/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(),N) -> activate(N)
    2: U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
    3: U31(tt()) -> 0()
    4: U41(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
    5: and(tt(),X) -> activate(X)
    6: isNat(n__0()) -> tt()
    7: isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
    8: isNat(n__s(V1)) -> isNat(activate(V1))
    9: isNat(n__x(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
    10: plus(N,0()) -> U11(isNat(N),N)
    11: plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
    12: x(N,0()) -> U31(isNat(N))
    13: x(N,s(M)) -> U41(and(isNat(M),n__isNat(N)),M,N)
    14: 0() -> n__0()
    15: plus(X1,X2) -> n__plus(X1,X2)
    16: isNat(X) -> n__isNat(X)
    17: s(X) -> n__s(X)
    18: x(X1,X2) -> n__x(X1,X2)
    19: activate(n__0()) -> 0()
    20: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
    21: activate(n__isNat(X)) -> isNat(X)
    22: activate(n__s(X)) -> s(activate(X))
    23: activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
    24: activate(X) -> X
Number of strict rules: 24
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #U21(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #2: #U21(tt(),M,N) -> #plus(activate(N),activate(M))
   #3: #U21(tt(),M,N) -> #activate(N)
   #4: #U21(tt(),M,N) -> #activate(M)
   #5: #x(N,s(M)) -> #U41(and(isNat(M),n__isNat(N)),M,N)
   #6: #x(N,s(M)) -> #and(isNat(M),n__isNat(N))
   #7: #x(N,s(M)) -> #isNat(M)
   #8: #isNat(n__x(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2)))
   #9: #isNat(n__x(V1,V2)) -> #isNat(activate(V1))
   #10: #isNat(n__x(V1,V2)) -> #activate(V1)
   #11: #isNat(n__x(V1,V2)) -> #activate(V2)
   #12: #plus(N,s(M)) -> #U21(and(isNat(M),n__isNat(N)),M,N)
   #13: #plus(N,s(M)) -> #and(isNat(M),n__isNat(N))
   #14: #plus(N,s(M)) -> #isNat(M)
   #15: #activate(n__x(X1,X2)) -> #x(activate(X1),activate(X2))
   #16: #activate(n__x(X1,X2)) -> #activate(X1)
   #17: #activate(n__x(X1,X2)) -> #activate(X2)
   #18: #x(N,0()) -> #U31(isNat(N))
   #19: #x(N,0()) -> #isNat(N)
   #20: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2))
   #21: #activate(n__plus(X1,X2)) -> #activate(X1)
   #22: #activate(n__plus(X1,X2)) -> #activate(X2)
   #23: #isNat(n__plus(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2)))
   #24: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1))
   #25: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #26: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #27: #plus(N,0()) -> #U11(isNat(N),N)
   #28: #plus(N,0()) -> #isNat(N)
   #29: #and(tt(),X) -> #activate(X)
   #30: #activate(n__s(X)) -> #s(activate(X))
   #31: #activate(n__s(X)) -> #activate(X)
   #32: #activate(n__0()) -> #0()
   #33: #activate(n__isNat(X)) -> #isNat(X)
   #34: #U31(tt()) -> #0()
   #35: #U11(tt(),N) -> #activate(N)
   #36: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #37: #isNat(n__s(V1)) -> #activate(V1)
   #38: #U41(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #39: #U41(tt(),M,N) -> #x(activate(N),activate(M))
   #40: #U41(tt(),M,N) -> #activate(N)
   #41: #U41(tt(),M,N) -> #activate(M)
   #42: #U41(tt(),M,N) -> #activate(N)
Number of SCCs: 1, DPs: 37
	SCC { #2..17 #19..29 #31 #33 #35..42 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 40417 + x2, x1})
  U11(x1,x2)		w: (max{x2, 0})
  s(x1)		w: (x1)
  #isNat(x1)		w: (24452 + x1)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, 0})
  #plus(x1,x2)		w: (max{64869 + x2, 24452 + x1})
  #activate(x1)		w: (24452 + x1)
  x(x1,x2)		w: (max{x2, 40417 + x1})
  n__s(x1)		w: (x1)
  0()		w: (592)
  #x(x1,x2)		w: (max{24452 + x2, 64869 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{40417 + x2, x1})
  n__0()		w: (592)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{x2, 40417 + x1})
  plus(x1,x2)		w: (max{40417 + x2, x1})
  #U11(x1,x2)		w: (max{24452 + x2, 0})
  U31(x1)		w: (593 + x1)
  #U41(x1,x2,x3)		w: (max{64869 + x3, 24452 + x2, 64868 + x1})
  #U21(x1,x2,x3)		w: (max{24452 + x3, 64869 + x2, 0})
  tt()		w: (592)
  U41(x1,x2,x3)		w: (max{40417 + x3, x2, 39825 + x1})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{24452 + x2, 24452 + x1})
    USABLE RULES: { 1..24 }
    Removed DPs: #4 #9 #10 #14 #16 #19 #22 #26 #40 #42
Number of SCCs: 1, DPs: 27
	SCC { #2 #3 #5..8 #11..13 #15 #17 #20 #21 #23..25 #27..29 #31 #33 #35..39 #41 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 3 + x2, x1})
  U11(x1,x2)		w: (max{x2, 0})
  s(x1)		w: (x1)
  #isNat(x1)		w: (4 + x1)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, 0})
  #plus(x1,x2)		w: (max{7 + x2, 4 + x1})
  #activate(x1)		w: (4 + x1)
  x(x1,x2)		w: (max{x2, 3 + x1})
  n__s(x1)		w: (x1)
  0()		w: (2)
  #x(x1,x2)		w: (max{4 + x2, 7 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{3 + x2, x1})
  n__0()		w: (2)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{x2, 3 + x1})
  plus(x1,x2)		w: (max{3 + x2, x1})
  #U11(x1,x2)		w: (max{4 + x2, 0})
  U31(x1)		w: (3 + x1)
  #U41(x1,x2,x3)		w: (max{7 + x3, 4 + x2, 3 + x1})
  #U21(x1,x2,x3)		w: (max{4 + x3, 7 + x2, 0})
  tt()		w: (2)
  U41(x1,x2,x3)		w: (max{3 + x3, x2, 1 + x1})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{4 + x2, 1 + x1})
    USABLE RULES: { 1..24 }
    Removed DPs: #6 #23
Number of SCCs: 1, DPs: 25
	SCC { #2 #3 #5 #7 #8 #11..13 #15 #17 #20 #21 #24 #25 #27..29 #31 #33 #35..39 #41 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 2 + x2, x1})
  U11(x1,x2)		w: (max{x2, 0})
  s(x1)		w: (x1)
  #isNat(x1)		w: (x1)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, 0})
  #plus(x1,x2)		w: (max{2 + x2, x1})
  #activate(x1)		w: (x1)
  x(x1,x2)		w: (max{1 + x2, 40403 + x1})
  n__s(x1)		w: (x1)
  0()		w: (1)
  #x(x1,x2)		w: (max{1 + x2, 40403 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{2 + x2, x1})
  n__0()		w: (1)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{1 + x2, 40403 + x1})
  plus(x1,x2)		w: (max{2 + x2, x1})
  #U11(x1,x2)		w: (max{x2, 0})
  U31(x1)		w: (3 + x1)
  #U41(x1,x2,x3)		w: (max{40403 + x3, 1 + x2, 0})
  #U21(x1,x2,x3)		w: (max{x3, 2 + x2, 0})
  tt()		w: (1)
  U41(x1,x2,x3)		w: (max{40403 + x3, 1 + x2, 12832 + x1})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{x2, 0})
    USABLE RULES: { 1..24 }
    Removed DPs: #7 #8 #11 #17 #41
Number of SCCs: 1, DPs: 20
	SCC { #2 #3 #5 #12 #13 #15 #20 #21 #24 #25 #27..29 #31 #33 #35..39 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  U21(x1,x2,x3)	4[x3,x2,x1]
  U11(x1,x2)	x2
  s(x1)	1[x1]
  #isNat(x1)	x1
  activate(x1)	x1
  and(x1,x2)	3[x1,x2]
  #plus(x1,x2)	x1
  #activate(x1)	x1
  x(x1,x2)	5[x2,x1]
  n__s(x1)	1[x1]
  0()	6
  #x(x1,x2)	5[x2,x1]
  #s(x1)	0[]
  n__isNat(x1)	x1
  n__plus(x1,x2)	4[x1,x2]
  n__0()	6
  isNat(x1)	x1
  n__x(x1,x2)	5[x2,x1]
  plus(x1,x2)	4[x1,x2]
  #U11(x1,x2)	x2
  U31(x1)	6[]
  #U41(x1,x2,x3)	5[x2,x3]
  #U21(x1,x2,x3)	x3
  tt()	2
  U41(x1,x2,x3)	5[x2,x3,x1]
  #U31(x1)	0[]
  #and(x1,x2)	x2
    USABLE RULES: { 1..24 }
    Removed DPs: #20 #21 #24 #25 #31 #36 #37
Number of SCCs: 1, DPs: 11
	SCC { #2 #3 #5 #12 #13 #15 #27 #29 #35 #38 #39 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 2 + x2, 1 + x1})
  U11(x1,x2)		w: (max{x2, x1})
  s(x1)		w: (x1)
  #isNat(x1)		w: (0)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, 0})
  #plus(x1,x2)		w: (max{22099 + x2, 22096 + x1})
  #activate(x1)		w: (22096 + x1)
  x(x1,x2)		w: (max{0, 4 + x1})
  n__s(x1)		w: (x1)
  0()		w: (0)
  #x(x1,x2)		w: (max{0, 22100 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (1)
  n__plus(x1,x2)		w: (max{2 + x2, x1})
  n__0()		w: (0)
  isNat(x1)		w: (1)
  n__x(x1,x2)		w: (max{0, 4 + x1})
  plus(x1,x2)		w: (max{2 + x2, x1})
  #U11(x1,x2)		w: (max{22096 + x2, x1})
  U31(x1)		w: (1 + x1)
  #U41(x1,x2,x3)		w: (max{22100 + x3, 0, 22094 + x1})
  #U21(x1,x2,x3)		w: (max{22096 + x3, 22099 + x2, 0})
  tt()		w: (1)
  U41(x1,x2,x3)		w: (max{4 + x3, 0})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{22097 + x2, 0})
    USABLE RULES: { 1..24 }
    Removed DPs: #13 #29
Number of SCCs: 1, DPs: 9
	SCC { #2 #3 #5 #12 #15 #27 #35 #38 #39 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  U21(x1,x2,x3)	4[x3,x2,x1]
  U11(x1,x2)	x2
  s(x1)	0[x1]
  #isNat(x1)	x1
  activate(x1)	x1
  and(x1,x2)	1[x1,x2]
  #plus(x1,x2)	x1
  #activate(x1)	x1
  x(x1,x2)	5[x2,x1]
  n__s(x1)	0[x1]
  0()	8
  #x(x1,x2)	5[x2,x1]
  #s(x1)	0[]
  n__isNat(x1)	x1
  n__plus(x1,x2)	4[x1,x2]
  n__0()	8
  isNat(x1)	x1
  n__x(x1,x2)	5[x2,x1]
  plus(x1,x2)	4[x1,x2]
  #U11(x1,x2)	x2
  U31(x1)	8[]
  #U41(x1,x2,x3)	5[x2,x3]
  #U21(x1,x2,x3)	x3
  tt()	7
  U41(x1,x2,x3)	5[x2,x3,x1]
  #U31(x1)	0[]
  #and(x1,x2)	x2
    USABLE RULES: { 1..24 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2
	SCC { #2 #12 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  U21(x1,x2,x3)	3[x3,x2,x1]
  U11(x1,x2)	3[x2]
  s(x1)	2[x1]
  #isNat(x1)	5[]
  activate(x1)	x1
  and(x1,x2)	x2
  #plus(x1,x2)	7[x2,x1]
  #activate(x1)	4[]
  x(x1,x2)	5[x1,x2]
  n__s(x1)	2[x1]
  0()	7
  #x(x1,x2)	5[]
  #s(x1)	0[]
  n__isNat(x1)	x1
  n__plus(x1,x2)	3[x1,x2]
  n__0()	7
  isNat(x1)	x1
  n__x(x1,x2)	5[x1,x2]
  plus(x1,x2)	3[x1,x2]
  #U11(x1,x2)	3[]
  U31(x1)	7[]
  #U41(x1,x2,x3)	5[x2]
  #U21(x1,x2,x3)	7[x2,x3,x1]
  tt()	6
  U41(x1,x2,x3)	5[x3,x2,x1]
  #U31(x1)	0[]
  #and(x1,x2)	6[]
    USABLE RULES: { 1..24 }
    Removed DPs: #2 #12
Number of SCCs: 0, DPs: 0