1,x2,x3)	weight: 0
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: 0
#a__U51(x1,x2)	weight: (/ 1 8) + x2
   U23(x1)	weight: 0
a__U22(x1,x2)	weight: 0
   U93(x1,x2,x3)	weight: 0
a__U94(x1,x2)	weight: 0
#a__U11(x1,x2)	weight: 0
   U94(x1,x2)	weight: 0
 zeros()	weight: 0
a__U31(x1,x2)	weight: 0
a__U51(x1,x2)	weight: (/ 1 4)
a__U81(x1,x2,x3)	weight: 0
   U12(x1,x2)	weight: 0
#a__U84(x1,x2,x3)	weight: 0
a__isNatList(x1)	weight: 0
a__U43(x1,x2,x3)	weight: 0
#a__U42(x1,x2,x3)	weight: 0
a__U41(x1,x2,x3)	weight: 0
#a__U12(x1,x2)	weight: 0
#a__U21(x1,x2)	weight: 0
#a__isNatIList(x1)	weight: 0
#a__U81(x1,x2,x3)	weight: 0
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: 0
a__U32(x1,x2)	weight: 0
a__U91(x1,x2,x3)	weight: 0
   nil()	weight: 0
isNatIListKind(x1)	weight: (/ 1 4) + x1
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: 0
  mark(x1)	weight: 0
a__U11(x1,x2)	weight: 0
   U32(x1,x2)	weight: 0
a__U42(x1,x2,x3)	weight: 0
a__U93(x1,x2,x3)	weight: 0
   U33(x1)	weight: 0
#a__U45(x1,x2)	weight: 0
a__U52(x1)	weight: (/ 3 8)
#a__length(x1)	weight: 0
a__U12(x1,x2)	weight: 0
a__isNatIListKind(x1)	weight: (/ 1 8)
 isNat(x1)	weight: 0
   U46(x1)	weight: 0
   U52(x1)	weight: (/ 1 2) + x1
   U61(x1)	weight: 0
a__U46(x1)	weight: 0
#a__U22(x1,x2)	weight: 0
a__U13(x1)	weight: 0
#a__U85(x1,x2)	weight: 0
   U31(x1,x2)	weight: 0
   U85(x1,x2)	weight: 0
#a__U83(x1,x2,x3)	weight: 0
#a__isNatList(x1)	weight: 0
a__U71(x1)	weight: (/ 1 4)
   U92(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
a__U92(x1,x2,x3)	weight: 0
a__U61(x1)	weight: 0
   U81(x1,x2,x3)	weight: 0
#a__U41(x1,x2,x3)	weight: 0
   U82(x1,x2,x3)	weight: 0
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U13(x1)	weight: 0
a__U23(x1)	weight: 0
a__isNatKind(x1)	weight: (/ 1 8)
   U22(x1,x2)	weight: 0
   U51(x1,x2)	weight: (/ 3 8) + x1 + x2
length(x1)	weight: (/ 1 8) + x1
   U41(x1,x2,x3)	weight: 0
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: 0
a__length(x1)	weight: 0
    Usable rules: { 19 40 41 96 111 }
    Removed DPs: #12 #14 #80 #81 #105
Number of SCCs: 3, DPs: 62, edges: 1255
	SCC { #40 #44 #61 #69 #112 #125 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: 0
a__U83(x1,x2,x3)	weight: (/ 9 16)
#a__isNatKind(x1)	weight: (/ 1 16)
isNatKind(x1)	weight: (/ 1 8) + x1
   U21(x1,x2)	weight: (/ 3 16) + x1 + x2
#a__U82(x1,x2,x3)	weight: 0
a__U45(x1,x2)	weight: 0
isNatList(x1)	weight: (/ 1 8)
a__U85(x1,x2)	weight: (/ 11 16)
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: (/ 3 16) + x1 + x2
#a__U92(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 16) + x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: 0
a__isNatIList(x1)	weight: 0
a__U33(x1)	weight: 0
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: 0
   U91(x1,x2,x3)	weight: 0
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: (/ 1 2) + x1 + x2
   U71(x1)	weight: (/ 3 16) + x1
a__U84(x1,x2,x3)	weight: (/ 5 8)
a__U86(x1)	weight: (/ 3 4)
a__U44(x1,x2,x3)	weight: 0
isNatIList(x1)	weight: 0
#a__U43(x1,x2,x3)	weight: (/ 3 16) + x3
   U43(x1,x2,x3)	weight: 0
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: (/ 1 8) + x3
   U86(x1)	weight: (/ 13 16) + x1
   U44(x1,x2,x3)	weight: 0
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: (/ 11 16) + x1 + x2 + x3
#a__U51(x1,x2)	weight: (/ 1 16)
   U23(x1)	weight: (/ 5 16)
a__U22(x1,x2)	weight: (/ 3 16)
   U93(x1,x2,x3)	weight: 0
a__U94(x1,x2)	weight: 0
#a__U11(x1,x2)	weight: 0
   U94(x1,x2)	weight: 0
 zeros()	weight: 0
a__U31(x1,x2)	weight: 0
a__U51(x1,x2)	weight: (/ 1 8)
a__U81(x1,x2,x3)	weight: (/ 1 2)
   U12(x1,x2)	weight: (/ 1 4) + x1 + x2
#a__U84(x1,x2,x3)	weight: 0
a__isNatList(x1)	weight: (/ 1 16) + x1
a__U43(x1,x2,x3)	weight: 0
#a__U42(x1,x2,x3)	weight: (/ 1 4) + x3
a__U41(x1,x2,x3)	weight: 0
#a__U12(x1,x2)	weight: 0
#a__U21(x1,x2)	weight: 0
#a__isNatIList(x1)	weight: x1
#a__U81(x1,x2,x3)	weight: 0
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: (/ 5 8) + x2 + x3
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: (/ 1 8)
a__U32(x1,x2)	weight: 0
a__U91(x1,x2,x3)	weight: 0
   nil()	weight: 0
isNatIListKind(x1)	weight: (/ 1 8) + x1
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: 0
  mark(x1)	weight: 0
a__U11(x1,x2)	weight: (/ 1 8)
   U32(x1,x2)	weight: 0
a__U42(x1,x2,x3)	weight: 0
a__U93(x1,x2,x3)	weight: 0
   U33(x1)	weight: 0
#a__U45(x1,x2)	weight: (/ 1 16) + x2
a__U52(x1)	weight: (/ 3 16)
#a__length(x1)	weight: 0
a__U12(x1,x2)	weight: (/ 3 16)
a__isNatIListKind(x1)	weight: (/ 1 16)
 isNat(x1)	weight: (/ 1 8) + x1
   U46(x1)	weight: 0
   U52(x1)	weight: (/ 1 4)
   U61(x1)	weight: (/ 3 16) + x1
a__U46(x1)	weight: 0
#a__U22(x1,x2)	weight: 0
a__U13(x1)	weight: (/ 1 4)
#a__U85(x1,x2)	weight: 0
   U31(x1,x2)	weight: 0
   U85(x1,x2)	weight: (/ 3 4) + x2
#a__U83(x1,x2,x3)	weight: 0
#a__isNatList(x1)	weight: 0
a__U71(x1)	weight: (/ 1 8)
   U92(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: (/ 3 8) + x1 + x2
a__U92(x1,x2,x3)	weight: 0
a__U61(x1)	weight: (/ 1 8)
   U81(x1,x2,x3)	weight: (/ 9 16) + x1 + x2 + x3
#a__U41(x1,x2,x3)	weight: (/ 5 16) + x3
   U82(x1,x2,x3)	weight: (/ 9 16)
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 16)
   U13(x1)	weight: (/ 5 16) + x1
a__U23(x1)	weight: (/ 1 4)
a__isNatKind(x1)	weight: (/ 1 16)
   U22(x1,x2)	weight: (/ 1 4) + x1
   U51(x1,x2)	weight: (/ 3 16) + x1 + x2
length(x1)	weight: (/ 1 16) + x1
   U41(x1,x2,x3)	weight: 0
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: 0
a__length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #40 #44 #61 #69 #112 #125
Number of SCCs: 2, DPs: 56, edges: 1249
	SCC { #1 #33 #49 #50 #53 #79 #84 #88 #90 #96 #106 #114 #117 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: 0
a__U83(x1,x2,x3)	weight: (/ 9 16)
#a__isNatKind(x1)	weight: (/ 1 16)
isNatKind(x1)	weight: (/ 1 8) + x1
   U21(x1,x2)	weight: (/ 3 16) + x1 + x2
#a__U82(x1,x2,x3)	weight: (/ 1 4) + x2 + x3
a__U45(x1,x2)	weight: 0
isNatList(x1)	weight: (/ 1 8)
a__U85(x1,x2)	weight: (/ 11 16)
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: (/ 3 16) + x1 + x2
#a__U92(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 3 16) + x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: 0
a__isNatIList(x1)	weight: 0
a__U33(x1)	weight: 0
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: 0
   U91(x1,x2,x3)	weight: 0
#a__isNat(x1)	weight: x1
a__U82(x1,x2,x3)	weight: (/ 1 2) + x1 + x2
   U71(x1)	weight: (/ 3 16) + x1
a__U84(x1,x2,x3)	weight: (/ 5 8)
a__U86(x1)	weight: (/ 3 4)
a__U44(x1,x2,x3)	weight: 0
isNatIList(x1)	weight: 0
#a__U43(x1,x2,x3)	weight: (/ 3 16)
   U43(x1,x2,x3)	weight: 0
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: (/ 1 8)
   U86(x1)	weight: (/ 13 16) + x1
   U44(x1,x2,x3)	weight: 0
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: (/ 11 16) + x1 + x2 + x3
#a__U51(x1,x2)	weight: (/ 1 16)
   U23(x1)	weight: (/ 5 16)
a__U22(x1,x2)	weight: (/ 3 16)
   U93(x1,x2,x3)	weight: 0
a__U94(x1,x2)	weight: 0
#a__U11(x1,x2)	weight: (/ 1 8) + x2
   U94(x1,x2)	weight: 0
 zeros()	weight: 0
a__U31(x1,x2)	weight: 0
a__U51(x1,x2)	weight: (/ 1 8)
a__U81(x1,x2,x3)	weight: (/ 1 2)
   U12(x1,x2)	weight: (/ 1 4) + x1 + x2
#a__U84(x1,x2,x3)	weight: (/ 1 8) + x2 + x3
a__isNatList(x1)	weight: (/ 1 16) + x1
a__U43(x1,x2,x3)	weight: 0
#a__U42(x1,x2,x3)	weight: (/ 1 4)
a__U41(x1,x2,x3)	weight: 0
#a__U12(x1,x2)	weight: (/ 1 16) + x2
#a__U21(x1,x2)	weight: (/ 1 8) + x2
#a__isNatIList(x1)	weight: 0
#a__U81(x1,x2,x3)	weight: (/ 5 16) + x2 + x3
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: (/ 5 8) + x2 + x3
#mark(x1)	weight: 0
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: (/ 1 8)
a__U32(x1,x2)	weight: 0
a__U91(x1,x2,x3)	weight: 0
   nil()	weight: 0
isNatIListKind(x1)	weight: (/ 1 8) + x1
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: 0
  mark(x1)	weight: 0
a__U11(x1,x2)	weight: (/ 1 8)
   U32(x1,x2)	weight: 0
a__U42(x1,x2,x3)	weight: 0
a__U93(x1,x2,x3)	weight: 0
   U33(x1)	weight: 0
#a__U45(x1,x2)	weight: (/ 1 16)
a__U52(x1)	weight: (/ 3 16)
#a__length(x1)	weight: 0
a__U12(x1,x2)	weight: (/ 3 16)
a__isNatIListKind(x1)	weight: (/ 1 16)
 isNat(x1)	weight: (/ 1 8) + x1
   U46(x1)	weight: 0
   U52(x1)	weight: (/ 1 4) + x1
   U61(x1)	weight: (/ 3 16) + x1
a__U46(x1)	weight: 0
#a__U22(x1,x2)	weight: (/ 1 16) + x2
a__U13(x1)	weight: (/ 1 4)
#a__U85(x1,x2)	weight: (/ 1 16) + x2
   U31(x1,x2)	weight: 0
   U85(x1,x2)	weight: (/ 3 4) + x2
#a__U83(x1,x2,x3)	weight: (/ 3 16) + x2 + x3
#a__isNatList(x1)	weight: x1
a__U71(x1)	weight: (/ 1 8)
   U92(x1,x2,x3)	weight: 0
  cons(x1,x2)	weight: (/ 3 8) + x1 + x2
a__U92(x1,x2,x3)	weight: 0
a__U61(x1)	weight: (/ 1 8)
   U81(x1,x2,x3)	weight: (/ 9 16) + x1 + x2 + x3
#a__U41(x1,x2,x3)	weight: (/ 5 16)
   U82(x1,x2,x3)	weight: (/ 9 16)
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 16)
   U13(x1)	weight: (/ 5 16) + x1
a__U23(x1)	weight: (/ 1 4)
a__isNatKind(x1)	weight: (/ 1 16)
   U22(x1,x2)	weight: (/ 1 4) + x1
   U51(x1,x2)	weight: (/ 3 16)
length(x1)	weight: (/ 3 16) + x1
   U41(x1,x2,x3)	weight: 0
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: 0
a__length(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #33 #49 #50 #53 #79 #84 #88 #90 #96 #106 #114 #117
Number of SCCs: 1, DPs: 43, edges: 1233
	SCC { #3 #4 #6 #8 #9 #16 #19 #21 #23 #25 #27 #29 #31 #35 #39 #48 #52 #55..58 #60 #63 #64 #66..68 #72..74 #77 #83 #87 #93 #94 #100 #103 #109 #111 #119 #121 #126 #127 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: x2
a__U83(x1,x2,x3)	weight: x1
#a__isNatKind(x1)	weight: (/ 1 8)
isNatKind(x1)	weight: 0
   U21(x1,x2)	weight: x1
#a__U82(x1,x2,x3)	weight: (/ 1 2)
a__U45(x1,x2)	weight: (/ 1 8) + x1
isNatList(x1)	weight: 0
a__U85(x1,x2)	weight: x1
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: x1
#a__U92(x1,x2,x3)	weight: x2
     s(x1)	weight: x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: x2
a__isNatIList(x1)	weight: (/ 1 8)
a__U33(x1)	weight: (/ 1 8) + x1
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: (/ 1 8) + x1
   U91(x1,x2,x3)	weight: x1 + x2
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: x1
   U71(x1)	weight: x1
a__U84(x1,x2,x3)	weight: x1
a__U86(x1)	weight: x1
a__U44(x1,x2,x3)	weight: (/ 1 8) + x1
isNatIList(x1)	weight: (/ 1 8)
#a__U43(x1,x2,x3)	weight: (/ 3 8)
   U43(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: (/ 1 4)
   U86(x1)	weight: x1
   U44(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: x1
#a__U51(x1,x2)	weight: (/ 1 8)
   U23(x1)	weight: x1
a__U22(x1,x2)	weight: x1
   U93(x1,x2,x3)	weight: x1 + x2
a__U94(x1,x2)	weight: x1 + x2
#a__U11(x1,x2)	weight: (/ 1 4)
   U94(x1,x2)	weight: x1 + x2
 zeros()	weight: 0
a__U31(x1,x2)	weight: (/ 1 8) + x1
a__U51(x1,x2)	weight: x1
a__U81(x1,x2,x3)	weight: x1
   U12(x1,x2)	weight: x1
#a__U84(x1,x2,x3)	weight: (/ 1 4)
a__isNatList(x1)	weight: 0
a__U43(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U42(x1,x2,x3)	weight: (/ 1 2)
a__U41(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U12(x1,x2)	weight: (/ 1 8)
#a__U21(x1,x2)	weight: (/ 1 4)
#a__isNatIList(x1)	weight: 0
#a__U81(x1,x2,x3)	weight: (/ 5 8)
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: x1
#mark(x1)	weight: x1
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: x1
a__U32(x1,x2)	weight: (/ 1 8) + x1
a__U91(x1,x2,x3)	weight: x1 + x2
   nil()	weight: 0
isNatIListKind(x1)	weight: 0
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: (/ 1 8) + x1
  mark(x1)	weight: x1
a__U11(x1,x2)	weight: x1
   U32(x1,x2)	weight: (/ 1 8) + x1
a__U42(x1,x2,x3)	weight: (/ 1 8) + x1
a__U93(x1,x2,x3)	weight: x1 + x2
   U33(x1)	weight: (/ 1 8) + x1
#a__U45(x1,x2)	weight: (/ 1 8)
a__U52(x1)	weight: x1
#a__length(x1)	weight: x1
a__U12(x1,x2)	weight: x1
a__isNatIListKind(x1)	weight: 0
 isNat(x1)	weight: 0
   U46(x1)	weight: x1
   U52(x1)	weight: x1
   U61(x1)	weight: x1
a__U46(x1)	weight: x1
#a__U22(x1,x2)	weight: (/ 1 8)
a__U13(x1)	weight: x1
#a__U85(x1,x2)	weight: (/ 1 8)
   U31(x1,x2)	weight: (/ 1 8) + x1
   U85(x1,x2)	weight: x1
#a__U83(x1,x2,x3)	weight: (/ 3 8)
#a__isNatList(x1)	weight: 0
a__U71(x1)	weight: x1
   U92(x1,x2,x3)	weight: x1 + x2
  cons(x1,x2)	weight: x1 + x2
a__U92(x1,x2,x3)	weight: x1 + x2
a__U61(x1)	weight: x1
   U81(x1,x2,x3)	weight: x1
#a__U41(x1,x2,x3)	weight: (/ 5 8)
   U82(x1,x2,x3)	weight: x1
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U13(x1)	weight: x1
a__U23(x1)	weight: x1
a__isNatKind(x1)	weight: 0
   U22(x1,x2)	weight: x1
   U51(x1,x2)	weight: x1
length(x1)	weight: x1
   U41(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: x2
a__length(x1)	weight: x1
    Usable rules: { 1..123 }
    Removed DPs: #29 #31 #35 #72 #83 #93 #103 #109
Number of SCCs: 1, DPs: 35, edges: 737
	SCC { #3 #4 #6 #8 #9 #16 #19 #21 #23 #25 #27 #39 #48 #52 #55..58 #60 #63 #64 #66..68 #73 #74 #77 #87 #94 #100 #111 #119 #121 #126 #127 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: (/ 1 8) + x2
a__U83(x1,x2,x3)	weight: x1
#a__isNatKind(x1)	weight: (/ 1 8)
isNatKind(x1)	weight: 0
   U21(x1,x2)	weight: x1
#a__U82(x1,x2,x3)	weight: (/ 1 2)
a__U45(x1,x2)	weight: (/ 1 8)
isNatList(x1)	weight: 0
a__U85(x1,x2)	weight: x1
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: x1
#a__U92(x1,x2,x3)	weight: (/ 1 8) + x2
     s(x1)	weight: x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: (/ 1 8) + x2
a__isNatIList(x1)	weight: (/ 1 8)
a__U33(x1)	weight: (/ 1 8) + x1
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: (/ 1 8)
   U91(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: x1
   U71(x1)	weight: x1
a__U84(x1,x2,x3)	weight: x1
a__U86(x1)	weight: x1
a__U44(x1,x2,x3)	weight: (/ 1 8) + x1
isNatIList(x1)	weight: (/ 1 8)
#a__U43(x1,x2,x3)	weight: (/ 3 8)
   U43(x1,x2,x3)	weight: (/ 1 8)
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: (/ 1 4)
   U86(x1)	weight: x1
   U44(x1,x2,x3)	weight: (/ 1 8) + x1
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: x1
#a__U51(x1,x2)	weight: (/ 1 8)
   U23(x1)	weight: x1
a__U22(x1,x2)	weight: x1
   U93(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
a__U94(x1,x2)	weight: (/ 1 8) + x1 + x2
#a__U11(x1,x2)	weight: (/ 1 4)
   U94(x1,x2)	weight: (/ 1 8) + x1 + x2
 zeros()	weight: 0
a__U31(x1,x2)	weight: (/ 1 8) + x1
a__U51(x1,x2)	weight: x1
a__U81(x1,x2,x3)	weight: x1
   U12(x1,x2)	weight: x1
#a__U84(x1,x2,x3)	weight: (/ 1 4)
a__isNatList(x1)	weight: 0
a__U43(x1,x2,x3)	weight: (/ 1 8)
#a__U42(x1,x2,x3)	weight: (/ 1 2)
a__U41(x1,x2,x3)	weight: (/ 1 8)
#a__U12(x1,x2)	weight: (/ 1 8)
#a__U21(x1,x2)	weight: (/ 1 4)
#a__isNatIList(x1)	weight: 0
#a__U81(x1,x2,x3)	weight: (/ 5 8)
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: x1
#mark(x1)	weight: x1
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: x1
a__U32(x1,x2)	weight: (/ 1 8) + x1
a__U91(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
   nil()	weight: 0
isNatIListKind(x1)	weight: 0
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: (/ 1 8)
  mark(x1)	weight: x1
a__U11(x1,x2)	weight: x1
   U32(x1,x2)	weight: (/ 1 8) + x1
a__U42(x1,x2,x3)	weight: (/ 1 8)
a__U93(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
   U33(x1)	weight: (/ 1 8) + x1
#a__U45(x1,x2)	weight: (/ 1 8)
a__U52(x1)	weight: x1
#a__length(x1)	weight: (/ 1 8) + x1
a__U12(x1,x2)	weight: x1
a__isNatIListKind(x1)	weight: 0
 isNat(x1)	weight: 0
   U46(x1)	weight: x1
   U52(x1)	weight: x1
   U61(x1)	weight: x1
a__U46(x1)	weight: x1
#a__U22(x1,x2)	weight: (/ 1 8)
a__U13(x1)	weight: x1
#a__U85(x1,x2)	weight: (/ 1 8)
   U31(x1,x2)	weight: (/ 1 8) + x1
   U85(x1,x2)	weight: x1
#a__U83(x1,x2,x3)	weight: (/ 3 8)
#a__isNatList(x1)	weight: 0
a__U71(x1)	weight: x1
   U92(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
  cons(x1,x2)	weight: x1 + x2
a__U92(x1,x2,x3)	weight: (/ 1 8) + x1 + x2
a__U61(x1)	weight: x1
   U81(x1,x2,x3)	weight: x1
#a__U41(x1,x2,x3)	weight: (/ 5 8)
   U82(x1,x2,x3)	weight: x1
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U13(x1)	weight: x1
a__U23(x1)	weight: x1
a__isNatKind(x1)	weight: 0
   U22(x1,x2)	weight: x1
   U51(x1,x2)	weight: x1
length(x1)	weight: (/ 1 8) + x1
   U41(x1,x2,x3)	weight: (/ 1 8)
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: (/ 1 8) + x2
a__length(x1)	weight: (/ 1 8) + x1
    Usable rules: { 1..123 }
    Removed DPs: #56 #58 #64 #68 #74 #127
Number of SCCs: 2, DPs: 24, edges: 366
	SCC { #4 #9 #73 #94 #100 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
#a__U94(x1,x2)	weight: (/ 5 8) + x2_1; 0
a__U83(x1,x2,x3)	weight: (/ 1 16) + x1_1; (/ 1 8) + x3_1 + x3_2 + x2_2
#a__isNatKind(x1)	weight: 0; 0
isNatKind(x1)	weight: (/ 1 4) + x1_1 + x1_2; (/ 1 16)
   U21(x1,x2)	weight: (/ 3 8); (/ 1 16)
#a__U82(x1,x2,x3)	weight: 0; 0
a__U45(x1,x2)	weight: (/ 3 4) + x1_2; (/ 1 16)
isNatList(x1)	weight: (/ 1 16) + x1_2; (/ 1 16) + x1_1
a__U85(x1,x2)	weight: (/ 13 16); (/ 1 8)
#a__U71(x1)	weight: 0; 0
   U11(x1,x2)	weight: (/ 7 16); (/ 1 16)
#a__U92(x1,x2,x3)	weight: (/ 3 4) + x2_1; 0
     s(x1)	weight: x1_1; (/ 1 8) + x1_1
#a__U31(x1,x2)	weight: 0; 0
#a__U33(x1)	weight: 0; 0
#a__U93(x1,x2,x3)	weight: (/ 5 8) + x2_1 + x1_2; 0
a__isNatIList(x1)	weight: (/ 7 8) + x1_1; (/ 7 8) + x1_2
a__U33(x1)	weight: (/ 13 16); (/ 1 16) + x1_1
#a__U86(x1)	weight: 0; 0
#a__isNatIListKind(x1)	weight: 0; 0
#a__U23(x1)	weight: 0; 0
   U42(x1,x2,x3)	weight: (/ 3 8) + x3_1 + x3_2; (/ 1 16)
   U91(x1,x2,x3)	weight: (/ 1 16); (/ 11 16) + x3_2 + x1_2
#a__isNat(x1)	weight: 0; 0
a__U82(x1,x2,x3)	weight: (/ 7 8); (/ 1 8) + x3_1 + x3_2 + x2_2
   U71(x1)	weight: (/ 3 4) + x1_2; x1_2
a__U84(x1,x2,x3)	weight: (/ 13 16); (/ 1 16) + x1_2
a__U86(x1)	weight: (/ 13 16); (/ 1 16)
a__U44(x1,x2,x3)	weight: (/ 3 4) + x1_2; (/ 1 16)
isNatIList(x1)	weight: (/ 7 16) + x1_1; (/ 7 16) + x1_2
#a__U43(x1,x2,x3)	weight: 0; 0
   U43(x1,x2,x3)	weight: (/ 3 8) + x3_1 + x3_2; (/ 1 16)
#a__U13(x1)	weight: 0; 0
#a__U44(x1,x2,x3)	weight: 0; 0
   U86(x1)	weight: (/ 3 8); 0
   U44(x1,x2,x3)	weight: (/ 3 4) + x1_2; (/ 1 16)
#a__U46(x1)	weight: 0; 0
   U84(x1,x2,x3)	weight: (/ 3 8); (/ 1 16) + x1_2
#a__U51(x1,x2)	weight: 0; 0
   U23(x1)	weight: (/ 3 4) + x1_2; x1_2
a__U22(x1,x2)	weight: (/ 13 16); (/ 1 16)
   U93(x1,x2,x3)	weight: (/ 1 16); x1_1
a__U94(x1,x2)	weight: (/ 1 16); (/ 1 2)
#a__U11(x1,x2)	weight: 0; 0
   U94(x1,x2)	weight: (/ 1 16); (/ 1 16)
 zeros()	weight: (/ 1 16); (/ 3 8)
a__U31(x1,x2)	weight: (/ 7 8) + x2_1; (/ 7 8) + x2_2
a__U51(x1,x2)	weight: (/ 3 4) + x1_2; (/ 1 16)
a__U81(x1,x2,x3)	weight: (/ 13 16) + x1_2; (/ 1 8) + x3_1 + x3_2 + x2_2
   U12(x1,x2)	weight: (/ 1 16) + x1_1; (/ 1 16)
#a__U84(x1,x2,x3)	weight: 0; 0
a__isNatList(x1)	weight: (/ 1 16) + x1_2; (/ 1 8) + x1_1
a__U43(x1,x2,x3)	weight: (/ 13 16) + x3_1 + x3_2; (/ 1 16)
#a__U42(x1,x2,x3)	weight: 0; 0
a__U41(x1,x2,x3)	weight: (/ 3 4) + x3_1 + x3_2 + x2_2 + x1_2; (/ 1 16) + x1_2
#a__U12(x1,x2)	weight: 0; 0
#a__U21(x1,x2)	weight: 0; 0
#a__isNatIList(x1)	weight: 0; 0
#a__U81(x1,x2,x3)	weight: 0; 0
#a__U61(x1)	weight: 0; 0
   U83(x1,x2,x3)	weight: (/ 1 16) + x1_1; (/ 1 16) + x3_1 + x3_2 + x2_2
#mark(x1)	weight: 0; 0
     0()	weight: (/ 1 16); (/ 1 16)
#a__zeros()	weight: 0; 0
a__U21(x1,x2)	weight: (/ 13 16); (/ 1 16)
a__U32(x1,x2)	weight: (/ 1 16) + x1_1; (/ 1 16) + x2_2 + x1_1
a__U91(x1,x2,x3)	weight: (/ 1 16); (/ 11 16) + x3_2 + x1_2
   nil()	weight: (/ 1 16); (/ 3 4)
isNatIListKind(x1)	weight: (/ 3 8); (/ 1 16) + x1_1 + x1_2
#a__U52(x1)	weight: 0; 0
   U45(x1,x2)	weight: (/ 3 4) + x1_2; 0
  mark(x1)	weight: (/ 7 16) + x1_1; (/ 7 16) + x1_2
a__U11(x1,x2)	weight: (/ 7 8); (/ 1 16)
   U32(x1,x2)	weight: (/ 1 16) + x1_1; (/ 1 16) + x2_2 + x1_1
a__U42(x1,x2,x3)	weight: (/ 13 16) + x3_1 + x3_2; (/ 1 16)
a__U93(x1,x2,x3)	weight: (/ 1 16); x1_1
   U33(x1)	weight: (/ 3 8); (/ 1 16) + x1_1
#a__U45(x1,x2)	weight: 0; 0
a__U52(x1)	weight: x1_1; (/ 1 16)
#a__length(x1)	weight: (/ 1 8) + x1_1; 0
a__U12(x1,x2)	weight: (/ 1 16) + x1_1; (/ 1 16)
a__isNatIListKind(x1)	weight: (/ 13 16); (/ 1 16) + x1_1 + x1_2
 isNat(x1)	weight: (/ 5 16) + x1_2; (/ 1 16)
   U46(x1)	weight: (/ 3 8); 0
   U52(x1)	weight: x1_1; (/ 1 16)
   U61(x1)	weight: (/ 3 8); (/ 1 16)
a__U46(x1)	weight: (/ 13 16); (/ 1 16)
#a__U22(x1,x2)	weight: 0; 0
a__U13(x1)	weight: (/ 13 16); (/ 1 16)
#a__U85(x1,x2)	weight: 0; 0
   U31(x1,x2)	weight: (/ 7 16) + x2_1; (/ 7 16) + x2_2
   U85(x1,x2)	weight: (/ 3 8); (/ 1 16)
#a__U83(x1,x2,x3)	weight: 0; 0
#a__isNatList(x1)	weight: 0; 0
a__U71(x1)	weight: (/ 3 4) + x1_2; x1_2
   U92(x1,x2,x3)	weight: (/ 1 16); (/ 5 16) + x3_2
  cons(x1,x2)	weight: x2_1 + x2_2 + x1_2; (/ 13 16)
a__U92(x1,x2,x3)	weight: (/ 1 16); (/ 3 4) + x3_2
a__U61(x1)	weight: (/ 13 16); (/ 1 16)
   U81(x1,x2,x3)	weight: (/ 13 16) + x1_2; (/ 1 16) + x3_1 + x3_2 + x2_2
#a__U41(x1,x2,x3)	weight: 0; 0
   U82(x1,x2,x3)	weight: (/ 7 16); x3_1 + x3_2 + x2_2
    tt()	weight: (/ 13 16); (/ 1 16)
a__isNat(x1)	weight: (/ 3 4) + x1_2; (/ 1 16)
   U13(x1)	weight: (/ 3 8); (/ 1 16)
a__U23(x1)	weight: (/ 3 4) + x1_2; x1_2
a__isNatKind(x1)	weight: (/ 11 16) + x1_1 + x1_2; (/ 1 16)
   U22(x1,x2)	weight: (/ 3 8); (/ 1 16)
   U51(x1,x2)	weight: (/ 3 4) + x1_2; 0
length(x1)	weight: 0; (/ 13 16) + x1_1
   U41(x1,x2,x3)	weight: (/ 3 4) + x3_1 + x3_2 + x2_2 + x1_2; (/ 1 16) + x1_2
#a__U32(x1,x2)	weight: 0; 0
a__zeros()	weight: (/ 1 2); (/ 13 16)
#a__U91(x1,x2,x3)	weight: x2_1 + x1_1; 0
a__length(x1)	weight: (/ 1 16); (/ 13 16) + x1_1
    Usable rules: { 1..123 }
    Removed DPs: #4 #9 #73 #94 #100
Number of SCCs: 1, DPs: 19, edges: 361
	SCC { #3 #6 #8 #16 #19 #21 #23 #25 #27 #39 #48 #52 #60 #66 #77 #87 #111 #119 #121 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#a__U94(x1,x2)	weight: (/ 1 16)
a__U83(x1,x2,x3)	weight: (/ 1 8) + x2
#a__isNatKind(x1)	weight: (/ 1 16)
isNatKind(x1)	weight: (/ 1 8) + x1
   U21(x1,x2)	weight: (/ 1 4) + x1 + x2
#a__U82(x1,x2,x3)	weight: (/ 1 4)
a__U45(x1,x2)	weight: (/ 7 16)
isNatList(x1)	weight: (/ 1 16) + x1
a__U85(x1,x2)	weight: (/ 1 4) + x2
#a__U71(x1)	weight: 0
   U11(x1,x2)	weight: (/ 5 16) + x1
#a__U92(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 16) + x1
#a__U31(x1,x2)	weight: 0
#a__U33(x1)	weight: 0
#a__U93(x1,x2,x3)	weight: 0
a__isNatIList(x1)	weight: (/ 1 16) + x1
a__U33(x1)	weight: (/ 1 4)
#a__U86(x1)	weight: 0
#a__isNatIListKind(x1)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1,x2,x3)	weight: (/ 1 8) + x1 + x2 + x3
   U91(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: (/ 1 16) + x3
   U71(x1)	weight: (/ 3 16) + x1
a__U84(x1,x2,x3)	weight: (/ 3 16) + x2
a__U86(x1)	weight: (/ 5 16) + x1
a__U44(x1,x2,x3)	weight: (/ 3 8) + x1 + x3
isNatIList(x1)	weight: (/ 1 8) + x1
#a__U43(x1,x2,x3)	weight: (/ 3 16)
   U43(x1,x2,x3)	weight: (/ 3 16) + x1 + x2 + x3
#a__U13(x1)	weight: 0
#a__U44(x1,x2,x3)	weight: (/ 1 8)
   U86(x1)	weight: (/ 3 8) + x1
   U44(x1,x2,x3)	weight: (/ 7 16)
#a__U46(x1)	weight: 0
   U84(x1,x2,x3)	weight: (/ 1 4) + x1 + x3
#a__U51(x1,x2)	weight: (/ 1 16)
   U23(x1)	weight: (/ 1 8) + x1
a__U22(x1,x2)	weight: (/ 3 16) + x1
   U93(x1,x2,x3)	weight: (/ 3 16) + x3
a__U94(x1,x2)	weight: (/ 1 8) + x1
#a__U11(x1,x2)	weight: (/ 1 8)
   U94(x1,x2)	weight: (/ 1 16) + x1 + x2
 zeros()	weight: 0
a__U31(x1,x2)	weight: (/ 1 8) + x1
a__U51(x1,x2)	weight: (/ 1 16) + x1
a__U81(x1,x2,x3)	weight: x1
   U12(x1,x2)	weight: (/ 3 8) + x1 + x2
#a__U84(x1,x2,x3)	weight: (/ 1 8)
a__isNatList(x1)	weight: 0
a__U43(x1,x2,x3)	weight: (/ 5 16)
#a__U42(x1,x2,x3)	weight: (/ 1 4)
a__U41(x1,x2,x3)	weight: (/ 3 16) + x2
#a__U12(x1,x2)	weight: (/ 1 16)
#a__U21(x1,x2)	weight: (/ 1 8)
#a__isNatIList(x1)	weight: 0
#a__U81(x1,x2,x3)	weight: (/ 5 16)
#a__U61(x1)	weight: 0
   U83(x1,x2,x3)	weight: (/ 3 16) + x1
#mark(x1)	weight: x1
     0()	weight: 0
#a__zeros()	weight: 0
a__U21(x1,x2)	weight: (/ 3 16) + x1
a__U32(x1,x2)	weight: (/ 3 16) + x1
a__U91(x1,x2,x3)	weight: (/ 3 16) + x3
   nil()	weight: 0
isNatIListKind(x1)	weight: (/ 1 16)
#a__U52(x1)	weight: 0
   U45(x1,x2)	weight: (/ 5 16) + x1
  mark(x1)	weight: (/ 1 16) + x1
a__U11(x1,x2)	weight: (/ 1 4) + x1 + x2
   U32(x1,x2)	weight: (/ 1 4) + x2
a__U42(x1,x2,x3)	weight: (/ 1 4)
a__U93(x1,x2,x3)	weight: (/ 1 8) + x1
   U33(x1)	weight: (/ 5 16) + x1
#a__U45(x1,x2)	weight: (/ 1 16)
a__U52(x1)	weight: (/ 1 8) + x1
#a__length(x1)	weight: 0
a__U12(x1,x2)	weight: (/ 5 16) + x1
a__isNatIListKind(x1)	weight: x1
 isNat(x1)	weight: (/ 1 16)
   U46(x1)	weight: (/ 1 2) + x1
   U52(x1)	weight: (/ 3 16) + x1
   U61(x1)	weight: (/ 3 8) + x1
a__U46(x1)	weight: (/ 7 16) + x1
#a__U22(x1,x2)	weight: (/ 1 16)
a__U13(x1)	weight: (/ 3 8) + x1
#a__U85(x1,x2)	weight: (/ 1 16)
   U31(x1,x2)	weight: (/ 3 16)
   U85(x1,x2)	weight: (/ 5 16) + x1
#a__U83(x1,x2,x3)	weight: (/ 3 16)
#a__isNatList(x1)	weight: 0
a__U71(x1)	weight: (/ 1 8) + x1
   U92(x1,x2,x3)	weight: (/ 5 16) + x1 + x2
  cons(x1,x2)	weight: (/ 1 16) + x1
a__U92(x1,x2,x3)	weight: (/ 1 4)
a__U61(x1)	weight: (/ 5 16) + x1
   U81(x1,x2,x3)	weight: (/ 1 16) + x1 + x2 + x3
#a__U41(x1,x2,x3)	weight: (/ 5 16)
   U82(x1,x2,x3)	weight: (/ 1 8) + x1
    tt()	weight: 0
a__isNat(x1)	weight: (/ 3 16)
   U13(x1)	weight: (/ 7 16) + x1
a__U23(x1)	weight: (/ 1 16) + x1
a__isNatKind(x1)	weight: (/ 1 16) + x1
   U22(x1,x2)	weight: (/ 1 4) + x1 + x2
   U51(x1,x2)	weight: (/ 1 8) + x1 + x2
length(x1)	weight: (/ 3 16)
   U41(x1,x2,x3)	weight: (/ 1 4) + x2
#a__U32(x1,x2)	weight: 0
a__zeros()	weight: 0
#a__U91(x1,x2,x3)	weight: 0
a__length(x1)	weight: (/ 1 8)
    Usable rules: { }
    Removed DPs: #3 #6 #8 #16 #19 #21 #23 #25 #27 #39 #48 #52 #60 #66 #77 #87 #111 #119 #121
Number of SCCs: 0, DPs: 0, edges: 0
YES