/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: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2))
    2: U12(tt(),V2) -> U13(isNat(activate(V2)))
    3: U13(tt()) -> tt()
    4: U21(tt(),V1) -> U22(isNat(activate(V1)))
    5: U22(tt()) -> tt()
    6: U31(tt(),V1,V2) -> U32(isNat(activate(V1)),activate(V2))
    7: U32(tt(),V2) -> U33(isNat(activate(V2)))
    8: U33(tt()) -> tt()
    9: U41(tt(),N) -> activate(N)
    10: U51(tt(),M,N) -> s(plus(activate(N),activate(M)))
    11: U61(tt()) -> 0()
    12: U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
    13: and(tt(),X) -> activate(X)
    14: isNat(n__0()) -> tt()
    15: isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
    16: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
    17: isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
    18: isNatKind(n__0()) -> tt()
    19: isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
    20: isNatKind(n__s(V1)) -> isNatKind(activate(V1))
    21: isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
    22: plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N)
    23: plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N)
    24: x(N,0()) -> U61(and(isNat(N),n__isNatKind(N)))
    25: x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N)
    26: 0() -> n__0()
    27: plus(X1,X2) -> n__plus(X1,X2)
    28: isNatKind(X) -> n__isNatKind(X)
    29: s(X) -> n__s(X)
    30: x(X1,X2) -> n__x(X1,X2)
    31: and(X1,X2) -> n__and(X1,X2)
    32: isNat(X) -> n__isNat(X)
    33: activate(n__0()) -> 0()
    34: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
    35: activate(n__isNatKind(X)) -> isNatKind(X)
    36: activate(n__s(X)) -> s(activate(X))
    37: activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
    38: activate(n__and(X1,X2)) -> and(activate(X1),X2)
    39: activate(n__isNat(X)) -> isNat(X)
    40: activate(X) -> X
Number of strict rules: 40
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U12(tt(),V2) -> #U13(isNat(activate(V2)))
   #2: #U12(tt(),V2) -> #isNat(activate(V2))
   #3: #U12(tt(),V2) -> #activate(V2)
   #4: #activate(n__isNatKind(X)) -> #isNatKind(X)
   #5: #activate(n__x(X1,X2)) -> #x(activate(X1),activate(X2))
   #6: #activate(n__x(X1,X2)) -> #activate(X1)
   #7: #activate(n__x(X1,X2)) -> #activate(X2)
   #8: #activate(n__and(X1,X2)) -> #and(activate(X1),X2)
   #9: #activate(n__and(X1,X2)) -> #activate(X1)
   #10: #U31(tt(),V1,V2) -> #U32(isNat(activate(V1)),activate(V2))
   #11: #U31(tt(),V1,V2) -> #isNat(activate(V1))
   #12: #U31(tt(),V1,V2) -> #activate(V1)
   #13: #U31(tt(),V1,V2) -> #activate(V2)
   #14: #and(tt(),X) -> #activate(X)
   #15: #U41(tt(),N) -> #activate(N)
   #16: #U61(tt()) -> #0()
   #17: #x(N,0()) -> #U61(and(isNat(N),n__isNatKind(N)))
   #18: #x(N,0()) -> #and(isNat(N),n__isNatKind(N))
   #19: #x(N,0()) -> #isNat(N)
   #20: #plus(N,s(M)) -> #U51(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N)
   #21: #plus(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))
   #22: #plus(N,s(M)) -> #and(isNat(M),n__isNatKind(M))
   #23: #plus(N,s(M)) -> #isNat(M)
   #24: #U71(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #25: #U71(tt(),M,N) -> #x(activate(N),activate(M))
   #26: #U71(tt(),M,N) -> #activate(N)
   #27: #U71(tt(),M,N) -> #activate(M)
   #28: #U71(tt(),M,N) -> #activate(N)
   #29: #x(N,s(M)) -> #U71(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N)
   #30: #x(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))
   #31: #x(N,s(M)) -> #and(isNat(M),n__isNatKind(M))
   #32: #x(N,s(M)) -> #isNat(M)
   #33: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
   #34: #isNatKind(n__s(V1)) -> #activate(V1)
   #35: #U32(tt(),V2) -> #U33(isNat(activate(V2)))
   #36: #U32(tt(),V2) -> #isNat(activate(V2))
   #37: #U32(tt(),V2) -> #activate(V2)
   #38: #activate(n__isNat(X)) -> #isNat(X)
   #39: #U51(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #40: #U51(tt(),M,N) -> #plus(activate(N),activate(M))
   #41: #U51(tt(),M,N) -> #activate(N)
   #42: #U51(tt(),M,N) -> #activate(M)
   #43: #activate(n__0()) -> #0()
   #44: #plus(N,0()) -> #U41(and(isNat(N),n__isNatKind(N)),N)
   #45: #plus(N,0()) -> #and(isNat(N),n__isNatKind(N))
   #46: #plus(N,0()) -> #isNat(N)
   #47: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2))
   #48: #activate(n__plus(X1,X2)) -> #activate(X1)
   #49: #activate(n__plus(X1,X2)) -> #activate(X2)
   #50: #isNat(n__x(V1,V2)) -> #U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
   #51: #isNat(n__x(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #52: #isNat(n__x(V1,V2)) -> #isNatKind(activate(V1))
   #53: #isNat(n__x(V1,V2)) -> #activate(V1)
   #54: #isNat(n__x(V1,V2)) -> #activate(V2)
   #55: #isNat(n__x(V1,V2)) -> #activate(V1)
   #56: #isNat(n__x(V1,V2)) -> #activate(V2)
   #57: #isNatKind(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #58: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #59: #isNatKind(n__plus(V1,V2)) -> #activate(V1)
   #60: #isNatKind(n__plus(V1,V2)) -> #activate(V2)
   #61: #activate(n__s(X)) -> #s(activate(X))
   #62: #activate(n__s(X)) -> #activate(X)
   #63: #isNatKind(n__x(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #64: #isNatKind(n__x(V1,V2)) -> #isNatKind(activate(V1))
   #65: #isNatKind(n__x(V1,V2)) -> #activate(V1)
   #66: #isNatKind(n__x(V1,V2)) -> #activate(V2)
   #67: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1))
   #68: #isNat(n__s(V1)) -> #isNatKind(activate(V1))
   #69: #isNat(n__s(V1)) -> #activate(V1)
   #70: #isNat(n__s(V1)) -> #activate(V1)
   #71: #U11(tt(),V1,V2) -> #U12(isNat(activate(V1)),activate(V2))
   #72: #U11(tt(),V1,V2) -> #isNat(activate(V1))
   #73: #U11(tt(),V1,V2) -> #activate(V1)
   #74: #U11(tt(),V1,V2) -> #activate(V2)
   #75: #isNat(n__plus(V1,V2)) -> #U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
   #76: #isNat(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #77: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #78: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #79: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #80: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #81: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #82: #U21(tt(),V1) -> #U22(isNat(activate(V1)))
   #83: #U21(tt(),V1) -> #isNat(activate(V1))
   #84: #U21(tt(),V1) -> #activate(V1)
Number of SCCs: 1, DPs: 76
	SCC { #2..15 #18..34 #36..38 #40..42 #44..60 #62..81 #83 #84 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U32(x1,x2)		w: (max{3 + x2, 4 + x1})
  isNatKind(x1)		w: (x1)
  U21(x1,x2)		w: (0)
  U11(x1,x2,x3)		w: (max{4 + x3, 0, x1})
  s(x1)		w: (x1)
  #isNat(x1)		w: (2 + x1)
  activate(x1)		w: (x1)
  U71(x1,x2,x3)		w: (max{4 + x3, 14102 + x2, 2 + x1})
  n__isNatKind(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, x1})
  #plus(x1,x2)		w: (max{6 + x2, 2 + x1})
  #activate(x1)		w: (2 + x1)
  #U13(x1)		w: (0)
  U12(x1,x2)		w: (max{2 + x2, 0})
  #U33(x1)		w: (0)
  x(x1,x2)		w: (max{14102 + x2, 4 + x1})
  n__s(x1)		w: (x1)
  #U12(x1,x2)		w: (max{3 + x2, 0})
  0()		w: (0)
  #x(x1,x2)		w: (max{14104 + x2, 6 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{4 + x2, x1})
  U32(x1,x2)		w: (max{0, 3 + x1})
  U33(x1)		w: (1)
  n__0()		w: (0)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{14102 + x2, 4 + x1})
  plus(x1,x2)		w: (max{4 + x2, x1})
  U61(x1)		w: (1 + x1)
  #U51(x1,x2,x3)		w: (max{2 + x3, 6 + x2, 1 + x1})
  #U11(x1,x2,x3)		w: (max{5 + x3, 2 + x2, 1 + x1})
  U31(x1,x2,x3)		w: (max{0, 3 + x2, 2 + x1})
  #U41(x1,x2)		w: (max{2 + x2, 1 + x1})
  #U21(x1,x2)		w: (max{2 + x2, 1 + x1})
  #U22(x1)		w: (0)
  tt()		w: (0)
  n__and(x1,x2)		w: (max{x2, x1})
  #U71(x1,x2,x3)		w: (max{6 + x3, 14104 + x2, 3 + x1})
  U13(x1)		w: (1)
  U22(x1)		w: (0)
  U51(x1,x2,x3)		w: (max{x3, 4 + x2, 0})
  #isNatKind(x1)		w: (2 + x1)
  U41(x1,x2)		w: (max{x2, 0})
  #U31(x1,x2,x3)		w: (max{4 + x3, 5 + x2, 4 + x1})
  #and(x1,x2)		w: (max{2 + x2, 0})
  #U61(x1)		w: (0)
    USABLE RULES: { 1..40 }
    Removed DPs: #2 #3 #6 #7 #10..13 #18 #19 #22 #23 #26..28 #30..32 #36 #37 #42 #49..57 #60 #63..66 #71 #74 #76 #79 #81
Number of SCCs: 1, DPs: 36
	SCC { #4 #5 #8 #9 #14 #15 #20 #21 #24 #25 #29 #33 #34 #38 #40 #41 #44..48 #58 #59 #62 #67..70 #72 #73 #75 #77 #78 #80 #83 #84 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U32(x1,x2)	0[x2]
  isNatKind(x1)	3[x1]
  U21(x1,x2)	5[x2,x1]
  U11(x1,x2,x3)	x1
  s(x1)	7[x1]
  #isNat(x1)	4[x1]
  activate(x1)	x1
  U71(x1,x2,x3)	10[x3,x2,x1]
  n__isNatKind(x1)	3[x1]
  and(x1,x2)	2[x1,x2]
  #plus(x1,x2)	6[x1]
  #activate(x1)	x1
  #U13(x1)	0[]
  U12(x1,x2)	9[]
  #U33(x1)	0[]
  x(x1,x2)	10[x1,x2]
  n__s(x1)	7[x1]
  #U12(x1,x2)	0[x1]
  0()	9
  #x(x1,x2)	10[x1,x2]
  #s(x1)	0[]
  n__isNat(x1)	5[x1]
  n__plus(x1,x2)	8[x2,x1]
  U32(x1,x2)	x1
  U33(x1)	9[]
  n__0()	9
  isNat(x1)	5[x1]
  n__x(x1,x2)	10[x1,x2]
  plus(x1,x2)	8[x2,x1]
  U61(x1)	9[]
  #U51(x1,x2,x3)	6[x3]
  #U11(x1,x2,x3)	4[x2,x3]
  U31(x1,x2,x3)	5[x2,x1,x3]
  #U41(x1,x2)	x2
  #U21(x1,x2)	4[x2]
  #U22(x1)	0[]
  tt()	9
  n__and(x1,x2)	2[x1,x2]
  #U71(x1,x2,x3)	10[x3,x2,x1]
  U13(x1)	9[]
  U22(x1)	x1
  U51(x1,x2,x3)	8[x2,x3,x1]
  #isNatKind(x1)	2[x1]
  U41(x1,x2)	7[x2,x1]
  #U31(x1,x2,x3)	0[x1,x3,x2]
  #and(x1,x2)	1[x2]
  #U61(x1)	0[]
    USABLE RULES: { 1..40 }
    Removed DPs: #4 #8 #9 #14 #21 #24 #25 #29 #33 #34 #38 #41 #44..48 #58 #59 #62 #67..70 #72 #73 #75 #77 #78 #80 #84
Number of SCCs: 1, DPs: 2
	SCC { #20 #40 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U32(x1,x2)	0[x2]
  isNatKind(x1)	4[x1]
  U21(x1,x2)	5[x2,x1]
  U11(x1,x2,x3)	x1
  s(x1)	8[x1]
  #isNat(x1)	4[x1]
  activate(x1)	x1
  U71(x1,x2,x3)	10[x3,x2,x1]
  n__isNatKind(x1)	4[x1]
  and(x1,x2)	3[x1,x2]
  #plus(x1,x2)	7[x1,x2]
  #activate(x1)	x1
  #U13(x1)	0[]
  U12(x1,x2)	6[]
  #U33(x1)	0[]
  x(x1,x2)	10[x1,x2]
  n__s(x1)	8[x1]
  #U12(x1,x2)	0[x1]
  0()	6
  #x(x1,x2)	10[x1,x2]
  #s(x1)	0[]
  n__isNat(x1)	5[x1]
  n__plus(x1,x2)	9[x2,x1]
  U32(x1,x2)	x1
  U33(x1)	6[]
  n__0()	6
  isNat(x1)	5[x1]
  n__x(x1,x2)	10[x1,x2]
  plus(x1,x2)	9[x2,x1]
  U61(x1)	6[]
  #U51(x1,x2,x3)	7[x3,x2]
  #U11(x1,x2,x3)	4[x2,x3]
  U31(x1,x2,x3)	5[x2,x1,x3]
  #U41(x1,x2)	x2
  #U21(x1,x2)	4[x2]
  #U22(x1)	0[]
  tt()	6
  n__and(x1,x2)	3[x1,x2]
  #U71(x1,x2,x3)	10[x3,x2,x1]
  U13(x1)	6[]
  U22(x1)	x1
  U51(x1,x2,x3)	9[x2,x3,x1]
  #isNatKind(x1)	2[x1]
  U41(x1,x2)	5[x2,x1]
  #U31(x1,x2,x3)	0[x1,x3,x2]
  #and(x1,x2)	1[x2]
  #U61(x1)	0[]
    USABLE RULES: { 1..40 }
    Removed DPs: #20
Number of SCCs: 0, DPs: 0