/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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(activate(X1),activate(X2))
    51: activate(n__s(X)) -> s(activate(X))
    52: activate(n__x(X1,X2)) -> x(activate(X1),activate(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(activate(X))
   #35: #activate(n__s(X)) -> #activate(X)
   #36: #U15(tt(),V2) -> #U16(isNat(activate(V2)))
   #37: #U15(tt(),V2) -> #isNat(activate(V2))
   #38: #U15(tt(),V2) -> #activate(V2)
   #39: #U21(tt(),V1) -> #U22(isNatKind(activate(V1)),activate(V1))
   #40: #U21(tt(),V1) -> #isNatKind(activate(V1))
   #41: #U21(tt(),V1) -> #activate(V1)
   #42: #U21(tt(),V1) -> #activate(V1)
   #43: #U61(tt(),V2) -> #U62(isNatKind(activate(V2)))
   #44: #U61(tt(),V2) -> #isNatKind(activate(V2))
   #45: #U61(tt(),V2) -> #activate(V2)
   #46: #U22(tt(),V1) -> #U23(isNat(activate(V1)))
   #47: #U22(tt(),V1) -> #isNat(activate(V1))
   #48: #U22(tt(),V1) -> #activate(V1)
   #49: #U91(tt(),N) -> #U92(isNatKind(activate(N)))
   #50: #U91(tt(),N) -> #isNatKind(activate(N))
   #51: #U91(tt(),N) -> #activate(N)
   #52: #U31(tt(),V1,V2) -> #U32(isNatKind(activate(V1)),activate(V1),activate(V2))
   #53: #U31(tt(),V1,V2) -> #isNatKind(activate(V1))
   #54: #U31(tt(),V1,V2) -> #activate(V1)
   #55: #U31(tt(),V1,V2) -> #activate(V1)
   #56: #U31(tt(),V1,V2) -> #activate(V2)
   #57: #U84(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #58: #U84(tt(),M,N) -> #plus(activate(N),activate(M))
   #59: #U84(tt(),M,N) -> #activate(N)
   #60: #U84(tt(),M,N) -> #activate(M)
   #61: #activate(n__x(X1,X2)) -> #x(activate(X1),activate(X2))
   #62: #activate(n__x(X1,X2)) -> #activate(X1)
   #63: #activate(n__x(X1,X2)) -> #activate(X2)
   #64: #activate(n__0()) -> #0()
   #65: #U71(tt(),N) -> #U72(isNatKind(activate(N)),activate(N))
   #66: #U71(tt(),N) -> #isNatKind(activate(N))
   #67: #U71(tt(),N) -> #activate(N)
   #68: #U71(tt(),N) -> #activate(N)
   #69: #U41(tt(),V2) -> #U42(isNatKind(activate(V2)))
   #70: #U41(tt(),V2) -> #isNatKind(activate(V2))
   #71: #U41(tt(),V2) -> #activate(V2)
   #72: #U13(tt(),V1,V2) -> #U14(isNatKind(activate(V2)),activate(V1),activate(V2))
   #73: #U13(tt(),V1,V2) -> #isNatKind(activate(V2))
   #74: #U13(tt(),V1,V2) -> #activate(V2)
   #75: #U13(tt(),V1,V2) -> #activate(V1)
   #76: #U13(tt(),V1,V2) -> #activate(V2)
   #77: #isNatKind(n__s(V1)) -> #U51(isNatKind(activate(V1)))
   #78: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
   #79: #isNatKind(n__s(V1)) -> #activate(V1)
   #80: #U11(tt(),V1,V2) -> #U12(isNatKind(activate(V1)),activate(V1),activate(V2))
   #81: #U11(tt(),V1,V2) -> #isNatKind(activate(V1))
   #82: #U11(tt(),V1,V2) -> #activate(V1)
   #83: #U11(tt(),V1,V2) -> #activate(V1)
   #84: #U11(tt(),V1,V2) -> #activate(V2)
   #85: #x(N,s(M)) -> #U101(isNat(M),M,N)
   #86: #x(N,s(M)) -> #isNat(M)
   #87: #U82(tt(),M,N) -> #U83(isNat(activate(N)),activate(M),activate(N))
   #88: #U82(tt(),M,N) -> #isNat(activate(N))
   #89: #U82(tt(),M,N) -> #activate(N)
   #90: #U82(tt(),M,N) -> #activate(M)
   #91: #U82(tt(),M,N) -> #activate(N)
   #92: #isNat(n__plus(V1,V2)) -> #U11(isNatKind(activate(V1)),activate(V1),activate(V2))
   #93: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #94: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #95: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #96: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #97: #U81(tt(),M,N) -> #U82(isNatKind(activate(M)),activate(M),activate(N))
   #98: #U81(tt(),M,N) -> #isNatKind(activate(M))
   #99: #U81(tt(),M,N) -> #activate(M)
   #100: #U81(tt(),M,N) -> #activate(M)
   #101: #U81(tt(),M,N) -> #activate(N)
   #102: #U34(tt(),V1,V2) -> #U35(isNat(activate(V1)),activate(V2))
   #103: #U34(tt(),V1,V2) -> #isNat(activate(V1))
   #104: #U34(tt(),V1,V2) -> #activate(V1)
   #105: #U34(tt(),V1,V2) -> #activate(V2)
   #106: #U92(tt()) -> #0()
   #107: #U72(tt(),N) -> #activate(N)
   #108: #isNat(n__x(V1,V2)) -> #U31(isNatKind(activate(V1)),activate(V1),activate(V2))
   #109: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1))
   #110: #isNat(n__x(V1,V2)) -> #activate(V1)
   #111: #isNat(n__x(V1,V2)) -> #activate(V1)
   #112: #isNat(n__x(V1,V2)) -> #activate(V2)
   #113: #U33(tt(),V1,V2) -> #U34(isNatKind(activate(V2)),activate(V1),activate(V2))
   #114: #U33(tt(),V1,V2) -> #isNatKind(activate(V2))
   #115: #U33(tt(),V1,V2) -> #activate(V2)
   #116: #U33(tt(),V1,V2) -> #activate(V1)
   #117: #U33(tt(),V1,V2) -> #activate(V2)
   #118: #U103(tt(),M,N) -> #U104(isNatKind(activate(N)),activate(M),activate(N))
   #119: #U103(tt(),M,N) -> #isNatKind(activate(N))
   #120: #U103(tt(),M,N) -> #activate(N)
   #121: #U103(tt(),M,N) -> #activate(M)
   #122: #U103(tt(),M,N) -> #activate(N)
   #123: #U101(tt(),M,N) -> #U102(isNatKind(activate(M)),activate(M),activate(N))
   #124: #U101(tt(),M,N) -> #isNatKind(activate(M))
   #125: #U101(tt(),M,N) -> #activate(M)
   #126: #U101(tt(),M,N) -> #activate(M)
   #127: #U101(tt(),M,N) -> #activate(N)
   #128: #U14(tt(),V1,V2) -> #U15(isNat(activate(V1)),activate(V2))
   #129: #U14(tt(),V1,V2) -> #isNat(activate(V1))
   #130: #U14(tt(),V1,V2) -> #activate(V1)
   #131: #U14(tt(),V1,V2) -> #activate(V2)
   #132: #U32(tt(),V1,V2) -> #U33(isNatKind(activate(V2)),activate(V1),activate(V2))
   #133: #U32(tt(),V1,V2) -> #isNatKind(activate(V2))
   #134: #U32(tt(),V1,V2) -> #activate(V2)
   #135: #U32(tt(),V1,V2) -> #activate(V1)
   #136: #U32(tt(),V1,V2) -> #activate(V2)
   #137: #U104(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #138: #U104(tt(),M,N) -> #x(activate(N),activate(M))
   #139: #U104(tt(),M,N) -> #activate(N)
   #140: #U104(tt(),M,N) -> #activate(M)
   #141: #U104(tt(),M,N) -> #activate(N)
   #142: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2))
   #143: #activate(n__plus(X1,X2)) -> #activate(X1)
   #144: #activate(n__plus(X1,X2)) -> #activate(X2)
   #145: #U35(tt(),V2) -> #U36(isNat(activate(V2)))
   #146: #U35(tt(),V2) -> #isNat(activate(V2))
   #147: #U35(tt(),V2) -> #activate(V2)
Number of SCCs: 1, DPs: 136
	SCC { #1..33 #35 #37..42 #44 #45 #47 #48 #50..56 #58..63 #65..68 #70..76 #78..105 #107..144 #146 #147 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U72(x1,x2)		w: (max{2 + x2, 0})
  #U32(x1,x2,x3)		w: (max{8 + x3, 6 + x2, 0})
  isNatKind(x1)		w: (x1)
  U16(x1)		w: (0)
  U21(x1,x2)		w: (max{2 + x2, 0})
  #U83(x1,x2,x3)		w: (max{2 + x3, 23 + x2, 0})
  U11(x1,x2,x3)		w: (max{0, 27571 + x2})
  s(x1)		w: (x1)
  #isNat(x1)		w: (2 + x1)
  U42(x1)		w: (11)
  U91(x1,x2)		w: (max{16 + x2, 0})
  #U35(x1,x2)		w: (max{3 + x2, 0})
  #U101(x1,x2,x3)		w: (max{23 + x3, 10 + x2, 0})
  activate(x1)		w: (x1)
  #U82(x1,x2,x3)		w: (max{2 + x3, 23 + x2, 23 + x1})
  #U104(x1,x2,x3)		w: (max{23 + x3, 10 + x2, 0})
  U71(x1,x2)		w: (max{x2, 0})
  #U81(x1,x2,x3)		w: (max{2 + x3, 23 + x2, 0})
  #U92(x1)		w: (0)
  #plus(x1,x2)		w: (max{23 + x2, 2 + x1})
  U101(x1,x2,x3)		w: (max{21 + x3, 8 + x2, 0})
  #activate(x1)		w: (2 + x1)
  U103(x1,x2,x3)		w: (max{21 + x3, 8 + x2, 0})
  #U23(x1)		w: (0)
  U84(x1,x2,x3)		w: (max{x3, 21 + x2, x1})
  U23(x1)		w: (0)
  U35(x1,x2)		w: (max{31262 + x2, 6 + x1})
  U72(x1,x2)		w: (max{x2, 0})
  #U13(x1,x2,x3)		w: (max{11 + x3, 2 + x2, 0})
  U34(x1,x2,x3)		w: (max{11 + x3, 31261 + x2, 0})
  #U103(x1,x2,x3)		w: (max{23 + x3, 10 + x2, 0})
  U12(x1,x2,x3)		w: (max{27572 + x3, 0, 27574 + x1})
  #U33(x1,x2,x3)		w: (max{5 + x3, 5 + x2, 7 + x1})
  x(x1,x2)		w: (max{8 + x2, 21 + x1})
  #U16(x1)		w: (0)
  n__s(x1)		w: (x1)
  U104(x1,x2,x3)		w: (max{21 + x3, 8 + x2, 3 + x1})
  #U42(x1)		w: (0)
  #U12(x1,x2,x3)		w: (max{11 + x3, 2 + x2, 2 + x1})
  #U62(x1)		w: (0)
  U83(x1,x2,x3)		w: (max{x3, 21 + x2, 0})
  0()		w: (11)
  #U14(x1,x2,x3)		w: (max{11 + x3, 2 + x2, 11 + x1})
  #U36(x1)		w: (0)
  U36(x1)		w: (7)
  #U102(x1,x2,x3)		w: (max{23 + x3, 10 + x2, x1})
  #x(x1,x2)		w: (max{10 + x2, 23 + x1})
  #s(x1)		w: (0)
  U62(x1)		w: (20)
  n__plus(x1,x2)		w: (max{21 + x2, x1})
  #U15(x1,x2)		w: (max{10 + x2, 0})
  U32(x1,x2,x3)		w: (max{9 + x3, 0})
  U33(x1,x2,x3)		w: (max{10 + x3, 31261 + x2, x1})
  n__0()		w: (11)
  #U34(x1,x2,x3)		w: (max{4 + x3, 4 + x2, 0})
  U14(x1,x2,x3)		w: (max{0, 27574 + x2})
  isNat(x1)		w: (1)
  n__x(x1,x2)		w: (max{8 + x2, 21 + x1})
  plus(x1,x2)		w: (max{21 + x2, x1})
  U15(x1,x2)		w: (max{27575 + x2, 0})
  U61(x1,x2)		w: (max{8 + x2, 19 + x1})
  #U51(x1)		w: (0)
  #U11(x1,x2,x3)		w: (max{11 + x3, 2 + x2, 1 + x1})
  U31(x1,x2,x3)		w: (max{0, 1 + x2, 6813 + x1})
  U92(x1)		w: (11)
  #U41(x1,x2)		w: (max{8 + x2, x1})
  U102(x1,x2,x3)		w: (max{21 + x3, 8 + x2, 4 + x1})
  #U21(x1,x2)		w: (max{2 + x2, 1 + x1})
  U81(x1,x2,x3)		w: (max{x3, 21 + x2, 0})
  U82(x1,x2,x3)		w: (max{x3, 21 + x2, 7 + x1})
  #U22(x1,x2)		w: (max{2 + x2, 1 + x1})
  tt()		w: (11)
  #U84(x1,x2,x3)		w: (max{2 + x3, 23 + x2, 2 + x1})
  #U71(x1,x2)		w: (max{2 + x2, 0})
  U13(x1,x2,x3)		w: (max{27573 + x3, 0})
  U22(x1,x2)		w: (max{1 + x2, 0})
  U51(x1)		w: (x1)
  #isNatKind(x1)		w: (2 + x1)
  U41(x1,x2)		w: (max{21 + x2, x1})
  #U31(x1,x2,x3)		w: (max{9 + x3, 19 + x2, 11 + x1})
  #U91(x1,x2)		w: (max{22 + x2, 0})
  #U61(x1,x2)		w: (max{7 + x2, 21 + x1})
    USABLE RULES: { 1..4 20..32 37..53 }
    Removed DPs: #2..7 #11 #18 #21 #24 #26 #27 #29..33 #37 #38 #44 #45 #50..56 #60 #62 #63 #70 #71 #73 #74 #76 #84 #86 #90 #96 #98..100 #102..105 #108..117 #119..122 #124..128 #131..136 #139..141 #144 #146 #147
Number of SCCs: 1, DPs: 58
	SCC { #1 #8..10 #12..17 #19 #20 #22 #23 #25 #28 #35 #39..42 #47 #48 #58 #59 #61 #65..68 #72 #75 #78..83 #85 #87..89 #91..95 #97 #101 #107 #118 #123 #129 #130 #137 #138 #142 #143 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2)	3[x2]
  #U32(x1,x2,x3)	0[x3,x2]
  isNatKind(x1)	4[]
  U16(x1)	4[]
  U21(x1,x2)	x1
  #U83(x1,x2,x3)	7[x2,x3,x1]
  U11(x1,x2,x3)	x1
  s(x1)	4[x1]
  #isNat(x1)	4[x1]
  U42(x1)	x1
  U91(x1,x2)	5[]
  #U35(x1,x2)	0[]
  #U101(x1,x2,x3)	9[x3,x2,x1]
  activate(x1)	x1
  #U82(x1,x2,x3)	7[x2,x3,x1]
  #U104(x1,x2,x3)	9[x3,x2,x1]
  U71(x1,x2)	0[x1,x2]
  #U81(x1,x2,x3)	7[x2,x3,x1]
  #U92(x1)	0[]
  #plus(x1,x2)	7[x2,x1]
  U101(x1,x2,x3)	9[x3,x2,x1]
  #activate(x1)	2[x1]
  U103(x1,x2,x3)	9[x3,x2,x1]
  #U23(x1)	0[]
  U84(x1,x2,x3)	8[x3,x2,x1]
  U23(x1)	4[]
  U35(x1,x2)	4[]
  U72(x1,x2)	0[x1,x2]
  #U13(x1,x2,x3)	4[x2]
  U34(x1,x2,x3)	x1
  #U103(x1,x2,x3)	9[x3,x2,x1]
  U12(x1,x2,x3)	x1
  #U33(x1,x2,x3)	0[x3,x1]
  x(x1,x2)	9[x1,x2]
  #U16(x1)	0[]
  n__s(x1)	4[x1]
  U104(x1,x2,x3)	9[x3,x2,x1]
  #U42(x1)	0[]
  #U12(x1,x2,x3)	4[x2,x3]
  #U62(x1)	0[]
  U83(x1,x2,x3)	8[x3,x2,x1]
  0()	5
  #U14(x1,x2,x3)	4[x2]
  #U36(x1)	0[]
  U36(x1)	x1
  #U102(x1,x2,x3)	9[x3,x2,x1]
  #x(x1,x2)	9[x1,x2]
  #s(x1)	0[]
  U62(x1)	4[]
  n__plus(x1,x2)	8[x1,x2]
  #U15(x1,x2)	0[]
  U32(x1,x2,x3)	4[]
  U33(x1,x2,x3)	4[]
  n__0()	5
  #U34(x1,x2,x3)	0[x3,x1]
  U14(x1,x2,x3)	x1
  isNat(x1)	4[]
  n__x(x1,x2)	9[x1,x2]
  plus(x1,x2)	8[x1,x2]
  U15(x1,x2)	4[]
  U61(x1,x2)	4[]
  #U51(x1)	0[]
  #U11(x1,x2,x3)	4[x2,x3]
  U31(x1,x2,x3)	4[]
  U92(x1)	5[]
  #U41(x1,x2)	0[x2]
  U102(x1,x2,x3)	9[x3,x2,x1]
  #U21(x1,x2)	4[x2]
  U81(x1,x2,x3)	8[x3,x2,x1]
  U82(x1,x2,x3)	8[x3,x2,x1]
  #U22(x1,x2)	4[x2]
  tt()	4
  #U84(x1,x2,x3)	7[x2,x3]
  #U71(x1,x2)	6[x2]
  U13(x1,x2,x3)	x1
  U22(x1,x2)	x1
  U51(x1)	x1
  #isNatKind(x1)	4[x1]
  U41(x1,x2)	4[]
  #U31(x1,x2,x3)	0[x3,x2,x1]
  #U91(x1,x2)	0[x1]
  #U61(x1,x2)	0[x1,x2]
    USABLE RULES: { 1..53 }
    Removed DPs: #8..10 #12..17 #19 #20 #22 #23 #25 #28 #35 #41 #42 #48 #59 #61 #65..68 #75 #78 #79 #81..83 #85 #88 #89 #91..95 #101 #107 #130 #137 #138 #142 #143
Number of SCCs: 0, DPs: 0