/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
Input TRS:
    1: U101(tt(),M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N))
    2: U102(tt(),M,N) -> U103(isNat(activate(N)),activate(M),activate(N))
    3: U103(tt(),M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N))
    4: U104(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
    5: U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
    6: U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
    7: U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
    8: U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
    9: U15(tt(),V2) -> U16(isNat(activate(V2)))
    10: U16(tt()) -> tt()
    11: U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
    12: U22(tt(),V1) -> U23(isNat(activate(V1)))
    13: U23(tt()) -> tt()
    14: U31(tt(),V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2))
    15: U32(tt(),V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2))
    16: U33(tt(),V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2))
    17: U34(tt(),V1,V2) -> U35(isNat(activate(V1)),activate(V2))
    18: U35(tt(),V2) -> U36(isNat(activate(V2)))
    19: U36(tt()) -> tt()
    20: U41(tt(),V2) -> U42(isNatKind(activate(V2)))
    21: U42(tt()) -> tt()
    22: U51(tt()) -> tt()
    23: U61(tt(),V2) -> U62(isNatKind(activate(V2)))
    24: U62(tt()) -> tt()
    25: U71(tt(),N) -> U72(isNatKind(activate(N)),activate(N))
    26: U72(tt(),N) -> activate(N)
    27: U81(tt(),M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N))
    28: U82(tt(),M,N) -> U83(isNat(activate(N)),activate(M),activate(N))
    29: U83(tt(),M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N))
    30: U84(tt(),M,N) -> s(plus(activate(N),activate(M)))
    31: U91(tt(),N) -> U92(isNatKind(activate(N)))
    32: U92(tt()) -> 0()
    33: isNat(n__0()) -> tt()
    34: isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
    35: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
    36: isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2))
    37: isNatKind(n__0()) -> tt()
    38: isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2))
    39: isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1)))
    40: isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2))
    41: plus(N,0()) -> U71(isNat(N),N)
    42: plus(N,s(M)) -> U81(isNat(M),M,N)
    43: x(N,0()) -> U91(isNat(N),N)
    44: x(N,s(M)) -> U101(isNat(M),M,N)
    45: 0() -> n__0()
    46: plus(X1,X2) -> n__plus(X1,X2)
    47: s(X) -> n__s(X)
    48: x(X1,X2) -> n__x(X1,X2)
    49: activate(n__0()) -> 0()
    50: activate(n__plus(X1,X2)) -> plus(X1,X2)
    51: activate(n__s(X)) -> s(X)
    52: activate(n__x(X1,X2)) -> x(X1,X2)
    53: activate(X) -> X
Number of strict rules: 53
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U102(tt(),M,N) -> #U103(isNat(activate(N)),activate(M),activate(N))
   #2: #U102(tt(),M,N) -> #isNat(activate(N))
   #3: #U102(tt(),M,N) -> #activate(N)
   #4: #U102(tt(),M,N) -> #activate(M)
   #5: #U102(tt(),M,N) -> #activate(N)
   #6: #x(N,0()) -> #U91(isNat(N),N)
   #7: #x(N,0()) -> #isNat(N)
   #8: #U83(tt(),M,N) -> #U84(isNatKind(activate(N)),activate(M),activate(N))
   #9: #U83(tt(),M,N) -> #isNatKind(activate(N))
   #10: #U83(tt(),M,N) -> #activate(N)
   #11: #U83(tt(),M,N) -> #activate(M)
   #12: #U83(tt(),M,N) -> #activate(N)
   #13: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1))
   #14: #isNat(n__s(V1)) -> #isNatKind(activate(V1))
   #15: #isNat(n__s(V1)) -> #activate(V1)
   #16: #isNat(n__s(V1)) -> #activate(V1)
   #17: #plus(N,s(M)) -> #U81(isNat(M),M,N)
   #18: #plus(N,s(M)) -> #isNat(M)
   #19: #plus(N,0()) -> #U71(isNat(N),N)
   #20: #plus(N,0()) -> #isNat(N)
   #21: #isNatKind(n__plus(V1,V2)) -> #U41(isNatKind(activate(V1)),activate(V2))
   #22: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #23: #isNatKind(n__plus(V1,V2)) -> #activate(V1)
   #24: #isNatKind(n__plus(V1,V2)) -> #activate(V2)
   #25: #U12(tt(),V1,V2) -> #U13(isNatKind(activate(V2)),activate(V1),activate(V2))
   #26: #U12(tt(),V1,V2) -> #isNatKind(activate(V2))
   #27: #U12(tt(),V1,V2) -> #activate(V2)
   #28: #U12(tt(),V1,V2) -> #activate(V1)
   #29: #U12(tt(),V1,V2) -> #activate(V2)
   #30: #isNatKind(n__x(V1,V2)) -> #U61(isNatKind(activate(V1)),activate(V2))
   #31: #isNatKind(n__x(V1,V2)) -> #isNatKind(activate(V1))
   #32: #isNatKind(n__x(V1,V2)) -> #activate(V1)
   #33: #isNatKind(n__x(V1,V2)) -> #activate(V2)
   #34: #activate(n__s(X)) -> #s(X)
   #35: #U15(tt(),V2) -> #U16(isNat(activate(V2)))
   #36: #U15(tt(),V2) -> #isNat(activate(V2))
   #37: #U15(tt(),V2) -> #activate(V2)
   #38: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1))
   #39: #U21(tt(),V1) -> #isNatKind(activate(V1))
   #40: #U21(tt(),V1) -> #activate(V1)
   #41: #U21(tt(),V1) -> #activate(V1)
   #42: #U61(tt(),V2) -> #U62(isNatKind(activate(V2)))
   #43: #U61(tt(),V2) -> #isNatKind(activate(V2))
   #44: #U61(tt(),V2) -> #activate(V2)
   #45: #U22(tt(),V1) -> #U23(isNat(activate(V1)))
   #46: #U22(tt(),V1) -> #isNat(activate(V1))
   #47: #U22(tt(),V1) -> #activate(V1)
   #48: #U91(tt(),N) -> #U92(isNatKind(activate(N)))
   #49: #U91(tt(),N) -> #isNatKind(activate(N))
   #50: #U91(tt(),N) -> #activate(N)
   #51: #U31(tt(),V1,V2) -> #U32(isNatKind(activate(V1)),activate(V1),activate(V2))
   #52: #U31(tt(),V1,V2) -> #isNatKind(activate(V1))
   #53: #U31(tt(),V1,V2) -> #activate(V1)
   #54: #U31(tt(),V1,V2) -> #activate(V1)
   #55: #U31(tt(),V1,V2) -> #activate(V2)
   #56: #U84(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #57: #U84(tt(),M,N) -> #plus(activate(N),activate(M))
   #58: #U84(tt(),M,N) -> #activate(N)
   #59: #U84(tt(),M,N) -> #activate(M)
   #60: #activate(n__x(X1,X2)) -> #x(X1,X2)
   #61: #activate(n__0()) -> #0()
   #62: #U71(tt(),N) -> #U72(isNatKind(activate(N)),activate(N))
   #63: #U71(tt(),N) -> #isNatKind(activate(N))
   #64: #U71(tt(),N) -> #activate(N)
   #65: #U71(tt(),N) -> #activate(N)
   #66: #U41(tt(),V2) -> #U42(isNatKind(activate(V2)))
   #67: #U41(tt(),V2) -> #isNatKind(activate(V2))
   #68: #U41(tt(),V2) -> #activate(V2)
   #69: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2))
   #70: #U13(tt(),V1,V2) -> #isNatKind(activate(V2))
   #71: #U13(tt(),V1,V2) -> #activate(V2)
   #72: #U13(tt(),V1,V2) -> #activate(V1)
   #73: #U13(tt(),V1,V2) -> #activate(V2)
   #74: #isNatKind(n__s(V1)) -> #U51(isNatKind(activate(V1)))
   #75: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
   #76: #isNatKind(n__s(V1)) -> #activate(V1)
   #77: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2))
   #78: #U11(tt(),V1,V2) -> #isNatKind(activate(V1))
   #79: #U11(tt(),V1,V2) -> #activate(V1)
   #80: #U11(tt(),V1,V2) -> #activate(V1)
   #81: #U11(tt(),V1,V2) -> #activate(V2)
   #82: #x(N,s(M)) -> #U101(isNat(M),M,N)
   #83: #x(N,s(M)) -> #isNat(M)
   #84: #U82(tt(),M,N) -> #U83(isNat(activate(N)),activate(M),activate(N))
   #85: #U82(tt(),M,N) -> #isNat(activate(N))
   #86: #U82(tt(),M,N) -> #activate(N)
   #87: #U82(tt(),M,N) -> #activate(M)
   #88: #U82(tt(),M,N) -> #activate(N)
   #89: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2))
   #90: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #91: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #92: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #93: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #94: #U81(tt(),M,N) -> #U82(isNatKind(activate(M)),activate(M),activate(N))
   #95: #U81(tt(),M,N) -> #isNatKind(activate(M))
   #96: #U81(tt(),M,N) -> #activate(M)
   #97: #U81(tt(),M,N) -> #activate(M)
   #98: #U81(tt(),M,N) -> #activate(N)
   #99: #U34(tt(),V1,V2) -> #U35(isNat(activate(V1)),activate(V2))
   #100: #U34(tt(),V1,V2) -> #isNat(activate(V1))
   #101: #U34(tt(),V1,V2) -> #activate(V1)
   #102: #U34(tt(),V1,V2) -> #activate(V2)
   #103: #U92(tt()) -> #0()
   #104: #U72(tt(),N) -> #activate(N)
   #105: #isNat(n__x(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V1),activate(V2))
   #106: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1))
   #107: #isNat(n__x(V1,V2)) -> #activate(V1)
   #108: #isNat(n__x(V1,V2)) -> #activate(V1)
   #109: #isNat(n__x(V1,V2)) -> #activate(V2)
   #110: #U33(tt(),V1,V2) -> #U34(isNatKind(activate(V2)),activate(V1),activate(V2))
   #111: #U33(tt(),V1,V2) -> #isNatKind(activate(V2))
   #112: #U33(tt(),V1,V2) -> #activate(V2)
   #113: #U33(tt(),V1,V2) -> #activate(V1)
   #114: #U33(tt(),V1,V2) -> #activate(V2)
   #115: #U103(tt(),M,N) -> #U104(isNatKind(activate(N)),activate(M),activate(N))
   #116: #U103(tt(),M,N) -> #isNatKind(activate(N))
   #117: #U103(tt(),M,N) -> #activate(N)
   #118: #U103(tt(),M,N) -> #activate(M)
   #119: #U103(tt(),M,N) -> #activate(N)
   #120: #U101(tt(),M,N) -> #U102(isNatKind(activate(M)),activate(M),activate(N))
   #121: #U101(tt(),M,N) -> #isNatKind(activate(M))
   #122: #U101(tt(),M,N) -> #activate(M)
   #123: #U101(tt(),M,N) -> #activate(M)
   #124: #U101(tt(),M,N) -> #activate(N)
   #125: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2))
   #126: #U14(tt(),V1,V2) -> #isNat(activate(V1))
   #127: #U14(tt(),V1,V2) -> #activate(V1)
   #128: #U14(tt(),V1,V2) -> #activate(V2)
   #129: #U32(tt(),V1,V2) -> #U33(isNatKind(activate(V2)),activate(V1),activate(V2))
   #130: #U32(tt(),V1,V2) -> #isNatKind(activate(V2))
   #131: #U32(tt(),V1,V2) -> #activate(V2)
   #132: #U32(tt(),V1,V2) -> #activate(V1)
   #133: #U32(tt(),V1,V2) -> #activate(V2)
   #134: #U104(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #135: #U104(tt(),M,N) -> #x(activate(N),activate(M))
   #136: #U104(tt(),M,N) -> #activate(N)
   #137: #U104(tt(),M,N) -> #activate(M)
   #138: #U104(tt(),M,N) -> #activate(N)
   #139: #activate(n__plus(X1,X2)) -> #plus(X1,X2)
   #140: #U35(tt(),V2) -> #U36(isNat(activate(V2)))
   #141: #U35(tt(),V2) -> #isNat(activate(V2))
   #142: #U35(tt(),V2) -> #activate(V2)
Number of SCCs: 1, DPs: 131
	SCC { #1..33 #36..41 #43 #44 #46 #47 #49..55 #57..60 #62..65 #67..73 #75..102 #104..139 #141 #142 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U72(x1,x2)		w: (max{x2, 0})
  #U32(x1,x2,x3)		w: (max{31256 + x3, 31260 + x2, 31255 + x1})
  isNatKind(x1)		w: (3)
  U16(x1)		w: (2)
  U21(x1,x2)		w: (max{0, 14922 + x1})
  #U83(x1,x2,x3)		w: (max{x3, x2, 0})
  U11(x1,x2,x3)		w: (max{6823 + x3, 1 + x2, 0})
  s(x1)		w: (x1)
  #isNat(x1)		w: (x1)
  U42(x1)		w: (x1)
  U91(x1,x2)		w: (max{25730 + x2, 0})
  #U35(x1,x2)		w: (max{1 + x2, 0})
  #U101(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 0})
  activate(x1)		w: (x1)
  #U82(x1,x2,x3)		w: (max{x3, x2, 0})
  #U104(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 31260 + x1})
  U71(x1,x2)		w: (max{x2, 0})
  #U81(x1,x2,x3)		w: (max{x3, x2, 0})
  #U92(x1)		w: (0)
  #plus(x1,x2)		w: (max{x2, x1})
  U101(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 0})
  #activate(x1)		w: (x1)
  U103(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 0})
  #U23(x1)		w: (0)
  U84(x1,x2,x3)		w: (max{x3, 6821 + x2, 6818 + x1})
  U23(x1)		w: (22776 + x1)
  U35(x1,x2)		w: (max{0, 2 + x1})
  U72(x1,x2)		w: (max{x2, 0})
  #U13(x1,x2,x3)		w: (max{6815 + x3, x2, 6814 + x1})
  U34(x1,x2,x3)		w: (max{2 + x3, 3 + x2, 0})
  #U103(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 0})
  U12(x1,x2,x3)		w: (max{0, 1 + x2, 6821 + x1})
  #U33(x1,x2,x3)		w: (max{31253 + x3, 31255 + x2, 31256 + x1})
  x(x1,x2)		w: (max{31263 + x2, 31262 + x1})
  #U16(x1)		w: (0)
  n__s(x1)		w: (x1)
  U104(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 31260 + x1})
  #U42(x1)		w: (0)
  #U12(x1,x2,x3)		w: (max{6820 + x3, x2, 6813 + x1})
  #U62(x1)		w: (0)
  U83(x1,x2,x3)		w: (max{x3, 6821 + x2, 0})
  0()		w: (1)
  #U14(x1,x2,x3)		w: (max{2 + x3, x2, 6811 + x1})
  #U36(x1)		w: (0)
  U36(x1)		w: (2)
  #U102(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 31260 + x1})
  #x(x1,x2)		w: (max{31263 + x2, 31262 + x1})
  #s(x1)		w: (0)
  U62(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{6821 + x2, x1})
  #U15(x1,x2)		w: (max{1 + x2, 0})
  U32(x1,x2,x3)		w: (0)
  U33(x1,x2,x3)		w: (max{0, x1})
  n__0()		w: (1)
  #U34(x1,x2,x3)		w: (max{2 + x3, 31254 + x2, 31249 + x1})
  U14(x1,x2,x3)		w: (0)
  isNat(x1)		w: (1 + x1)
  n__x(x1,x2)		w: (max{31263 + x2, 31262 + x1})
  plus(x1,x2)		w: (max{6821 + x2, x1})
  U15(x1,x2)		w: (0)
  U61(x1,x2)		w: (max{0, x1})
  #U51(x1)		w: (0)
  #U11(x1,x2,x3)		w: (max{6821 + x3, x2, 119 + x1})
  U31(x1,x2,x3)		w: (max{31264 + x3, 31265 + x2, 0})
  U92(x1)		w: (x1)
  #U41(x1,x2)		w: (max{4732 + x2, 3565 + x1})
  U102(x1,x2,x3)		w: (max{31262 + x3, 31263 + x2, 31260 + x1})
  #U21(x1,x2)		w: (max{x2, 0})
  U81(x1,x2,x3)		w: (max{x3, 6821 + x2, 0})
  U82(x1,x2,x3)		w: (max{x3, 6821 + x2, 0})
  #U22(x1,x2)		w: (max{x2, 0})
  tt()		w: (3)
  #U84(x1,x2,x3)		w: (max{x3, x2, 0})
  #U71(x1,x2)		w: (max{x2, 0})
  U13(x1,x2,x3)		w: (0)
  U22(x1,x2)		w: (0)
  U51(x1)		w: (3)
  #isNatKind(x1)		w: (x1)
  U41(x1,x2)		w: (max{0, x1})
  #U31(x1,x2,x3)		w: (max{31257 + x3, 31261 + x2, 31254 + x1})
  #U91(x1,x2)		w: (max{12063 + x2, 0})
  #U61(x1,x2)		w: (max{1 + x2, 31258 + x1})
    USABLE RULES: { 1..4 20..32 37..53 }
    Removed DPs: #2..7 #21 #24 #26 #27 #29..33 #36 #37 #43 #44 #49..55 #67 #68 #70 #71 #73 #81 #83 #93 #99..102 #105..114 #116..119 #121..125 #128..133 #136..138 #141 #142
Number of SCCs: 1, DPs: 63
	SCC { #1 #8..20 #22 #23 #25 #28 #38..41 #46 #47 #57..60 #62..65 #69 #72 #75..80 #82 #84..92 #94..98 #104 #115 #120 #126 #127 #134 #135 #139 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U72(x1,x2)		w: (max{1 + x2, 0})
  #U32(x1,x2,x3)		w: (0)
  isNatKind(x1)		w: (3 + x1)
  U16(x1)		w: (21902 + x1)
  U21(x1,x2)		w: (max{2 + x2, 1 + x1})
  #U83(x1,x2,x3)		w: (max{1 + x3, 3 + x2, 0})
  U11(x1,x2,x3)		w: (max{2 + x3, 0, 2 + x1})
  s(x1)		w: (x1)
  #isNat(x1)		w: (1 + x1)
  U42(x1)		w: (2)
  U91(x1,x2)		w: (max{1 + x2, 0})
  #U35(x1,x2)		w: (0)
  #U101(x1,x2,x3)		w: (max{4 + x3, 5 + x2, 0})
  activate(x1)		w: (x1)
  #U82(x1,x2,x3)		w: (max{1 + x3, 3 + x2, 0})
  #U104(x1,x2,x3)		w: (max{4 + x3, 5 + x2, 0})
  U71(x1,x2)		w: (max{x2, 0})
  #U81(x1,x2,x3)		w: (max{1 + x3, 3 + x2, 0})
  #U92(x1)		w: (0)
  #plus(x1,x2)		w: (max{3 + x2, 1 + x1})
  U101(x1,x2,x3)		w: (max{3 + x3, 4 + x2, 0})
  #activate(x1)		w: (1 + x1)
  U103(x1,x2,x3)		w: (max{3 + x3, 4 + x2, 0})
  #U23(x1)		w: (0)
  U84(x1,x2,x3)		w: (max{x3, 3 + x2, 0})
  U23(x1)		w: (4)
  U35(x1,x2)		w: (max{3 + x2, 15 + x1})
  U72(x1,x2)		w: (max{x2, 0})
  #U13(x1,x2,x3)		w: (max{2 + x3, 1 + x2, 0})
  U34(x1,x2,x3)		w: (max{15 + x3, 15 + x2, 12 + x1})
  #U103(x1,x2,x3)		w: (max{4 + x3, 5 + x2, 0})
  U12(x1,x2,x3)		w: (max{2 + x3, 8 + x2, x1})
  #U33(x1,x2,x3)		w: (0)
  x(x1,x2)		w: (max{4 + x2, 3 + x1})
  #U16(x1)		w: (0)
  n__s(x1)		w: (x1)
  U104(x1,x2,x3)		w: (max{3 + x3, 4 + x2, 0})
  #U42(x1)		w: (0)
  #U12(x1,x2,x3)		w: (max{3 + x3, 1 + x2, 0})
  #U62(x1)		w: (0)
  U83(x1,x2,x3)		w: (max{x3, 3 + x2, 0})
  0()		w: (1)
  #U14(x1,x2,x3)		w: (max{0, 1 + x2})
  #U36(x1)		w: (0)
  U36(x1)		w: (4)
  #U102(x1,x2,x3)		w: (max{4 + x3, 5 + x2, 0})
  #x(x1,x2)		w: (max{5 + x2, 4 + x1})
  #s(x1)		w: (0)
  U62(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{3 + x2, x1})
  #U15(x1,x2)		w: (0)
  U32(x1,x2,x3)		w: (max{10 + x3, 9 + x2, 6 + x1})
  U33(x1,x2,x3)		w: (max{0, 9 + x1})
  n__0()		w: (1)
  #U34(x1,x2,x3)		w: (0)
  U14(x1,x2,x3)		w: (max{10 + x3, 21895 + x2, 0})
  isNat(x1)		w: (1 + x1)
  n__x(x1,x2)		w: (max{4 + x2, 3 + x1})
  plus(x1,x2)		w: (max{3 + x2, x1})
  U15(x1,x2)		w: (max{21903 + x2, 10 + x1})
  U61(x1,x2)		w: (0)
  #U51(x1)		w: (0)
  #U11(x1,x2,x3)		w: (max{4 + x3, 1 + x2, 0})
  U31(x1,x2,x3)		w: (max{0, 9 + x2, 3 + x1})
  U92(x1)		w: (1)
  #U41(x1,x2)		w: (0)
  U102(x1,x2,x3)		w: (max{3 + x3, 4 + x2, 0})
  #U21(x1,x2)		w: (max{1 + x2, 0})
  U81(x1,x2,x3)		w: (max{x3, 3 + x2, 0})
  U82(x1,x2,x3)		w: (max{x3, 3 + x2, 0})
  #U22(x1,x2)		w: (max{1 + x2, 0})
  tt()		w: (5)
  #U84(x1,x2,x3)		w: (max{1 + x3, 3 + x2, 0})
  #U71(x1,x2)		w: (max{1 + x2, 0})
  U13(x1,x2,x3)		w: (max{9 + x3, 6 + x2, 0})
  U22(x1,x2)		w: (max{3 + x2, x1})
  U51(x1)		w: (4)
  #isNatKind(x1)		w: (1 + x1)
  U41(x1,x2)		w: (max{0, 7039 + x1})
  #U31(x1,x2,x3)		w: (0)
  #U91(x1,x2)		w: (0)
  #U61(x1,x2)		w: (0)
    USABLE RULES: { 1..4 25..32 41..53 }
    Removed DPs: #11 #18 #59 #87 #95..97
Number of SCCs: 1, DPs: 56
	SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #38..41 #46 #47 #57 #58 #60 #62..65 #69 #72 #75..80 #82 #84..86 #88..92 #94 #98 #104 #115 #120 #126 #127 #134 #135 #139 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2)	x2
  #U32(x1,x2,x3)	0[x1,x3]
  isNatKind(x1)	6[]
  U16(x1)	x1
  U21(x1,x2)	x1
  #U83(x1,x2,x3)	x3
  U11(x1,x2,x3)	6[]
  s(x1)	6[x1]
  #isNat(x1)	x1
  U42(x1)	x1
  U91(x1,x2)	6[]
  #U35(x1,x2)	0[x2]
  #U101(x1,x2,x3)	11[x2,x3]
  activate(x1)	x1
  #U82(x1,x2,x3)	x3
  #U104(x1,x2,x3)	11[x2,x3]
  U71(x1,x2)	2[x2]
  #U81(x1,x2,x3)	x3
  #U92(x1)	0[]
  #plus(x1,x2)	x1
  U101(x1,x2,x3)	11[x2,x3,x1]
  #activate(x1)	x1
  U103(x1,x2,x3)	11[x2,x3,x1]
  #U23(x1)	0[]
  U84(x1,x2,x3)	10[x2,x3,x1]
  U23(x1)	6[]
  U35(x1,x2)	x1
  U72(x1,x2)	x2
  #U13(x1,x2,x3)	x2
  U34(x1,x2,x3)	6[]
  #U103(x1,x2,x3)	11[x2,x3]
  U12(x1,x2,x3)	6[]
  #U33(x1,x2,x3)	0[x3,x1]
  x(x1,x2)	11[x2,x1]
  #U16(x1)	0[]
  n__s(x1)	6[x1]
  U104(x1,x2,x3)	11[x2,x3,x1]
  #U42(x1)	0[]
  #U12(x1,x2,x3)	x2
  #U62(x1)	0[]
  U83(x1,x2,x3)	10[x2,x3,x1]
  0()	6
  #U14(x1,x2,x3)	x2
  #U36(x1)	0[]
  U36(x1)	6[]
  #U102(x1,x2,x3)	11[x2,x3]
  #x(x1,x2)	11[x2,x1]
  #s(x1)	0[]
  U62(x1)	x1
  n__plus(x1,x2)	10[x2,x1]
  #U15(x1,x2)	0[x1]
  U32(x1,x2,x3)	x1
  U33(x1,x2,x3)	x1
  n__0()	6
  #U34(x1,x2,x3)	0[x1,x3]
  U14(x1,x2,x3)	x1
  isNat(x1)	6[]
  n__x(x1,x2)	11[x2,x1]
  plus(x1,x2)	10[x2,x1]
  U15(x1,x2)	x1
  U61(x1,x2)	x1
  #U51(x1)	0[]
  #U11(x1,x2,x3)	x2
  U31(x1,x2,x3)	x1
  U92(x1)	6[]
  #U41(x1,x2)	0[x2,x1]
  U102(x1,x2,x3)	11[x2,x3,x1]
  #U21(x1,x2)	x2
  U81(x1,x2,x3)	10[x2,x3,x1]
  U82(x1,x2,x3)	10[x2,x3,x1]
  #U22(x1,x2)	x2
  tt()	6
  #U84(x1,x2,x3)	x3
  #U71(x1,x2)	x2
  U13(x1,x2,x3)	6[]
  U22(x1,x2)	6[]
  U51(x1)	x1
  #isNatKind(x1)	x1
  U41(x1,x2)	x1
  #U31(x1,x2,x3)	0[x3,x1,x2]
  #U91(x1,x2)	0[x2]
  #U61(x1,x2)	0[x1,x2]
    USABLE RULES: { 1..53 }
    Removed DPs: #13..16 #22 #23 #75 #76 #89..92 #139
Number of SCCs: 1, DPs: 23
	SCC { #1 #8 #10 #12 #17 #19 #57 #58 #60 #62 #64 #65 #82 #84 #86 #88 #94 #98 #104 #115 #120 #134 #135 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2)	x2
  #U32(x1,x2,x3)	0[x1,x3]
  isNatKind(x1)	3[]
  U16(x1)	3[]
  U21(x1,x2)	x1
  #U83(x1,x2,x3)	x3
  U11(x1,x2,x3)	x1
  s(x1)	4[x1]
  #isNat(x1)	3[]
  U42(x1)	x1
  U91(x1,x2)	5[x2]
  #U35(x1,x2)	0[x2]
  #U101(x1,x2,x3)	6[x3,x2,x1]
  activate(x1)	x1
  #U82(x1,x2,x3)	x3
  #U104(x1,x2,x3)	6[x3,x2]
  U71(x1,x2)	1[x2]
  #U81(x1,x2,x3)	x3
  #U92(x1)	0[]
  #plus(x1,x2)	x1
  U101(x1,x2,x3)	6[x3,x2,x1]
  #activate(x1)	x1
  U103(x1,x2,x3)	6[x3,x2,x1]
  #U23(x1)	0[]
  U84(x1,x2,x3)	5[x2,x3,x1]
  U23(x1)	x1
  U35(x1,x2)	3[]
  U72(x1,x2)	x2
  #U13(x1,x2,x3)	11[]
  U34(x1,x2,x3)	x1
  #U103(x1,x2,x3)	6[x3,x2,x1]
  U12(x1,x2,x3)	x1
  #U33(x1,x2,x3)	0[x3,x1]
  x(x1,x2)	6[x1,x2]
  #U16(x1)	0[]
  n__s(x1)	4[x1]
  U104(x1,x2,x3)	6[x3,x2,x1]
  #U42(x1)	0[]
  #U12(x1,x2,x3)	8[x2,x3]
  #U62(x1)	0[]
  U83(x1,x2,x3)	5[x2,x3,x1]
  0()	4
  #U14(x1,x2,x3)	10[x3]
  #U36(x1)	0[]
  U36(x1)	3[]
  #U102(x1,x2,x3)	6[x3,x2,x1]
  #x(x1,x2)	6[x1,x2]
  #s(x1)	0[]
  U62(x1)	x1
  n__plus(x1,x2)	5[x2,x1]
  #U15(x1,x2)	0[x1]
  U32(x1,x2,x3)	3[]
  U33(x1,x2,x3)	x1
  n__0()	4
  #U34(x1,x2,x3)	0[x1,x3]
  U14(x1,x2,x3)	3[]
  isNat(x1)	3[]
  n__x(x1,x2)	6[x1,x2]
  plus(x1,x2)	5[x2,x1]
  U15(x1,x2)	3[]
  U61(x1,x2)	x1
  #U51(x1)	0[]
  #U11(x1,x2,x3)	7[x3]
  U31(x1,x2,x3)	3[]
  U92(x1)	5[]
  #U41(x1,x2)	0[x2,x1]
  U102(x1,x2,x3)	6[x3,x2,x1]
  #U21(x1,x2)	5[]
  U81(x1,x2,x3)	5[x2,x3,x1]
  U82(x1,x2,x3)	5[x2,x3,x1]
  #U22(x1,x2)	2[]
  tt()	3
  #U84(x1,x2,x3)	x3
  #U71(x1,x2)	x2
  U13(x1,x2,x3)	x1
  U22(x1,x2)	x1
  U51(x1)	x1
  #isNatKind(x1)	4[]
  U41(x1,x2)	3[]
  #U31(x1,x2,x3)	0[x3,x1,x2]
  #U91(x1,x2)	0[x2]
  #U61(x1,x2)	0[x1,x2]
    USABLE RULES: { 1..53 }
    Removed DPs: #82 #115
Number of SCCs: 1, DPs: 5
	SCC { #8 #17 #57 #84 #94 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2)	x2
  #U32(x1,x2,x3)	0[x1,x3]
  isNatKind(x1)	3[]
  U16(x1)	3[]
  U21(x1,x2)	x1
  #U83(x1,x2,x3)	4[x3,x2]
  U11(x1,x2,x3)	x1
  s(x1)	3[x1]
  #isNat(x1)	3[]
  U42(x1)	x1
  U91(x1,x2)	5[x2]
  #U35(x1,x2)	0[x2]
  #U101(x1,x2,x3)	6[x3,x2,x1]
  activate(x1)	x1
  #U82(x1,x2,x3)	4[x3,x2]
  #U104(x1,x2,x3)	6[x3,x2]
  U71(x1,x2)	2[x2]
  #U81(x1,x2,x3)	4[x3,x2,x1]
  #U92(x1)	0[]
  #plus(x1,x2)	4[x1,x2]
  U101(x1,x2,x3)	6[x3,x2,x1]
  #activate(x1)	x1
  U103(x1,x2,x3)	6[x3,x2,x1]
  #U23(x1)	0[]
  U84(x1,x2,x3)	5[x2,x3,x1]
  U23(x1)	x1
  U35(x1,x2)	3[]
  U72(x1,x2)	x2
  #U13(x1,x2,x3)	11[]
  U34(x1,x2,x3)	x1
  #U103(x1,x2,x3)	6[x3,x2,x1]
  U12(x1,x2,x3)	x1
  #U33(x1,x2,x3)	0[x3,x1]
  x(x1,x2)	6[x1,x2]
  #U16(x1)	0[]
  n__s(x1)	3[x1]
  U104(x1,x2,x3)	6[x3,x2,x1]
  #U42(x1)	0[]
  #U12(x1,x2,x3)	8[x2,x3]
  #U62(x1)	0[]
  U83(x1,x2,x3)	5[x2,x3,x1]
  0()	4
  #U14(x1,x2,x3)	10[x3]
  #U36(x1)	0[]
  U36(x1)	3[]
  #U102(x1,x2,x3)	6[x3,x2,x1]
  #x(x1,x2)	6[x1,x2]
  #s(x1)	0[]
  U62(x1)	x1
  n__plus(x1,x2)	5[x2,x1]
  #U15(x1,x2)	0[x1]
  U32(x1,x2,x3)	3[]
  U33(x1,x2,x3)	x1
  n__0()	4
  #U34(x1,x2,x3)	0[x1,x3]
  U14(x1,x2,x3)	3[]
  isNat(x1)	3[]
  n__x(x1,x2)	6[x1,x2]
  plus(x1,x2)	5[x2,x1]
  U15(x1,x2)	3[]
  U61(x1,x2)	x1
  #U51(x1)	0[]
  #U11(x1,x2,x3)	7[x3]
  U31(x1,x2,x3)	3[]
  U92(x1)	5[]
  #U41(x1,x2)	0[x2,x1]
  U102(x1,x2,x3)	6[x3,x2,x1]
  #U21(x1,x2)	5[]
  U81(x1,x2,x3)	5[x2,x3,x1]
  U82(x1,x2,x3)	5[x2,x3,x1]
  #U22(x1,x2)	2[]
  tt()	3
  #U84(x1,x2,x3)	4[x3,x2]
  #U71(x1,x2)	x2
  U13(x1,x2,x3)	x1
  U22(x1,x2)	x1
  U51(x1)	x1
  #isNatKind(x1)	4[]
  U41(x1,x2)	3[]
  #U31(x1,x2,x3)	0[x3,x1,x2]
  #U91(x1,x2)	0[x2]
  #U61(x1,x2)	0[x1,x2]
    USABLE RULES: { 1..53 }
    Removed DPs: #17 #94
Number of SCCs: 0, DPs: 0