Input TRS:
    1: a__U101(tt(),M,N) -> a__U102(a__isNatKind(M),M,N)
    2: a__U102(tt(),M,N) -> a__U103(a__isNat(N),M,N)
    3: a__U103(tt(),M,N) -> a__U104(a__isNatKind(N),M,N)
    4: a__U104(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    5: a__U11(tt(),V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
    6: a__U12(tt(),V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
    7: a__U13(tt(),V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
    8: a__U14(tt(),V1,V2) -> a__U15(a__isNat(V1),V2)
    9: a__U15(tt(),V2) -> a__U16(a__isNat(V2))
    10: a__U16(tt()) -> tt()
    11: a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
    12: a__U22(tt(),V1) -> a__U23(a__isNat(V1))
    13: a__U23(tt()) -> tt()
    14: a__U31(tt(),V1,V2) -> a__U32(a__isNatKind(V1),V1,V2)
    15: a__U32(tt(),V1,V2) -> a__U33(a__isNatKind(V2),V1,V2)
    16: a__U33(tt(),V1,V2) -> a__U34(a__isNatKind(V2),V1,V2)
    17: a__U34(tt(),V1,V2) -> a__U35(a__isNat(V1),V2)
    18: a__U35(tt(),V2) -> a__U36(a__isNat(V2))
    19: a__U36(tt()) -> tt()
    20: a__U41(tt(),V2) -> a__U42(a__isNatKind(V2))
    21: a__U42(tt()) -> tt()
    22: a__U51(tt()) -> tt()
    23: a__U61(tt(),V2) -> a__U62(a__isNatKind(V2))
    24: a__U62(tt()) -> tt()
    25: a__U71(tt(),N) -> a__U72(a__isNatKind(N),N)
    26: a__U72(tt(),N) -> mark(N)
    27: a__U81(tt(),M,N) -> a__U82(a__isNatKind(M),M,N)
    28: a__U82(tt(),M,N) -> a__U83(a__isNat(N),M,N)
    29: a__U83(tt(),M,N) -> a__U84(a__isNatKind(N),M,N)
    30: a__U84(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    31: a__U91(tt(),N) -> a__U92(a__isNatKind(N))
    32: a__U92(tt()) -> 0()
    33: a__isNat(0()) -> tt()
    34: a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
    35: a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
    36: a__isNat(x(V1,V2)) -> a__U31(a__isNatKind(V1),V1,V2)
    37: a__isNatKind(0()) -> tt()
    38: a__isNatKind(plus(V1,V2)) -> a__U41(a__isNatKind(V1),V2)
    39: a__isNatKind(s(V1)) -> a__U51(a__isNatKind(V1))
    40: a__isNatKind(x(V1,V2)) -> a__U61(a__isNatKind(V1),V2)
    41: a__plus(N,0()) -> a__U71(a__isNat(N),N)
    42: a__plus(N,s(M)) -> a__U81(a__isNat(M),M,N)
    43: a__x(N,0()) -> a__U91(a__isNat(N),N)
    44: a__x(N,s(M)) -> a__U101(a__isNat(M),M,N)
    45: mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
    46: mark(U102(X1,X2,X3)) -> a__U102(mark(X1),X2,X3)
    47: mark(isNatKind(X)) -> a__isNatKind(X)
    48: mark(U103(X1,X2,X3)) -> a__U103(mark(X1),X2,X3)
    49: mark(isNat(X)) -> a__isNat(X)
    50: mark(U104(X1,X2,X3)) -> a__U104(mark(X1),X2,X3)
    51: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    52: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    53: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    54: mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
    55: mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
    56: mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
    57: mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
    58: mark(U16(X)) -> a__U16(mark(X))
    59: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    60: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
    61: mark(U23(X)) -> a__U23(mark(X))
    62: mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
    63: mark(U32(X1,X2,X3)) -> a__U32(mark(X1),X2,X3)
    64: mark(U33(X1,X2,X3)) -> a__U33(mark(X1),X2,X3)
    65: mark(U34(X1,X2,X3)) -> a__U34(mark(X1),X2,X3)
    66: mark(U35(X1,X2)) -> a__U35(mark(X1),X2)
    67: mark(U36(X)) -> a__U36(mark(X))
    68: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
    69: mark(U42(X)) -> a__U42(mark(X))
    70: mark(U51(X)) -> a__U51(mark(X))
    71: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
    72: mark(U62(X)) -> a__U62(mark(X))
    73: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
    74: mark(U72(X1,X2)) -> a__U72(mark(X1),X2)
    75: mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
    76: mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
    77: mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3)
    78: mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3)
    79: mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
    80: mark(U92(X)) -> a__U92(mark(X))
    81: mark(tt()) -> tt()
    82: mark(s(X)) -> s(mark(X))
    83: mark(0()) -> 0()
    84: a__U101(X1,X2,X3) -> U101(X1,X2,X3)
    85: a__U102(X1,X2,X3) -> U102(X1,X2,X3)
    86: a__isNatKind(X) -> isNatKind(X)
    87: a__U103(X1,X2,X3) -> U103(X1,X2,X3)
    88: a__isNat(X) -> isNat(X)
    89: a__U104(X1,X2,X3) -> U104(X1,X2,X3)
    90: a__plus(X1,X2) -> plus(X1,X2)
    91: a__x(X1,X2) -> x(X1,X2)
    92: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    93: a__U12(X1,X2,X3) -> U12(X1,X2,X3)
    94: a__U13(X1,X2,X3) -> U13(X1,X2,X3)
    95: a__U14(X1,X2,X3) -> U14(X1,X2,X3)
    96: a__U15(X1,X2) -> U15(X1,X2)
    97: a__U16(X) -> U16(X)
    98: a__U21(X1,X2) -> U21(X1,X2)
    99: a__U22(X1,X2) -> U22(X1,X2)
    100: a__U23(X) -> U23(X)
    101: a__U31(X1,X2,X3) -> U31(X1,X2,X3)
    102: a__U32(X1,X2,X3) -> U32(X1,X2,X3)
    103: a__U33(X1,X2,X3) -> U33(X1,X2,X3)
    104: a__U34(X1,X2,X3) -> U34(X1,X2,X3)
    105: a__U35(X1,X2) -> U35(X1,X2)
    106: a__U36(X) -> U36(X)
    107: a__U41(X1,X2) -> U41(X1,X2)
    108: a__U42(X) -> U42(X)
    109: a__U51(X) -> U51(X)
    110: a__U61(X1,X2) -> U61(X1,X2)
    111: a__U62(X) -> U62(X)
    112: a__U71(X1,X2) -> U71(X1,X2)
    113: a__U72(X1,X2) -> U72(X1,X2)
    114: a__U81(X1,X2,X3) -> U81(X1,X2,X3)
    115: a__U82(X1,X2,X3) -> U82(X1,X2,X3)
    116: a__U83(X1,X2,X3) -> U83(X1,X2,X3)
    117: a__U84(X1,X2,X3) -> U84(X1,X2,X3)
    118: a__U91(X1,X2) -> U91(X1,X2)
    119: a__U92(X) -> U92(X)
Number of strict rules: 119
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U102(tt(),M,N) -> #a__U103(a__isNat(N),M,N)
   #2: #a__U102(tt(),M,N) -> #a__isNat(N)
   #3: #a__x(N,0()) -> #a__U91(a__isNat(N),N)
   #4: #a__x(N,0()) -> #a__isNat(N)
   #5: #a__U83(tt(),M,N) -> #a__U84(a__isNatKind(N),M,N)
   #6: #a__U83(tt(),M,N) -> #a__isNatKind(N)
   #7: #a__isNat(s(V1)) -> #a__U21(a__isNatKind(V1),V1)
   #8: #a__isNat(s(V1)) -> #a__isNatKind(V1)
   #9: #mark(U35(X1,X2)) -> #a__U35(mark(X1),X2)
   #10: #mark(U35(X1,X2)) -> #mark(X1)
   #11: #mark(U102(X1,X2,X3)) -> #a__U102(mark(X1),X2,X3)
   #12: #mark(U102(X1,X2,X3)) -> #mark(X1)
   #13: #a__plus(N,s(M)) -> #a__U81(a__isNat(M),M,N)
   #14: #a__plus(N,s(M)) -> #a__isNat(M)
   #15: #a__plus(N,0()) -> #a__U71(a__isNat(N),N)
   #16: #a__plus(N,0()) -> #a__isNat(N)
   #17: #mark(U71(X1,X2)) -> #a__U71(mark(X1),X2)
   #18: #mark(U71(X1,X2)) -> #mark(X1)
   #19: #mark(isNatKind(X)) -> #a__isNatKind(X)
   #20: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3)
   #21: #mark(U11(X1,X2,X3)) -> #mark(X1)
   #22: #mark(U61(X1,X2)) -> #a__U61(mark(X1),X2)
   #23: #mark(U61(X1,X2)) -> #mark(X1)
   #24: #mark(U103(X1,X2,X3)) -> #a__U103(mark(X1),X2,X3)
   #25: #mark(U103(X1,X2,X3)) -> #mark(X1)
   #26: #mark(U81(X1,X2,X3)) -> #a__U81(mark(X1),X2,X3)
   #27: #mark(U81(X1,X2,X3)) -> #mark(X1)
   #28: #mark(U72(X1,X2)) -> #a__U72(mark(X1),X2)
   #29: #mark(U72(X1,X2)) -> #mark(X1)
   #30: #mark(U16(X)) -> #a__U16(mark(X))
   #31: #mark(U16(X)) -> #mark(X)
   #32: #mark(U23(X)) -> #a__U23(mark(X))
   #33: #mark(U23(X)) -> #mark(X)
   #34: #a__isNatKind(plus(V1,V2)) -> #a__U41(a__isNatKind(V1),V2)
   #35: #a__isNatKind(plus(V1,V2)) -> #a__isNatKind(V1)
   #36: #a__U12(tt(),V1,V2) -> #a__U13(a__isNatKind(V2),V1,V2)
   #37: #a__U12(tt(),V1,V2) -> #a__isNatKind(V2)
   #38: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2)
   #39: #mark(U21(X1,X2)) -> #mark(X1)
   #40: #mark(U13(X1,X2,X3)) -> #a__U13(mark(X1),X2,X3)
   #41: #mark(U13(X1,X2,X3)) -> #mark(X1)
   #42: #mark(U36(X)) -> #a__U36(mark(X))
   #43: #mark(U36(X)) -> #mark(X)
   #44: #a__isNatKind(x(V1,V2)) -> #a__U61(a__isNatKind(V1),V2)
   #45: #a__isNatKind(x(V1,V2)) -> #a__isNatKind(V1)
   #46: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #47: #mark(plus(X1,X2)) -> #mark(X1)
   #48: #mark(plus(X1,X2)) -> #mark(X2)
   #49: #a__U15(tt(),V2) -> #a__U16(a__isNat(V2))
   #50: #a__U15(tt(),V2) -> #a__isNat(V2)
   #51: #a__U21(tt(),V1) -> #a__U22(a__isNatKind(V1),V1)
   #52: #a__U21(tt(),V1) -> #a__isNatKind(V1)
   #53: #mark(U15(X1,X2)) -> #a__U15(mark(X1),X2)
   #54: #mark(U15(X1,X2)) -> #mark(X1)
   #55: #mark(U82(X1,X2,X3)) -> #a__U82(mark(X1),X2,X3)
   #56: #mark(U82(X1,X2,X3)) -> #mark(X1)
   #57: #mark(U51(X)) -> #a__U51(mark(X))
   #58: #mark(U51(X)) -> #mark(X)
   #59: #a__U61(tt(),V2) -> #a__U62(a__isNatKind(V2))
   #60: #a__U61(tt(),V2) -> #a__isNatKind(V2)
   #61: #mark(U84(X1,X2,X3)) -> #a__U84(mark(X1),X2,X3)
   #62: #mark(U84(X1,X2,X3)) -> #mark(X1)
   #63: #mark(U101(X1,X2,X3)) -> #a__U101(mark(X1),X2,X3)
   #64: #mark(U101(X1,X2,X3)) -> #mark(X1)
   #65: #mark(U42(X)) -> #a__U42(mark(X))
   #66: #mark(U42(X)) -> #mark(X)
   #67: #a__U22(tt(),V1) -> #a__U23(a__isNat(V1))
   #68: #a__U22(tt(),V1) -> #a__isNat(V1)
   #69: #a__U91(tt(),N) -> #a__U92(a__isNatKind(N))
   #70: #a__U91(tt(),N) -> #a__isNatKind(N)
   #71: #mark(U91(X1,X2)) -> #a__U91(mark(X1),X2)
   #72: #mark(U91(X1,X2)) -> #mark(X1)
   #73: #mark(U14(X1,X2,X3)) -> #a__U14(mark(X1),X2,X3)
   #74: #mark(U14(X1,X2,X3)) -> #mark(X1)
   #75: #mark(s(X)) -> #mark(X)
   #76: #a__U31(tt(),V1,V2) -> #a__U32(a__isNatKind(V1),V1,V2)
   #77: #a__U31(tt(),V1,V2) -> #a__isNatKind(V1)
   #78: #mark(U31(X1,X2,X3)) -> #a__U31(mark(X1),X2,X3)
   #79: #mark(U31(X1,X2,X3)) -> #mark(X1)
   #80: #a__U84(tt(),M,N) -> #a__plus(mark(N),mark(M))
   #81: #a__U84(tt(),M,N) -> #mark(N)
   #82: #a__U84(tt(),M,N) -> #mark(M)
   #83: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #84: #mark(x(X1,X2)) -> #mark(X1)
   #85: #mark(x(X1,X2)) -> #mark(X2)
   #86: #mark(isNat(X)) -> #a__isNat(X)
   #87: #a__U71(tt(),N) -> #a__U72(a__isNatKind(N),N)
   #88: #a__U71(tt(),N) -> #a__isNatKind(N)
   #89: #a__U41(tt(),V2) -> #a__U42(a__isNatKind(V2))
   #90: #a__U41(tt(),V2) -> #a__isNatKind(V2)
   #91: #a__U13(tt(),V1,V2) -> #a__U14(a__isNatKind(V2),V1,V2)
   #92: #a__U13(tt(),V1,V2) -> #a__isNatKind(V2)
   #93: #a__isNatKind(s(V1)) -> #a__U51(a__isNatKind(V1))
   #94: #a__isNatKind(s(V1)) -> #a__isNatKind(V1)
   #95: #mark(U33(X1,X2,X3)) -> #a__U33(mark(X1),X2,X3)
   #96: #mark(U33(X1,X2,X3)) -> #mark(X1)
   #97: #mark(U62(X)) -> #a__U62(mark(X))
   #98: #mark(U62(X)) -> #mark(X)
   #99: #a__U11(tt(),V1,V2) -> #a__U12(a__isNatKind(V1),V1,V2)
   #100: #a__U11(tt(),V1,V2) -> #a__isNatKind(V1)
   #101: #a__x(N,s(M)) -> #a__U101(a__isNat(M),M,N)
   #102: #a__x(N,s(M)) -> #a__isNat(M)
   #103: #mark(U34(X1,X2,X3)) -> #a__U34(mark(X1),X2,X3)
   #104: #mark(U34(X1,X2,X3)) -> #mark(X1)
   #105: #a__U82(tt(),M,N) -> #a__U83(a__isNat(N),M,N)
   #106: #a__U82(tt(),M,N) -> #a__isNat(N)
   #107: #a__isNat(plus(V1,V2)) -> #a__U11(a__isNatKind(V1),V1,V2)
   #108: #a__isNat(plus(V1,V2)) -> #a__isNatKind(V1)
   #109: #a__U81(tt(),M,N) -> #a__U82(a__isNatKind(M),M,N)
   #110: #a__U81(tt(),M,N) -> #a__isNatKind(M)
   #111: #mark(U22(X1,X2)) -> #a__U22(mark(X1),X2)
   #112: #mark(U22(X1,X2)) -> #mark(X1)
   #113: #a__U34(tt(),V1,V2) -> #a__U35(a__isNat(V1),V2)
   #114: #a__U34(tt(),V1,V2) -> #a__isNat(V1)
   #115: #mark(U32(X1,X2,X3)) -> #a__U32(mark(X1),X2,X3)
   #116: #mark(U32(X1,X2,X3)) -> #mark(X1)
   #117: #a__U72(tt(),N) -> #mark(N)
   #118: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2)
   #119: #mark(U41(X1,X2)) -> #mark(X1)
   #120: #a__isNat(x(V1,V2)) -> #a__U31(a__isNatKind(V1),V1,V2)
   #121: #a__isNat(x(V1,V2)) -> #a__isNatKind(V1)
   #122: #a__U33(tt(),V1,V2) -> #a__U34(a__isNatKind(V2),V1,V2)
   #123: #a__U33(tt(),V1,V2) -> #a__isNatKind(V2)
   #124: #a__U103(tt(),M,N) -> #a__U104(a__isNatKind(N),M,N)
   #125: #a__U103(tt(),M,N) -> #a__isNatKind(N)
   #126: #mark(U83(X1,X2,X3)) -> #a__U83(mark(X1),X2,X3)
   #127: #mark(U83(X1,X2,X3)) -> #mark(X1)
   #128: #a__U101(tt(),M,N) -> #a__U102(a__isNatKind(M),M,N)
   #129: #a__U101(tt(),M,N) -> #a__isNatKind(M)
   #130: #mark(U12(X1,X2,X3)) -> #a__U12(mark(X1),X2,X3)
   #131: #mark(U12(X1,X2,X3)) -> #mark(X1)
   #132: #a__U14(tt(),V1,V2) -> #a__U15(a__isNat(V1),V2)
   #133: #a__U14(tt(),V1,V2) -> #a__isNat(V1)
   #134: #a__U32(tt(),V1,V2) -> #a__U33(a__isNatKind(V2),V1,V2)
   #135: #a__U32(tt(),V1,V2) -> #a__isNatKind(V2)
   #136: #a__U104(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #137: #a__U104(tt(),M,N) -> #a__x(mark(N),mark(M))
   #138: #a__U104(tt(),M,N) -> #mark(N)
   #139: #a__U104(tt(),M,N) -> #mark(M)
   #140: #a__U104(tt(),M,N) -> #mark(N)
   #141: #mark(U92(X)) -> #a__U92(mark(X))
   #142: #mark(U92(X)) -> #mark(X)
   #143: #mark(U104(X1,X2,X3)) -> #a__U104(mark(X1),X2,X3)
   #144: #mark(U104(X1,X2,X3)) -> #mark(X1)
   #145: #a__U35(tt(),V2) -> #a__U36(a__isNat(V2))
   #146: #a__U35(tt(),V2) -> #a__isNat(V2)
Number of SCCs: 3, DPs: 92, edges: 2203
	SCC { #34 #35 #44 #45 #60 #90 #94 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
a__U83(x1,x2,x3)	weight: 0
#a__isNatKind(x1)	weight: x1
isNatKind(x1)	weight: (/ 1 4) + x1
a__plus(x1,x2)	weight: 0
   U16(x1)	weight: 0
   U21(x1,x2)	weight: 0
a__U102(x1,x2,x3)	weight: 0
#a__U82(x1,x2,x3)	weight: 0
#a__U15(x1,x2)	weight: 0
#a__U72(x1,x2)	weight: 0
#a__U71(x1,x2)	weight: 0
   U11(x1,x2,x3)	weight: 0
#a__U92(x1)	weight: 0
a__U104(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 1 8) + x1
#a__U31(x1,x2,x3)	weight: 0
#a__U33(x1,x2,x3)	weight: 0
a__U33(x1,x2,x3)	weight: 0
#a__U23(x1)	weight: 0
   U42(x1)	weight: (/ 3 8) + x1
   U91(x1,x2)	weight: 0
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: 0
#a__U14(x1,x2,x3)	weight: 0
   U71(x1,x2)	weight: 0
a__U84(x1,x2,x3)	weight: 0
a__U62(x1)	weight: (/ 3 8)
  U101(x1,x2,x3)	weight: 0
#a__U13(x1,x2,x3)	weight: 0
  U103(x1,x2,x3)	weight: 0
#a__U103(x1,x2,x3)	weight: 0
   U84(x1,x2,x3)	weight: 0
#a__U51(x1)	weight: 0
   U23(x1)	weight: 0
   U35(x1,x2)	weight: 0
#a__x(x1,x2)	weight: 0
a__U22(x1,x2)	weight: 0
   U72(x1,x2)	weight: 0
#a__U11(x1,x2,x3)	weight: 0
   U34(x1,x2,x3)	weight: 0
a__U31(x1,x2,x3)	weight: 0
a__U51(x1)	weight: (/ 1 4)
a__U81(x1,x2,x3)	weight: 0
  a__x(x1,x2)	weight: 0
   U12(x1,x2,x3)	weight: 0
#a__U84(x1,x2,x3)	weight: 0
#a__U62(x1)	weight: 0
a__U16(x1)	weight: 0
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: (/ 1 8) + x1 + x2
     x(x1,x2)	weight: (/ 1 4) + x1 + x2
#a__U12(x1,x2,x3)	weight: 0
  U104(x1,x2,x3)	weight: 0
a__U14(x1,x2,x3)	weight: 0
#a__U21(x1,x2)	weight: 0
#a__U81(x1,x2,x3)	weight: 0
#a__U61(x1,x2)	weight: (/ 1 8) + x2
a__U34(x1,x2,x3)	weight: 0
#a__plus(x1,x2)	weight: 0
   U83(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
a__U21(x1,x2)	weight: 0
   U36(x1)	weight: 0
a__U32(x1,x2,x3)	weight: 0
a__U91(x1,x2)	weight: 0
a__U36(x1)	weight: 0
   U62(x1)	weight: (/ 1 2) + x1
#a__U102(x1,x2,x3)	weight: 0
  mark(x1)	weight: 0
a__U72(x1,x2)	weight: 0
#a__U101(x1,x2,x3)	weight: 0
a__U11(x1,x2,x3)	weight: 0
#a__U36(x1)	weight: 0
   U32(x1,x2,x3)	weight: 0
a__U42(x1)	weight: (/ 1 4)
   U33(x1,x2,x3)	weight: 0
   U14(x1,x2,x3)	weight: 0
a__U12(x1,x2,x3)	weight: 0
#a__U104(x1,x2,x3)	weight: 0
 isNat(x1)	weight: 0
a__U35(x1,x2)	weight: 0
  plus(x1,x2)	weight: (/ 1 4) + x1 + x2
   U15(x1,x2)	weight: 0
   U61(x1,x2)	weight: (/ 3 8) + x1 + x2
#a__U35(x1,x2)	weight: 0
#a__U22(x1,x2)	weight: 0
a__U13(x1,x2,x3)	weight: 0
   U31(x1,x2,x3)	weight: 0
#a__U83(x1,x2,x3)	weight: 0
a__U71(x1,x2)	weight: 0
   U92(x1)	weight: 0
a__U92(x1)	weight: 0
a__U61(x1,x2)	weight: (/ 1 4)
  U102(x1,x2,x3)	weight: 0
   U81(x1,x2,x3)	weight: 0
#a__U41(x1,x2)	weight: (/ 1 8) + x2
a__U15(x1,x2)	weight: 0
   U82(x1,x2,x3)	weight: 0
#a__U16(x1)	weight: 0
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U13(x1,x2,x3)	weight: 0
a__U23(x1)	weight: 0
a__isNatKind(x1)	weight: (/ 1 8)
   U22(x1,x2)	weight: 0
   U51(x1)	weight: (/ 3 8) + x1
#a__U34(x1,x2,x3)	weight: 0
a__U103(x1,x2,x3)	weight: 0
   U41(x1,x2)	weight: (/ 1 4)
#a__U32(x1,x2,x3)	weight: 0
a__U101(x1,x2,x3)	weight: 0
#a__U91(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #34 #35 #44 #45 #60 #90 #94
Number of SCCs: 2, DPs: 85, edges: 2176
	SCC { #7 #36 #50 #51 #68 #76 #91 #99 #107 #113 #114 #120 #122 #132..134 #146 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
a__U83(x1,x2,x3)	weight: 0
#a__isNatKind(x1)	weight: 0
isNatKind(x1)	weight: (/ 1 16)
a__plus(x1,x2)	weight: 0
   U16(x1)	weight: (/ 1 2) + x1
   U21(x1,x2)	weight: (/ 3 16)
a__U102(x1,x2,x3)	weight: 0
#a__U82(x1,x2,x3)	weight: 0
#a__U15(x1,x2)	weight: (/ 1 16) + x2
#a__U72(x1,x2)	weight: 0
#a__U71(x1,x2)	weight: 0
   U11(x1,x2,x3)	weight: (/ 3 16) + x1 + x2 + x3
#a__U92(x1)	weight: 0
a__U104(x1,x2,x3)	weight: 0
     s(x1)	weight: (/ 3 16) + x1
#a__U31(x1,x2,x3)	weight: (/ 5 16) + x2 + x3
#a__U33(x1,x2,x3)	weight: (/ 3 16) + x2 + x3
a__U33(x1,x2,x3)	weight: (/ 1 4) + x3
#a__U23(x1)	weight: 0
   U42(x1)	weight: 0
   U91(x1,x2)	weight: 0
#a__isNat(x1)	weight: x1
a__U82(x1,x2,x3)	weight: 0
#a__U14(x1,x2,x3)	weight: (/ 1 8) + x2 + x3
   U71(x1,x2)	weight: 0
a__U84(x1,x2,x3)	weight: 0
a__U62(x1)	weight: (/ 1 16)
  U101(x1,x2,x3)	weight: 0
#a__U13(x1,x2,x3)	weight: (/ 3 16) + x2 + x3
  U103(x1,x2,x3)	weight: 0
#a__U103(x1,x2,x3)	weight: 0
   U84(x1,x2,x3)	weight: 0
#a__U51(x1)	weight: 0
   U23(x1)	weight: (/ 5 16) + x1
   U35(x1,x2)	weight: (/ 7 16) + x2
#a__x(x1,x2)	weight: 0
a__U22(x1,x2)	weight: (/ 3 16)
   U72(x1,x2)	weight: 0
#a__U11(x1,x2,x3)	weight: (/ 5 16) + x2 + x3
   U34(x1,x2,x3)	weight: (/ 3 8)
a__U31(x1,x2,x3)	weight: (/ 1 8) + x3
a__U51(x1)	weight: (/ 1 16)
a__U81(x1,x2,x3)	weight: 0
  a__x(x1,x2)	weight: 0
   U12(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
#a__U84(x1,x2,x3)	weight: 0
#a__U62(x1)	weight: 0
a__U16(x1)	weight: (/ 7 16)
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: x1
     x(x1,x2)	weight: (/ 3 8) + x1 + x2
#a__U12(x1,x2,x3)	weight: (/ 1 4) + x2 + x3
  U104(x1,x2,x3)	weight: 0
a__U14(x1,x2,x3)	weight: (/ 5 16)
#a__U21(x1,x2)	weight: (/ 1 8) + x2
#a__U81(x1,x2,x3)	weight: 0
#a__U61(x1,x2)	weight: (/ 1 16)
a__U34(x1,x2,x3)	weight: (/ 5 16) + x2 + x3
#a__plus(x1,x2)	weight: 0
   U83(x1,x2,x3)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
a__U21(x1,x2)	weight: (/ 1 8) + x2
   U36(x1)	weight: (/ 7 16)
a__U32(x1,x2,x3)	weight: (/ 3 16) + x3
a__U91(x1,x2)	weight: 0
a__U36(x1)	weight: (/ 3 8) + x1
   U62(x1)	weight: (/ 1 16)
#a__U102(x1,x2,x3)	weight: 0
  mark(x1)	weight: 0
a__U72(x1,x2)	weight: 0
#a__U101(x1,x2,x3)	weight: 0
a__U11(x1,x2,x3)	weight: (/ 1 8)
#a__U36(x1)	weight: 0
   U32(x1,x2,x3)	weight: (/ 1 4) + x1
a__U42(x1)	weight: 0
   U33(x1,x2,x3)	weight: (/ 5 16) + x1
   U14(x1,x2,x3)	weight: (/ 3 8) + x1 + x2 + x3
a__U12(x1,x2,x3)	weight: (/ 3 16)
#a__U104(x1,x2,x3)	weight: 0
 isNat(x1)	weight: (/ 1 8) + x1
a__U35(x1,x2)	weight: (/ 3 8)
  plus(x1,x2)	weight: (/ 3 8) + x1 + x2
   U15(x1,x2)	weight: (/ 7 16) + x1
   U61(x1,x2)	weight: (/ 1 16)
#a__U35(x1,x2)	weight: (/ 1 16) + x2
#a__U22(x1,x2)	weight: (/ 1 16) + x2
a__U13(x1,x2,x3)	weight: (/ 1 4) + x2 + x3
   U31(x1,x2,x3)	weight: (/ 3 16) + x1 + x2
#a__U83(x1,x2,x3)	weight: 0
a__U71(x1,x2)	weight: 0
   U92(x1)	weight: 0
a__U92(x1)	weight: 0
a__U61(x1,x2)	weight: (/ 1 16)
  U102(x1,x2,x3)	weight: 0
   U81(x1,x2,x3)	weight: 0
#a__U41(x1,x2)	weight: (/ 1 16)
a__U15(x1,x2)	weight: (/ 3 8) + x2
   U82(x1,x2,x3)	weight: 0
#a__U16(x1)	weight: 0
    tt()	weight: 0
a__isNat(x1)	weight: (/ 1 16)
   U13(x1,x2,x3)	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)	weight: (/ 1 16)
#a__U34(x1,x2,x3)	weight: (/ 1 8) + x2 + x3
a__U103(x1,x2,x3)	weight: 0
   U41(x1,x2)	weight: 0
#a__U32(x1,x2,x3)	weight: (/ 1 4) + x2 + x3
a__U101(x1,x2,x3)	weight: 0
#a__U91(x1,x2)	weight: 0
    Usable rules: { 20..24 37..40 86 107..111 }
    Removed DPs: #7 #36 #50 #51 #68 #76 #91 #99 #107 #113 #114 #120 #122 #132..134 #146
Number of SCCs: 1, DPs: 68, edges: 2147
	SCC { #1 #5 #10..13 #15 #17 #18 #21 #23..29 #31 #33 #39 #41 #43 #46..48 #54..56 #58 #61..64 #66 #72 #74 #75 #79..85 #87 #96 #98 #101 #104 #105 #109 #112 #116 #117 #119 #124 #126..128 #131 #136..140 #142..144 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
a__U83(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 4) + x1}
#a__isNatKind(x1)	weight: 0
isNatKind(x1)	weight: 0
a__plus(x1,x2)	weight: max{(/ 1 2) + x2, x1}
   U16(x1)	weight: x1
   U21(x1,x2)	weight: max{0, x1}
a__U102(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U82(x1,x2,x3)	weight: max{0, x3, (/ 1 2) + x2}
#a__U15(x1,x2)	weight: 0
#a__U72(x1,x2)	weight: max{0, x2}
#a__U71(x1,x2)	weight: max{0, x2}
   U11(x1,x2,x3)	weight: max{0, x1}
#a__U92(x1)	weight: 0
a__U104(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
     s(x1)	weight: x1
#a__U31(x1,x2,x3)	weight: 0
#a__U33(x1,x2,x3)	weight: 0
a__U33(x1,x2,x3)	weight: max{0, x1}
#a__U23(x1)	weight: 0
   U42(x1)	weight: x1
   U91(x1,x2)	weight: max{0, (/ 1 4) + x1}
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 4) + x1}
#a__U14(x1,x2,x3)	weight: 0
   U71(x1,x2)	weight: max{x2, (/ 1 4) + x1}
a__U84(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 2) + x1}
a__U62(x1)	weight: x1
  U101(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U13(x1,x2,x3)	weight: 0
  U103(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U103(x1,x2,x3)	weight: max{0, (/ 1 2) + x3, (/ 1 2) + x2}
   U84(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U51(x1)	weight: 0
   U23(x1)	weight: x1
   U35(x1,x2)	weight: max{0, x1}
#a__x(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 2) + x1}
a__U22(x1,x2)	weight: max{0, x1}
   U72(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#a__U11(x1,x2,x3)	weight: 0
   U34(x1,x2,x3)	weight: max{0, x1}
a__U31(x1,x2,x3)	weight: max{0, x1}
a__U51(x1)	weight: x1
a__U81(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 2) + x1}
  a__x(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 2) + x1}
   U12(x1,x2,x3)	weight: max{0, x1}
#a__U84(x1,x2,x3)	weight: max{0, x3, (/ 1 2) + x2}
#a__U62(x1)	weight: 0
a__U16(x1)	weight: x1
#a__U42(x1)	weight: 0
a__U41(x1,x2)	weight: max{0, x1}
     x(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 2) + x1}
#a__U12(x1,x2,x3)	weight: 0
  U104(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
a__U14(x1,x2,x3)	weight: max{0, x1}
#a__U21(x1,x2)	weight: 0
#a__U81(x1,x2,x3)	weight: max{0, x3, (/ 1 2) + x2}
#a__U61(x1,x2)	weight: 0
a__U34(x1,x2,x3)	weight: max{0, x1}
#a__plus(x1,x2)	weight: max{(/ 1 2) + x2, x1}
   U83(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 4) + x1}
#mark(x1)	weight: x1
     0()	weight: 0
a__U21(x1,x2)	weight: max{0, x1}
   U36(x1)	weight: x1
a__U32(x1,x2,x3)	weight: max{0, x1}
a__U91(x1,x2)	weight: max{0, (/ 1 4) + x1}
a__U36(x1)	weight: x1
   U62(x1)	weight: x1
#a__U102(x1,x2,x3)	weight: max{0, (/ 1 2) + x3, (/ 1 2) + x2}
  mark(x1)	weight: x1
a__U72(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#a__U101(x1,x2,x3)	weight: max{0, (/ 1 2) + x3, (/ 1 2) + x2}
a__U11(x1,x2,x3)	weight: max{0, x1}
#a__U36(x1)	weight: 0
   U32(x1,x2,x3)	weight: max{0, x1}
a__U42(x1)	weight: x1
   U33(x1,x2,x3)	weight: max{0, x1}
   U14(x1,x2,x3)	weight: max{0, x1}
a__U12(x1,x2,x3)	weight: max{0, x1}
#a__U104(x1,x2,x3)	weight: max{0, (/ 1 2) + x3, (/ 1 2) + x2}
 isNat(x1)	weight: 0
a__U35(x1,x2)	weight: max{0, x1}
  plus(x1,x2)	weight: max{(/ 1 2) + x2, x1}
   U15(x1,x2)	weight: max{0, x1}
   U61(x1,x2)	weight: max{0, x1}
#a__U35(x1,x2)	weight: 0
#a__U22(x1,x2)	weight: 0
a__U13(x1,x2,x3)	weight: max{0, x1}
   U31(x1,x2,x3)	weight: max{0, x1}
#a__U83(x1,x2,x3)	weight: max{0, x3, (/ 1 2) + x2}
a__U71(x1,x2)	weight: max{x2, (/ 1 4) + x1}
   U92(x1)	weight: (/ 1 4) + x1
a__U92(x1)	weight: (/ 1 4) + x1
a__U61(x1,x2)	weight: max{0, x1}
  U102(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
   U81(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U41(x1,x2)	weight: 0
a__U15(x1,x2)	weight: max{0, x1}
   U82(x1,x2,x3)	weight: max{x3, (/ 1 2) + x2, (/ 1 4) + x1}
#a__U16(x1)	weight: 0
    tt()	weight: 0
a__isNat(x1)	weight: 0
   U13(x1,x2,x3)	weight: max{0, x1}
a__U23(x1)	weight: x1
a__isNatKind(x1)	weight: 0
   U22(x1,x2)	weight: max{0, x1}
   U51(x1)	weight: x1
#a__U34(x1,x2,x3)	weight: 0
a__U103(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
   U41(x1,x2)	weight: max{0, x1}
#a__U32(x1,x2,x3)	weight: 0
a__U101(x1,x2,x3)	weight: max{(/ 1 2) + x3, (/ 1 2) + x2, (/ 1 2) + x1}
#a__U91(x1,x2)	weight: 0
    Usable rules: { 1..119 }
    Removed DPs: #12 #18 #25 #27 #29 #48 #56 #62 #64 #72 #82 #84 #85 #127 #138..140 #142 #144
Number of SCCs: 1, DPs: 49, edges: 848
	SCC { #1 #5 #10 #11 #13 #15 #17 #21 #23 #24 #26 #28 #31 #33 #39 #41 #43 #46 #47 #54 #55 #58 #61 #63 #66 #74 #75 #79..81 #83 #87 #96 #98 #101 #104 #105 #109 #112 #116 #117 #119 #124 #126 #128 #131 #136 #137 #143 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
a__U83(x1,x2,x3)	weight: max{0, x3, (/ 13 64) + x2}
#a__isNatKind(x1)	weight: 0
isNatKind(x1)	weight: x1
a__plus(x1,x2)	weight: max{(/ 13 64) + x2, x1}
   U16(x1)	weight: (/ 1 64) + x1
   U21(x1,x2)	weight: max{(/ 1 8) + x2, (/ 7 64) + x1}
a__U102(x1,x2,x3)	weight: max{(/ 13 64) + x3, (/ 11 64) + x2, (/ 11 64) + x1}
#a__U82(x1,x2,x3)	weight: max{(/ 1 16) + x3, (/ 17 64) + x2, (/ 3 64) + x1}
#a__U15(x1,x2)	weight: 0
#a__U72(x1,x2)	weight: max{(/ 1 16) + x2, (/ 1 64) + x1}
#a__U71(x1,x2)	weight: max{0, (/ 1 16) + x2}
   U11(x1,x2,x3)	weight: max{(/ 9 64) + x3, (/ 1 8) + x2, (/ 1 8) + x1}
#a__U92(x1)	weight: 0
a__U104(x1,x2,x3)	weight: max{(/ 13 64) + x3, (/ 11 64) + x2, (/ 5 32) + x1}
     s(x1)	weight: x1
#a__U31(x1,x2,x3)	weight: 0
#a__U33(x1,x2,x3)	weight: 0
a__U33(x1,x2,x3)	weight: max{(/ 17 64) + x3, (/ 17 64) + x2, (/ 1 64) + x1}
#a__U23(x1)	weight: 0
   U42(x1)	weight: (/ 1 64) + x1
   U91(x1,x2)	weight: max{0, (/ 1 64) + x1}
#a__isNat(x1)	weight: 0
a__U82(x1,x2,x3)	weight: max{x3, (/ 13 64) + x2, (/ 1 64) + x1}
#a__U14(x1,x2,x3)	weight: 0
   U71(x1,x2)	weight: max{0, x2}
a__U84(x1,x2,x3)	weight: max{x3, (/ 13 64) + x2, x1}
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    Usable rules: { 1..119 }
    Removed DPs: #10 #21 #23 #31 #39 #41 #43 #66 #74 #79 #96 #98 #104 #112 #116 #131
Number of SCCs: 1, DPs: 33, edges: 176
	SCC { #1 #5 #11 #13 #15 #17 #24 #26 #28 #33 #46 #47 #54 #55 #58 #61 #63 #75 #80 #81 #83 #87 #101 #105 #109 #117 #119 #124 #126 #128 #136 #137 #143 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
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    Usable rules: { }
    Removed DPs: #33 #54 #58 #119
Number of SCCs: 1, DPs: 5, edges: 5
	SCC { #5 #13 #80 #105 #109 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... succeeded.
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