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


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YES
Input TRS:
    1: a__U11(tt(),V1,V2) -> a__U12(a__isNat(V1),V2)
    2: a__U12(tt(),V2) -> a__U13(a__isNat(V2))
    3: a__U13(tt()) -> tt()
    4: a__U21(tt(),V1) -> a__U22(a__isNat(V1))
    5: a__U22(tt()) -> tt()
    6: a__U31(tt(),V1,V2) -> a__U32(a__isNat(V1),V2)
    7: a__U32(tt(),V2) -> a__U33(a__isNat(V2))
    8: a__U33(tt()) -> tt()
    9: a__U41(tt(),N) -> mark(N)
    10: a__U51(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    11: a__U61(tt()) -> 0()
    12: a__U71(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    13: a__and(tt(),X) -> mark(X)
    14: a__isNat(0()) -> tt()
    15: a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
    16: a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
    17: a__isNat(x(V1,V2)) -> a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
    18: a__isNatKind(0()) -> tt()
    19: a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
    20: a__isNatKind(s(V1)) -> a__isNatKind(V1)
    21: a__isNatKind(x(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
    22: a__plus(N,0()) -> a__U41(a__and(a__isNat(N),isNatKind(N)),N)
    23: a__plus(N,s(M)) -> a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
    24: a__x(N,0()) -> a__U61(a__and(a__isNat(N),isNatKind(N)))
    25: a__x(N,s(M)) -> a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
    26: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    27: mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
    28: mark(isNat(X)) -> a__isNat(X)
    29: mark(U13(X)) -> a__U13(mark(X))
    30: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    31: mark(U22(X)) -> a__U22(mark(X))
    32: mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
    33: mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
    34: mark(U33(X)) -> a__U33(mark(X))
    35: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
    36: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
    37: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    38: mark(U61(X)) -> a__U61(mark(X))
    39: mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
    40: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    41: mark(and(X1,X2)) -> a__and(mark(X1),X2)
    42: mark(isNatKind(X)) -> a__isNatKind(X)
    43: mark(tt()) -> tt()
    44: mark(s(X)) -> s(mark(X))
    45: mark(0()) -> 0()
    46: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    47: a__U12(X1,X2) -> U12(X1,X2)
    48: a__isNat(X) -> isNat(X)
    49: a__U13(X) -> U13(X)
    50: a__U21(X1,X2) -> U21(X1,X2)
    51: a__U22(X) -> U22(X)
    52: a__U31(X1,X2,X3) -> U31(X1,X2,X3)
    53: a__U32(X1,X2) -> U32(X1,X2)
    54: a__U33(X) -> U33(X)
    55: a__U41(X1,X2) -> U41(X1,X2)
    56: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
    57: a__plus(X1,X2) -> plus(X1,X2)
    58: a__U61(X) -> U61(X)
    59: a__U71(X1,X2,X3) -> U71(X1,X2,X3)
    60: a__x(X1,X2) -> x(X1,X2)
    61: a__and(X1,X2) -> and(X1,X2)
    62: a__isNatKind(X) -> isNatKind(X)
Number of strict rules: 62
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__U12(tt(),V2) -> #a__U13(a__isNat(V2))
   #2: #a__U12(tt(),V2) -> #a__isNat(V2)
   #3: #mark(U13(X)) -> #a__U13(mark(X))
   #4: #mark(U13(X)) -> #mark(X)
   #5: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2)
   #6: #mark(U41(X1,X2)) -> #mark(X1)
   #7: #mark(isNatKind(X)) -> #a__isNatKind(X)
   #8: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
   #9: #mark(and(X1,X2)) -> #mark(X1)
   #10: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
   #11: #mark(plus(X1,X2)) -> #mark(X1)
   #12: #mark(plus(X1,X2)) -> #mark(X2)
   #13: #mark(U61(X)) -> #a__U61(mark(X))
   #14: #mark(U61(X)) -> #mark(X)
   #15: #a__U31(tt(),V1,V2) -> #a__U32(a__isNat(V1),V2)
   #16: #a__U31(tt(),V1,V2) -> #a__isNat(V1)
   #17: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
   #18: #mark(x(X1,X2)) -> #mark(X1)
   #19: #mark(x(X1,X2)) -> #mark(X2)
   #20: #a__and(tt(),X) -> #mark(X)
   #21: #a__U41(tt(),N) -> #mark(N)
   #22: #a__x(N,0()) -> #a__U61(a__and(a__isNat(N),isNatKind(N)))
   #23: #a__x(N,0()) -> #a__and(a__isNat(N),isNatKind(N))
   #24: #a__x(N,0()) -> #a__isNat(N)
   #25: #a__plus(N,s(M)) -> #a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
   #26: #a__plus(N,s(M)) -> #a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))
   #27: #a__plus(N,s(M)) -> #a__and(a__isNat(M),isNatKind(M))
   #28: #a__plus(N,s(M)) -> #a__isNat(M)
   #29: #a__U71(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
   #30: #a__U71(tt(),M,N) -> #a__x(mark(N),mark(M))
   #31: #a__U71(tt(),M,N) -> #mark(N)
   #32: #a__U71(tt(),M,N) -> #mark(M)
   #33: #a__U71(tt(),M,N) -> #mark(N)
   #34: #mark(U22(X)) -> #a__U22(mark(X))
   #35: #mark(U22(X)) -> #mark(X)
   #36: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2)
   #37: #mark(U21(X1,X2)) -> #mark(X1)
   #38: #a__x(N,s(M)) -> #a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
   #39: #a__x(N,s(M)) -> #a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))
   #40: #a__x(N,s(M)) -> #a__and(a__isNat(M),isNatKind(M))
   #41: #a__x(N,s(M)) -> #a__isNat(M)
   #42: #a__isNatKind(s(V1)) -> #a__isNatKind(V1)
   #43: #a__U32(tt(),V2) -> #a__U33(a__isNat(V2))
   #44: #a__U32(tt(),V2) -> #a__isNat(V2)
   #45: #mark(U71(X1,X2,X3)) -> #a__U71(mark(X1),X2,X3)
   #46: #mark(U71(X1,X2,X3)) -> #mark(X1)
   #47: #a__U51(tt(),M,N) -> #a__plus(mark(N),mark(M))
   #48: #a__U51(tt(),M,N) -> #mark(N)
   #49: #a__U51(tt(),M,N) -> #mark(M)
   #50: #mark(U32(X1,X2)) -> #a__U32(mark(X1),X2)
   #51: #mark(U32(X1,X2)) -> #mark(X1)
   #52: #mark(s(X)) -> #mark(X)
   #53: #mark(isNat(X)) -> #a__isNat(X)
   #54: #a__plus(N,0()) -> #a__U41(a__and(a__isNat(N),isNatKind(N)),N)
   #55: #a__plus(N,0()) -> #a__and(a__isNat(N),isNatKind(N))
   #56: #a__plus(N,0()) -> #a__isNat(N)
   #57: #mark(U33(X)) -> #a__U33(mark(X))
   #58: #mark(U33(X)) -> #mark(X)
   #59: #mark(U12(X1,X2)) -> #a__U12(mark(X1),X2)
   #60: #mark(U12(X1,X2)) -> #mark(X1)
   #61: #a__isNat(x(V1,V2)) -> #a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
   #62: #a__isNat(x(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
   #63: #a__isNat(x(V1,V2)) -> #a__isNatKind(V1)
   #64: #mark(U31(X1,X2,X3)) -> #a__U31(mark(X1),X2,X3)
   #65: #mark(U31(X1,X2,X3)) -> #mark(X1)
   #66: #a__isNatKind(plus(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
   #67: #a__isNatKind(plus(V1,V2)) -> #a__isNatKind(V1)
   #68: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3)
   #69: #mark(U11(X1,X2,X3)) -> #mark(X1)
   #70: #mark(U51(X1,X2,X3)) -> #a__U51(mark(X1),X2,X3)
   #71: #mark(U51(X1,X2,X3)) -> #mark(X1)
   #72: #a__isNatKind(x(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
   #73: #a__isNatKind(x(V1,V2)) -> #a__isNatKind(V1)
   #74: #a__isNat(s(V1)) -> #a__U21(a__isNatKind(V1),V1)
   #75: #a__isNat(s(V1)) -> #a__isNatKind(V1)
   #76: #a__U11(tt(),V1,V2) -> #a__U12(a__isNat(V1),V2)
   #77: #a__U11(tt(),V1,V2) -> #a__isNat(V1)
   #78: #a__isNat(plus(V1,V2)) -> #a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
   #79: #a__isNat(plus(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
   #80: #a__isNat(plus(V1,V2)) -> #a__isNatKind(V1)
   #81: #a__U21(tt(),V1) -> #a__U22(a__isNat(V1))
   #82: #a__U21(tt(),V1) -> #a__isNat(V1)
Number of SCCs: 1, DPs: 74
	SCC { #2 #4..12 #14..21 #23..33 #35..42 #44..56 #58..80 #82 }
Sum... Max... succeeded.
  #a__isNatKind(x1)		w: (1 + x1)
  isNatKind(x1)		w: (x1)
  a__plus(x1,x2)		w: (max{3 + x2, x1})
  U21(x1,x2)		w: (max{x2, x1})
  #a__U71(x1,x2,x3)		w: (max{7 + x3, 8 + x2, 0})
  U11(x1,x2,x3)		w: (max{3 + x3, x2, x1})
  s(x1)		w: (x1)
  #a__U31(x1,x2,x3)		w: (max{3 + x3, 3 + x2, 5 + x1})
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (x1)
  #a__isNat(x1)		w: (2 + x1)
  U71(x1,x2,x3)		w: (max{5 + x3, 6 + x2, 1 + x1})
  and(x1,x2)		w: (max{x2, x1})
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (max{2 + x3, 3 + x2, 2 + x1})
  #a__x(x1,x2)		w: (max{8 + x2, 7 + x1})
  a__U22(x1)		w: (x1)
  #a__U11(x1,x2,x3)		w: (max{4 + x3, 2 + x2, 0})
  a__U31(x1,x2,x3)		w: (max{2 + x3, 5 + x2, 4 + x1})
  a__U51(x1,x2,x3)		w: (max{x3, 3 + x2, x1})
  a__x(x1,x2)		w: (max{6 + x2, 5 + x1})
  U12(x1,x2)		w: (max{2 + x2, x1})
  a__U41(x1,x2)		w: (max{x2, x1})
  x(x1,x2)		w: (max{6 + x2, 5 + x1})
  #a__U12(x1,x2)		w: (max{3 + x2, 1 + x1})
  #a__U21(x1,x2)		w: (max{2 + x2, 0})
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (max{3 + x2, 2 + x1})
  #mark(x1)		w: (2 + x1)
  0()		w: (1)
  #a__and(x1,x2)		w: (max{2 + x2, 0})
  a__U21(x1,x2)		w: (max{x2, x1})
  a__U32(x1,x2)		w: (max{x2, 5 + x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3)		w: (max{3 + x3, x2, x1})
  U32(x1,x2)		w: (max{x2, 5 + x1})
  U33(x1)		w: (x1)
  a__U12(x1,x2)		w: (max{2 + x2, x1})
  isNat(x1)		w: (x1)
  plus(x1,x2)		w: (max{3 + x2, x1})
  U61(x1)		w: (1 + x1)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (2 + x1)
  U31(x1,x2,x3)		w: (max{2 + x3, 5 + x2, 4 + x1})
  a__U71(x1,x2,x3)		w: (max{5 + x3, 6 + x2, 1 + x1})
  a__U61(x1)		w: (1 + x1)
  #a__U41(x1,x2)		w: (max{2 + x2, 0})
  tt()		w: (0)
  a__isNat(x1)		w: (x1)
  U13(x1)		w: (2 + x1)
  a__isNatKind(x1)		w: (x1)
  U22(x1)		w: (x1)
  U51(x1,x2,x3)		w: (max{x3, 3 + x2, x1})
  a__and(x1,x2)		w: (max{x2, x1})
  U41(x1,x2)		w: (max{x2, x1})
  #a__U32(x1,x2)		w: (max{2 + x2, 2 + x1})
    USABLE RULES: { 1..62 }
    Removed DPs: #2 #4 #7 #12 #14..16 #18 #19 #23 #24 #27 #28 #31..33 #39..41 #46 #49 #51 #59 #61..66 #72 #73 #75 #76 #79 #80
Number of SCCs: 3, DPs: 33
	SCC { #42 #67 }
Sum... succeeded.
  #a__isNatKind(x1)		w: (2 + x1)
  isNatKind(x1)		w: (3 + x1)
  a__plus(x1,x2)		w: (5833)
  U21(x1,x2)		w: (4 + x1)
  #a__U71(x1,x2,x3)		w: (1)
  U11(x1,x2,x3)		w: (28941 + x1)
  s(x1)		w: (1 + x1)
  #a__U31(x1,x2,x3)		w: (1)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (10338 + x1)
  #a__isNat(x1)		w: (2)
  U71(x1,x2,x3)		w: (4)
  and(x1,x2)		w: (2810)
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (2)
  #a__x(x1,x2)		w: (2)
  a__U22(x1)		w: (2808)
  #a__U11(x1,x2,x3)		w: (1)
  a__U31(x1,x2,x3)		w: (3 + x3)
  a__U51(x1,x2,x3)		w: (3024 + x3 + x2 + x1)
  a__x(x1,x2)		w: (2)
  U12(x1,x2)		w: (28940)
  a__U41(x1,x2)		w: (5834 + x2)
  x(x1,x2)		w: (3 + x2 + x1)
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (0)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (1)
  #mark(x1)		w: (2)
  0()		w: (2811)
  #a__and(x1,x2)		w: (2)
  a__U21(x1,x2)		w: (3 + x2)
  a__U32(x1,x2)		w: (4 + x2)
  mark(x1)		w: (1)
  a__U11(x1,x2,x3)		w: (28940 + x3 + x2)
  U32(x1,x2)		w: (5)
  U33(x1)		w: (10339)
  a__U12(x1,x2)		w: (28939 + x1)
  isNat(x1)		w: (3)
  plus(x1,x2)		w: (1 + x2 + x1)
  U61(x1)		w: (2)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (2808)
  U31(x1,x2,x3)		w: (4 + x2 + x1)
  a__U71(x1,x2,x3)		w: (3 + x3 + x2)
  a__U61(x1)		w: (1 + x1)
  #a__U41(x1,x2)		w: (0)
  tt()		w: (2809)
  a__isNat(x1)		w: (2)
  U13(x1)		w: (2809 + x1)
  a__isNatKind(x1)		w: (2)
  U22(x1)		w: (2809)
  U51(x1,x2,x3)		w: (3025)
  a__and(x1,x2)		w: (x2)
  U41(x1,x2)		w: (5835)
  #a__U32(x1,x2)		w: (2)
    USABLE RULES: { }
    Removed DPs: #42 #67
Number of SCCs: 2, DPs: 31
	SCC { #74 #77 #78 #82 }
Sum... succeeded.
  #a__isNatKind(x1)		w: (2)
  isNatKind(x1)		w: (3 + x1)
  a__plus(x1,x2)		w: (5834)
  U21(x1,x2)		w: (4 + x1)
  #a__U71(x1,x2,x3)		w: (1)
  U11(x1,x2,x3)		w: (28941 + x1)
  s(x1)		w: (4 + x1)
  #a__U31(x1,x2,x3)		w: (1)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (10338 + x1)
  #a__isNat(x1)		w: (25727 + x1)
  U71(x1,x2,x3)		w: (4)
  and(x1,x2)		w: (22777)
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (2)
  #a__x(x1,x2)		w: (2)
  a__U22(x1)		w: (4)
  #a__U11(x1,x2,x3)		w: (25728 + x2)
  a__U31(x1,x2,x3)		w: (3 + x3)
  a__U51(x1,x2,x3)		w: (5832 + x3 + x2 + x1)
  a__x(x1,x2)		w: (2)
  U12(x1,x2)		w: (41640)
  a__U41(x1,x2)		w: (32962 + x2)
  x(x1,x2)		w: (3 + x2 + x1)
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (25728 + x2)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (1)
  #mark(x1)		w: (2)
  0()		w: (7)
  #a__and(x1,x2)		w: (2)
  a__U21(x1,x2)		w: (3 + x2)
  a__U32(x1,x2)		w: (4 + x2)
  mark(x1)		w: (1)
  a__U11(x1,x2,x3)		w: (28940 + x3 + x2)
  U32(x1,x2)		w: (5)
  U33(x1)		w: (10339)
  a__U12(x1,x2)		w: (41639 + x1)
  isNat(x1)		w: (3)
  plus(x1,x2)		w: (2 + x2 + x1)
  U61(x1)		w: (2)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (2)
  U31(x1,x2,x3)		w: (4 + x2 + x1)
  a__U71(x1,x2,x3)		w: (3 + x3 + x2)
  a__U61(x1)		w: (1 + x1)
  #a__U41(x1,x2)		w: (0)
  tt()		w: (5)
  a__isNat(x1)		w: (2)
  U13(x1)		w: (3 + x1)
  a__isNatKind(x1)		w: (2)
  U22(x1)		w: (5)
  U51(x1,x2,x3)		w: (5835)
  a__and(x1,x2)		w: (x2)
  U41(x1,x2)		w: (32963)
  #a__U32(x1,x2)		w: (2)
    USABLE RULES: { }
    Removed DPs: #74 #77 #78 #82
Number of SCCs: 1, DPs: 27
	SCC { #5 #6 #8..11 #17 #20 #21 #25 #26 #29 #30 #35 #37 #38 #45 #47 #48 #52 #54 #55 #58 #60 #69..71 }
Sum... Max... succeeded.
  #a__isNatKind(x1)		w: (1)
  isNatKind(x1)		w: (1)
  a__plus(x1,x2)		w: (max{30089 + x2, x1})
  U21(x1,x2)		w: (max{0, x1})
  #a__U71(x1,x2,x3)		w: (max{30090 + x3, 0})
  U11(x1,x2,x3)		w: (max{0, x1})
  s(x1)		w: (x1)
  #a__U31(x1,x2,x3)		w: (0)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (x1)
  #a__isNat(x1)		w: (2)
  U71(x1,x2,x3)		w: (max{30090 + x3, 0, 30088 + x1})
  and(x1,x2)		w: (max{x2, x1})
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (max{x3, 30089 + x2, 0})
  #a__x(x1,x2)		w: (max{0, 30090 + x1})
  a__U22(x1)		w: (x1)
  #a__U11(x1,x2,x3)		w: (0)
  a__U31(x1,x2,x3)		w: (max{0, x1})
  a__U51(x1,x2,x3)		w: (max{x3, 30089 + x2, 30087 + x1})
  a__x(x1,x2)		w: (max{0, 30090 + x1})
  U12(x1,x2)		w: (max{0, x1})
  a__U41(x1,x2)		w: (max{x2, 1 + x1})
  x(x1,x2)		w: (max{0, 30090 + x1})
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (0)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (max{30089 + x2, x1})
  #mark(x1)		w: (x1)
  0()		w: (0)
  #a__and(x1,x2)		w: (max{x2, 0})
  a__U21(x1,x2)		w: (max{0, x1})
  a__U32(x1,x2)		w: (max{0, x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3)		w: (max{0, x1})
  U32(x1,x2)		w: (max{0, x1})
  U33(x1)		w: (x1)
  a__U12(x1,x2)		w: (max{0, x1})
  isNat(x1)		w: (1)
  plus(x1,x2)		w: (max{30089 + x2, x1})
  U61(x1)		w: (x1)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (1)
  U31(x1,x2,x3)		w: (max{0, x1})
  a__U71(x1,x2,x3)		w: (max{30090 + x3, 0, 30088 + x1})
  a__U61(x1)		w: (x1)
  #a__U41(x1,x2)		w: (max{x2, 0})
  tt()		w: (1)
  a__isNat(x1)		w: (1)
  U13(x1)		w: (1)
  a__isNatKind(x1)		w: (1)
  U22(x1)		w: (x1)
  U51(x1,x2,x3)		w: (max{x3, 30089 + x2, 30087 + x1})
  a__and(x1,x2)		w: (max{x2, x1})
  U41(x1,x2)		w: (max{x2, 1 + x1})
  #a__U32(x1,x2)		w: (0)
    USABLE RULES: { 1..62 }
    Removed DPs: #6 #26 #55 #71
Number of SCCs: 1, DPs: 23
	SCC { #5 #8..11 #17 #20 #21 #25 #29 #30 #35 #37 #38 #45 #47 #48 #52 #54 #58 #60 #69 #70 }
Sum... succeeded.
  #a__isNatKind(x1)		w: (2)
  isNatKind(x1)		w: (0)
  a__plus(x1,x2)		w: (x1)
  U21(x1,x2)		w: (1 + x2 + x1)
  #a__U71(x1,x2,x3)		w: (1 + x2)
  U11(x1,x2,x3)		w: (1 + x2 + x1)
  s(x1)		w: (x1)
  #a__U31(x1,x2,x3)		w: (1)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (1 + x1)
  #a__isNat(x1)		w: (25727)
  U71(x1,x2,x3)		w: (1 + x2)
  and(x1,x2)		w: (x2 + x1)
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (x3)
  #a__x(x1,x2)		w: (1 + x2)
  a__U22(x1)		w: (x1)
  #a__U11(x1,x2,x3)		w: (25728)
  a__U31(x1,x2,x3)		w: (2 + x3)
  a__U51(x1,x2,x3)		w: (x3)
  a__x(x1,x2)		w: (1 + x2)
  U12(x1,x2)		w: (x1)
  a__U41(x1,x2)		w: (x2)
  x(x1,x2)		w: (1 + x2)
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (25728)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (x1)
  #mark(x1)		w: (x1)
  0()		w: (12114)
  #a__and(x1,x2)		w: (x2)
  a__U21(x1,x2)		w: (1 + x2 + x1)
  a__U32(x1,x2)		w: (2 + x2)
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3)		w: (1 + x2 + x1)
  U32(x1,x2)		w: (2 + x2)
  U33(x1)		w: (1 + x1)
  a__U12(x1,x2)		w: (x1)
  isNat(x1)		w: (1 + x1)
  plus(x1,x2)		w: (x1)
  U61(x1)		w: (12115)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (0)
  U31(x1,x2,x3)		w: (2 + x3)
  a__U71(x1,x2,x3)		w: (1 + x2)
  a__U61(x1)		w: (12115)
  #a__U41(x1,x2)		w: (x2)
  tt()		w: (0)
  a__isNat(x1)		w: (1 + x1)
  U13(x1)		w: (0)
  a__isNatKind(x1)		w: (0)
  U22(x1)		w: (x1)
  U51(x1,x2,x3)		w: (x3)
  a__and(x1,x2)		w: (x2 + x1)
  U41(x1,x2)		w: (x2)
  #a__U32(x1,x2)		w: (2)
    USABLE RULES: { 1..62 }
    Removed DPs: #37 #58 #69
Number of SCCs: 1, DPs: 20
	SCC { #5 #8..11 #17 #20 #21 #25 #29 #30 #35 #38 #45 #47 #48 #52 #54 #60 #70 }
Sum... Max... succeeded.
  #a__isNatKind(x1)		w: (1)
  isNatKind(x1)		w: (1 + x1)
  a__plus(x1,x2)		w: (max{43143 + x2, x1})
  U21(x1,x2)		w: (max{1 + x2, x1})
  #a__U71(x1,x2,x3)		w: (max{45391 + x3, 43143 + x2, 38647 + x1})
  U11(x1,x2,x3)		w: (max{0, 1 + x2})
  s(x1)		w: (x1)
  #a__U31(x1,x2,x3)		w: (0)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (1)
  #a__isNat(x1)		w: (2)
  U71(x1,x2,x3)		w: (max{45390 + x3, 43142 + x2, 38648 + x1})
  and(x1,x2)		w: (max{2247 + x2, x1})
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (max{1 + x3, 43144 + x2, 0})
  #a__x(x1,x2)		w: (max{43143 + x2, 45391 + x1})
  a__U22(x1)		w: (x1)
  #a__U11(x1,x2,x3)		w: (0)
  a__U31(x1,x2,x3)		w: (max{0, 1 + x2, x1})
  a__U51(x1,x2,x3)		w: (max{x3, 43143 + x2, 0})
  a__x(x1,x2)		w: (max{43142 + x2, 45390 + x1})
  U12(x1,x2)		w: (max{0, x1})
  a__U41(x1,x2)		w: (max{x2, 0})
  x(x1,x2)		w: (max{43142 + x2, 45390 + x1})
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (0)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (max{43144 + x2, 1 + x1})
  #mark(x1)		w: (1 + x1)
  0()		w: (0)
  #a__and(x1,x2)		w: (max{2 + x2, 0})
  a__U21(x1,x2)		w: (max{1 + x2, x1})
  a__U32(x1,x2)		w: (max{0, x1})
  mark(x1)		w: (x1)
  a__U11(x1,x2,x3)		w: (max{0, 1 + x2})
  U32(x1,x2)		w: (max{0, x1})
  U33(x1)		w: (1)
  a__U12(x1,x2)		w: (max{0, x1})
  isNat(x1)		w: (1 + x1)
  plus(x1,x2)		w: (max{43143 + x2, x1})
  U61(x1)		w: (43142 + x1)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (1)
  U31(x1,x2,x3)		w: (max{0, 1 + x2, x1})
  a__U71(x1,x2,x3)		w: (max{45390 + x3, 43142 + x2, 38648 + x1})
  a__U61(x1)		w: (43142 + x1)
  #a__U41(x1,x2)		w: (max{1 + x2, 0})
  tt()		w: (1)
  a__isNat(x1)		w: (1 + x1)
  U13(x1)		w: (1)
  a__isNatKind(x1)		w: (1 + x1)
  U22(x1)		w: (x1)
  U51(x1,x2,x3)		w: (max{x3, 43143 + x2, 0})
  a__and(x1,x2)		w: (max{2247 + x2, x1})
  U41(x1,x2)		w: (max{x2, 0})
  #a__U32(x1,x2)		w: (0)
    USABLE RULES: { 1..62 }
    Removed DPs: #8 #20
Number of SCCs: 1, DPs: 18
	SCC { #5 #9..11 #17 #21 #25 #29 #30 #35 #38 #45 #47 #48 #52 #54 #60 #70 }
Sum... Max... QLPOpS... succeeded.
  #a__isNatKind(x1)	0[]
  isNatKind(x1)	3[x1]
  a__plus(x1,x2)	5[x1,x2]
  U21(x1,x2)	4[]
  #a__U71(x1,x2,x3)	6[x3,x2]
  U11(x1,x2,x3)	4[]
  s(x1)	4[x1]
  #a__U31(x1,x2,x3)	0[x2]
  #a__U33(x1)	0[]
  a__U33(x1)	2[]
  #a__isNat(x1)	0[]
  U71(x1,x2,x3)	6[x3,x2,x1]
  and(x1,x2)	1[x1,x2]
  #a__U13(x1)	0[]
  #a__U51(x1,x2,x3)	x3
  #a__x(x1,x2)	6[x1,x2]
  a__U22(x1)	x1
  #a__U11(x1,x2,x3)	0[x1,x2,x3]
  a__U31(x1,x2,x3)	3[]
  a__U51(x1,x2,x3)	5[x3,x2,x1]
  a__x(x1,x2)	6[x1,x2]
  U12(x1,x2)	x1
  a__U41(x1,x2)	2[x2]
  x(x1,x2)	6[x1,x2]
  #a__U12(x1,x2)	0[x2]
  #a__U21(x1,x2)	0[]
  #a__U61(x1)	0[]
  #a__plus(x1,x2)	x1
  #mark(x1)	x1
  0()	10
  #a__and(x1,x2)	0[x2]
  a__U21(x1,x2)	4[]
  a__U32(x1,x2)	3[]
  mark(x1)	x1
  a__U11(x1,x2,x3)	4[]
  U32(x1,x2)	3[]
  U33(x1)	2[]
  a__U12(x1,x2)	x1
  isNat(x1)	4[]
  plus(x1,x2)	5[x1,x2]
  U61(x1)	10[]
  #a__U22(x1)	0[]
  a__U13(x1)	1[]
  U31(x1,x2,x3)	3[]
  a__U71(x1,x2,x3)	6[x3,x2,x1]
  a__U61(x1)	10[]
  #a__U41(x1,x2)	x2
  tt()	1
  a__isNat(x1)	4[]
  U13(x1)	1[]
  a__isNatKind(x1)	3[x1]
  U22(x1)	x1
  U51(x1,x2,x3)	5[x3,x2,x1]
  a__and(x1,x2)	1[x1,x2]
  U41(x1,x2)	2[x2]
  #a__U32(x1,x2)	0[]
    USABLE RULES: { 1..62 }
    Removed DPs: #5 #9..11 #45 #52 #70
Number of SCCs: 1, DPs: 11
	SCC { #17 #21 #25 #29 #30 #35 #38 #47 #48 #54 #60 }
Sum... Max... QLPOpS... succeeded.
  #a__isNatKind(x1)	0[]
  isNatKind(x1)	6[x1]
  a__plus(x1,x2)	8[x1,x2]
  U21(x1,x2)	7[]
  #a__U71(x1,x2,x3)	9[x3,x2]
  U11(x1,x2,x3)	7[]
  s(x1)	7[x1]
  #a__U31(x1,x2,x3)	0[x2]
  #a__U33(x1)	0[]
  a__U33(x1)	5[]
  #a__isNat(x1)	0[]
  U71(x1,x2,x3)	9[x3,x2,x1]
  and(x1,x2)	4[x1,x2]
  #a__U13(x1)	0[]
  #a__U51(x1,x2,x3)	x3
  #a__x(x1,x2)	9[x1,x2]
  a__U22(x1)	x1
  #a__U11(x1,x2,x3)	0[x1,x2,x3]
  a__U31(x1,x2,x3)	6[]
  a__U51(x1,x2,x3)	8[x3,x2,x1]
  a__x(x1,x2)	9[x1,x2]
  U12(x1,x2)	x1
  a__U41(x1,x2)	5[x2]
  x(x1,x2)	9[x1,x2]
  #a__U12(x1,x2)	0[x2]
  #a__U21(x1,x2)	0[]
  #a__U61(x1)	0[]
  #a__plus(x1,x2)	x1
  #mark(x1)	x1
  0()	13
  #a__and(x1,x2)	0[x2]
  a__U21(x1,x2)	7[]
  a__U32(x1,x2)	6[]
  mark(x1)	x1
  a__U11(x1,x2,x3)	7[]
  U32(x1,x2)	6[]
  U33(x1)	5[]
  a__U12(x1,x2)	x1
  isNat(x1)	7[]
  plus(x1,x2)	8[x1,x2]
  U61(x1)	13[]
  #a__U22(x1)	0[]
  a__U13(x1)	4[]
  U31(x1,x2,x3)	6[]
  a__U71(x1,x2,x3)	9[x3,x2,x1]
  a__U61(x1)	13[]
  #a__U41(x1,x2)	x2
  tt()	4
  a__isNat(x1)	7[]
  U13(x1)	4[]
  a__isNatKind(x1)	6[x1]
  U22(x1)	x1
  U51(x1,x2,x3)	8[x3,x2,x1]
  a__and(x1,x2)	4[x1,x2]
  U41(x1,x2)	5[x2]
  #a__U32(x1,x2)	0[]
    USABLE RULES: { 1..62 }
    Removed DPs: #38
Number of SCCs: 2, DPs: 4
	SCC { #35 #60 }
Sum... succeeded.
  #a__isNatKind(x1)		w: (2)
  isNatKind(x1)		w: (9765 + x1)
  a__plus(x1,x2)		w: (3 + x2)
  U21(x1,x2)		w: (9769 + x2)
  #a__U71(x1,x2,x3)		w: (3)
  U11(x1,x2,x3)		w: (9769 + x3)
  s(x1)		w: (9767)
  #a__U31(x1,x2,x3)		w: (1)
  #a__U33(x1)		w: (0)
  a__U33(x1)		w: (7 + x1)
  #a__isNat(x1)		w: (25727)
  U71(x1,x2,x3)		w: (9769 + x2)
  and(x1,x2)		w: (9766 + x2)
  #a__U13(x1)		w: (0)
  #a__U51(x1,x2,x3)		w: (3)
  #a__x(x1,x2)		w: (3)
  a__U22(x1)		w: (9769)
  #a__U11(x1,x2,x3)		w: (25728)
  a__U31(x1,x2,x3)		w: (9768 + x2)
  a__U51(x1,x2,x3)		w: (9771)
  a__x(x1,x2)		w: (9767)
  U12(x1,x2)		w: (9770 + x1)
  a__U41(x1,x2)		w: (14923)
  x(x1,x2)		w: (9768)
  #a__U12(x1,x2)		w: (0)
  #a__U21(x1,x2)		w: (25728)
  #a__U61(x1)		w: (0)
  #a__plus(x1,x2)		w: (2)
  #mark(x1)		w: (3 + x1)
  0()		w: (14919)
  #a__and(x1,x2)		w: (2)
  a__U21(x1,x2)		w: (9768)
  a__U32(x1,x2)		w: (2 + x1)
  mark(x1)		w: (9766)
  a__U11(x1,x2,x3)		w: (9768)
  U32(x1,x2)		w: (3)
  U33(x1)		w: (8)
  a__U12(x1,x2)		w: (9769)
  isNat(x1)		w: (9768)
  plus(x1,x2)		w: (4)
  U61(x1)		w: (14919 + x1)
  #a__U22(x1)		w: (0)
  a__U13(x1)		w: (9770)
  U31(x1,x2,x3)		w: (9769 + x1)
  a__U71(x1,x2,x3)		w: (9768 + x3)
  a__U61(x1)		w: (14918)
  #a__U41(x1,x2)		w: (1)
  tt()		w: (9771)
  a__isNat(x1)		w: (9767)
  U13(x1)		w: (9771 + x1)
  a__isNatKind(x1)		w: (9764)
  U22(x1)		w: (9770 + x1)
  U51(x1,x2,x3)		w: (9772)
  a__and(x1,x2)		w: (9765)
  U41(x1,x2)		w: (14924 + x1)
  #a__U32(x1,x2)		w: (2)
    USABLE RULES: { }
    Removed DPs: #35 #60
Number of SCCs: 1, DPs: 2
	SCC { #25 #47 }
Sum... Max... QLPOpS... succeeded.
  #a__isNatKind(x1)	0[]
  isNatKind(x1)	6[x1]
  a__plus(x1,x2)	8[x1,x2]
  U21(x1,x2)	7[]
  #a__U71(x1,x2,x3)	9[x3,x2]
  U11(x1,x2,x3)	7[]
  s(x1)	7[x1]
  #a__U31(x1,x2,x3)	0[x2]
  #a__U33(x1)	0[]
  a__U33(x1)	5[]
  #a__isNat(x1)	0[]
  U71(x1,x2,x3)	9[x3,x2,x1]
  and(x1,x2)	x2
  #a__U13(x1)	0[]
  #a__U51(x1,x2,x3)	7[x2,x3,x1]
  #a__x(x1,x2)	9[x1,x2]
  a__U22(x1)	x1
  #a__U11(x1,x2,x3)	0[x1,x2,x3]
  a__U31(x1,x2,x3)	6[]
  a__U51(x1,x2,x3)	8[x3,x2,x1]
  a__x(x1,x2)	9[x1,x2]
  U12(x1,x2)	x1
  a__U41(x1,x2)	5[x2]
  x(x1,x2)	9[x1,x2]
  #a__U12(x1,x2)	0[x2]
  #a__U21(x1,x2)	0[]
  #a__U61(x1)	0[]
  #a__plus(x1,x2)	7[x2,x1]
  #mark(x1)	x1
  0()	13
  #a__and(x1,x2)	0[x2]
  a__U21(x1,x2)	7[]
  a__U32(x1,x2)	6[]
  mark(x1)	x1
  a__U11(x1,x2,x3)	7[]
  U32(x1,x2)	6[]
  U33(x1)	5[]
  a__U12(x1,x2)	x1
  isNat(x1)	7[]
  plus(x1,x2)	8[x1,x2]
  U61(x1)	13[]
  #a__U22(x1)	0[]
  a__U13(x1)	4[]
  U31(x1,x2,x3)	6[]
  a__U71(x1,x2,x3)	9[x3,x2,x1]
  a__U61(x1)	13[]
  #a__U41(x1,x2)	x2
  tt()	4
  a__isNat(x1)	7[]
  U13(x1)	4[]
  a__isNatKind(x1)	6[x1]
  U22(x1)	x1
  U51(x1,x2,x3)	8[x3,x2,x1]
  a__and(x1,x2)	x2
  U41(x1,x2)	5[x2]
  #a__U32(x1,x2)	0[]
    USABLE RULES: { 1..62 }
    Removed DPs: #25 #47
Number of SCCs: 0, DPs: 0