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


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YES
Input TRS:
    1: U11(tt(),V2) -> U12(isNat(activate(V2)))
    2: U12(tt()) -> tt()
    3: U21(tt()) -> tt()
    4: U31(tt(),V2) -> U32(isNat(activate(V2)))
    5: U32(tt()) -> tt()
    6: U41(tt(),N) -> activate(N)
    7: U51(tt(),M,N) -> U52(isNat(activate(N)),activate(M),activate(N))
    8: U52(tt(),M,N) -> s(plus(activate(N),activate(M)))
    9: U61(tt()) -> 0()
    10: U71(tt(),M,N) -> U72(isNat(activate(N)),activate(M),activate(N))
    11: U72(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
    12: isNat(n__0()) -> tt()
    13: isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
    14: isNat(n__s(V1)) -> U21(isNat(activate(V1)))
    15: isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2))
    16: plus(N,0()) -> U41(isNat(N),N)
    17: plus(N,s(M)) -> U51(isNat(M),M,N)
    18: x(N,0()) -> U61(isNat(N))
    19: x(N,s(M)) -> U71(isNat(M),M,N)
    20: 0() -> n__0()
    21: plus(X1,X2) -> n__plus(X1,X2)
    22: s(X) -> n__s(X)
    23: x(X1,X2) -> n__x(X1,X2)
    24: activate(n__0()) -> 0()
    25: activate(n__plus(X1,X2)) -> plus(X1,X2)
    26: activate(n__s(X)) -> s(X)
    27: activate(n__x(X1,X2)) -> x(X1,X2)
    28: activate(X) -> X
Number of strict rules: 28
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U41(tt(),N) -> #activate(N)
   #2: #isNat(n__plus(V1,V2)) -> #U11(isNat(activate(V1)),activate(V2))
   #3: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1))
   #4: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #5: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #6: #U61(tt()) -> #0()
   #7: #U72(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #8: #U72(tt(),M,N) -> #x(activate(N),activate(M))
   #9: #U72(tt(),M,N) -> #activate(N)
   #10: #U72(tt(),M,N) -> #activate(M)
   #11: #U72(tt(),M,N) -> #activate(N)
   #12: #activate(n__0()) -> #0()
   #13: #isNat(n__s(V1)) -> #U21(isNat(activate(V1)))
   #14: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #15: #isNat(n__s(V1)) -> #activate(V1)
   #16: #activate(n__plus(X1,X2)) -> #plus(X1,X2)
   #17: #U51(tt(),M,N) -> #U52(isNat(activate(N)),activate(M),activate(N))
   #18: #U51(tt(),M,N) -> #isNat(activate(N))
   #19: #U51(tt(),M,N) -> #activate(N)
   #20: #U51(tt(),M,N) -> #activate(M)
   #21: #U51(tt(),M,N) -> #activate(N)
   #22: #U71(tt(),M,N) -> #U72(isNat(activate(N)),activate(M),activate(N))
   #23: #U71(tt(),M,N) -> #isNat(activate(N))
   #24: #U71(tt(),M,N) -> #activate(N)
   #25: #U71(tt(),M,N) -> #activate(M)
   #26: #U71(tt(),M,N) -> #activate(N)
   #27: #activate(n__x(X1,X2)) -> #x(X1,X2)
   #28: #plus(N,s(M)) -> #U51(isNat(M),M,N)
   #29: #plus(N,s(M)) -> #isNat(M)
   #30: #x(N,s(M)) -> #U71(isNat(M),M,N)
   #31: #x(N,s(M)) -> #isNat(M)
   #32: #activate(n__s(X)) -> #s(X)
   #33: #plus(N,0()) -> #U41(isNat(N),N)
   #34: #plus(N,0()) -> #isNat(N)
   #35: #U11(tt(),V2) -> #U12(isNat(activate(V2)))
   #36: #U11(tt(),V2) -> #isNat(activate(V2))
   #37: #U11(tt(),V2) -> #activate(V2)
   #38: #U52(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #39: #U52(tt(),M,N) -> #plus(activate(N),activate(M))
   #40: #U52(tt(),M,N) -> #activate(N)
   #41: #U52(tt(),M,N) -> #activate(M)
   #42: #isNat(n__x(V1,V2)) -> #U31(isNat(activate(V1)),activate(V2))
   #43: #isNat(n__x(V1,V2)) -> #isNat(activate(V1))
   #44: #isNat(n__x(V1,V2)) -> #activate(V1)
   #45: #isNat(n__x(V1,V2)) -> #activate(V2)
   #46: #U31(tt(),V2) -> #U32(isNat(activate(V2)))
   #47: #U31(tt(),V2) -> #isNat(activate(V2))
   #48: #U31(tt(),V2) -> #activate(V2)
   #49: #x(N,0()) -> #U61(isNat(N))
   #50: #x(N,0()) -> #isNat(N)
Number of SCCs: 1, DPs: 42
	SCC { #1..5 #7..11 #14..31 #33 #34 #36 #37 #39..45 #47 #48 #50 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U72(x1,x2,x3)		w: (max{21238 + x3, 44850 + x2, 0})
  #U32(x1)		w: (0)
  U21(x1)		w: (1 + x1)
  U11(x1,x2)		w: (max{2 + x2, x1})
  s(x1)		w: (x1)
  #isNat(x1)		w: (21238 + x1)
  activate(x1)		w: (x1)
  U71(x1,x2,x3)		w: (max{x3, 23612 + x2, 0})
  #plus(x1,x2)		w: (max{21238 + x2, 21238 + x1})
  #activate(x1)		w: (21238 + x1)
  U72(x1,x2,x3)		w: (max{x3, 23612 + x2, 0})
  #U52(x1,x2,x3)		w: (max{21238 + x3, 21238 + x2, 0})
  U12(x1)		w: (3)
  x(x1,x2)		w: (max{23612 + x2, x1})
  n__s(x1)		w: (x1)
  #U12(x1)		w: (0)
  0()		w: (0)
  #x(x1,x2)		w: (max{44850 + x2, 21238 + x1})
  #s(x1)		w: (0)
  n__plus(x1,x2)		w: (max{x2, x1})
  U32(x1)		w: (4 + x1)
  n__0()		w: (0)
  isNat(x1)		w: (1)
  n__x(x1,x2)		w: (max{23612 + x2, x1})
  U52(x1,x2,x3)		w: (max{x3, x2, 0})
  plus(x1,x2)		w: (max{x2, x1})
  U61(x1)		w: (10995)
  #U51(x1,x2,x3)		w: (max{21238 + x3, 21238 + x2, 0})
  #U11(x1,x2)		w: (max{21238 + x2, 0})
  U31(x1,x2)		w: (max{2 + x2, x1})
  #U41(x1,x2)		w: (max{21238 + x2, 0})
  #U21(x1)		w: (0)
  tt()		w: (4)
  #U71(x1,x2,x3)		w: (max{21238 + x3, 44850 + x2, 0})
  U51(x1,x2,x3)		w: (max{x3, x2, 0})
  U41(x1,x2)		w: (max{x2, 0})
  #U31(x1,x2)		w: (max{44850 + x2, 0})
  #U61(x1)		w: (0)
    USABLE RULES: { 6..11 16..28 }
    Removed DPs: #10 #25 #31 #45 #47 #48
Number of SCCs: 1, DPs: 35
	SCC { #1..5 #7..9 #11 #14..24 #26..30 #33 #34 #36 #37 #39..41 #43 #44 #50 }
Sum... Max... succeeded.
  #0()		w: (0)
  #U72(x1,x2,x3)		w: (max{48160 + x3, 48161 + x2, 0})
  #U32(x1)		w: (0)
  U21(x1)		w: (1 + x1)
  U11(x1,x2)		w: (max{12702 + x2, x1})
  s(x1)		w: (x1)
  #isNat(x1)		w: (22431 + x1)
  activate(x1)		w: (x1)
  U71(x1,x2,x3)		w: (max{25729 + x3, 25730 + x2, 0})
  #plus(x1,x2)		w: (max{22432 + x2, 22431 + x1})
  #activate(x1)		w: (22431 + x1)
  U72(x1,x2,x3)		w: (max{25729 + x3, 25730 + x2, 0})
  #U52(x1,x2,x3)		w: (max{22431 + x3, 22432 + x2, 0})
  U12(x1)		w: (12703)
  x(x1,x2)		w: (max{25730 + x2, 25729 + x1})
  n__s(x1)		w: (x1)
  #U12(x1)		w: (0)
  0()		w: (22775)
  #x(x1,x2)		w: (max{48161 + x2, 48160 + x1})
  #s(x1)		w: (0)
  n__plus(x1,x2)		w: (max{25729 + x2, x1})
  U32(x1)		w: (4380)
  n__0()		w: (22775)
  isNat(x1)		w: (1)
  n__x(x1,x2)		w: (max{25730 + x2, 25729 + x1})
  U52(x1,x2,x3)		w: (max{x3, 25729 + x2, 0})
  plus(x1,x2)		w: (max{25729 + x2, x1})
  U61(x1)		w: (25730)
  #U51(x1,x2,x3)		w: (max{22431 + x3, 22432 + x2, 0})
  #U11(x1,x2)		w: (max{48159 + x2, 0})
  U31(x1,x2)		w: (max{3301 + x2, x1})
  #U41(x1,x2)		w: (max{22431 + x2, 0})
  #U21(x1)		w: (0)
  tt()		w: (12704)
  #U71(x1,x2,x3)		w: (max{48160 + x3, 48161 + x2, 0})
  U51(x1,x2,x3)		w: (max{x3, 25729 + x2, 0})
  U41(x1,x2)		w: (max{x2, 0})
  #U31(x1,x2)		w: (0)
  #U61(x1)		w: (0)
    USABLE RULES: { 6..11 16..28 }
    Removed DPs: #2 #5 #9 #11 #20 #23 #24 #26 #29 #36 #37 #41 #43 #44 #50
Number of SCCs: 1, DPs: 20
	SCC { #1 #3 #4 #7 #8 #14..19 #21 #22 #27 #28 #30 #33 #34 #39 #40 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2,x3)	9[x3,x2,x1]
  #U32(x1)	0[]
  U21(x1)	x1
  U11(x1,x2)	8[]
  s(x1)	6[x1]
  #isNat(x1)	0[x1]
  activate(x1)	x1
  U71(x1,x2,x3)	9[x3,x2,x1]
  #plus(x1,x2)	5[x1]
  #activate(x1)	1[x1]
  U72(x1,x2,x3)	9[x3,x2,x1]
  #U52(x1,x2,x3)	5[x3]
  U12(x1)	8[]
  x(x1,x2)	9[x1,x2]
  n__s(x1)	6[x1]
  #U12(x1)	0[]
  0()	3
  #x(x1,x2)	9[x1,x2]
  #s(x1)	0[]
  n__plus(x1,x2)	8[x2,x1]
  U32(x1)	8[]
  n__0()	3
  isNat(x1)	8[]
  n__x(x1,x2)	9[x1,x2]
  U52(x1,x2,x3)	8[x2,x3,x1]
  plus(x1,x2)	8[x2,x1]
  U61(x1)	3[]
  #U51(x1,x2,x3)	5[x3]
  #U11(x1,x2)	0[x2]
  U31(x1,x2)	x1
  #U41(x1,x2)	2[x2]
  #U21(x1)	0[]
  tt()	8
  #U71(x1,x2,x3)	9[x3,x2,x1]
  U51(x1,x2,x3)	8[x2,x3,x1]
  U41(x1,x2)	x2
  #U31(x1,x2)	0[x2,x1]
  #U61(x1)	0[]
    USABLE RULES: { 1..28 }
    Removed DPs: #1 #3 #4 #7 #8 #14..16 #18 #19 #21 #27 #30 #33 #34 #40
Number of SCCs: 1, DPs: 3
	SCC { #17 #28 #39 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  #U72(x1,x2,x3)	9[x3,x2,x1]
  #U32(x1)	0[]
  U21(x1)	x1
  U11(x1,x2)	8[]
  s(x1)	6[x1]
  #isNat(x1)	0[x1]
  activate(x1)	x1
  U71(x1,x2,x3)	9[x3,x2,x1]
  #plus(x1,x2)	9[x1,x2]
  #activate(x1)	1[x1]
  U72(x1,x2,x3)	9[x3,x2,x1]
  #U52(x1,x2,x3)	9[x3,x2]
  U12(x1)	8[]
  x(x1,x2)	9[x1,x2]
  n__s(x1)	6[x1]
  #U12(x1)	0[]
  0()	3
  #x(x1,x2)	9[x1,x2]
  #s(x1)	0[]
  n__plus(x1,x2)	8[x2,x1]
  U32(x1)	8[]
  n__0()	3
  isNat(x1)	8[]
  n__x(x1,x2)	9[x1,x2]
  U52(x1,x2,x3)	8[x2,x3,x1]
  plus(x1,x2)	8[x2,x1]
  U61(x1)	3[]
  #U51(x1,x2,x3)	9[x3,x2]
  #U11(x1,x2)	0[x2]
  U31(x1,x2)	x1
  #U41(x1,x2)	2[x2]
  #U21(x1)	0[]
  tt()	8
  #U71(x1,x2,x3)	9[x3,x2,x1]
  U51(x1,x2,x3)	8[x2,x3,x1]
  U41(x1,x2)	x2
  #U31(x1,x2)	0[x2,x1]
  #U61(x1)	0[]
    USABLE RULES: { 1..28 }
    Removed DPs: #28
Number of SCCs: 0, DPs: 0