/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(X1,X2)
    21: activate(n__isNat(X)) -> isNat(X)
    22: activate(n__s(X)) -> s(X)
    23: activate(n__x(X1,X2)) -> x(X1,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(X1,X2)
   #16: #x(N,0()) -> #U31(isNat(N))
   #17: #x(N,0()) -> #isNat(N)
   #18: #activate(n__plus(X1,X2)) -> #plus(X1,X2)
   #19: #isNat(n__plus(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2)))
   #20: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1))
   #21: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #22: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #23: #plus(N,0()) -> #U11(isNat(N),N)
   #24: #plus(N,0()) -> #isNat(N)
   #25: #and(tt(),X) -> #activate(X)
   #26: #activate(n__s(X)) -> #s(X)
   #27: #activate(n__0()) -> #0()
   #28: #activate(n__isNat(X)) -> #isNat(X)
   #29: #U31(tt()) -> #0()
   #30: #U11(tt(),N) -> #activate(N)
   #31: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #32: #isNat(n__s(V1)) -> #activate(V1)
   #33: #U41(tt(),M,N) -> #plus(x(activate(N),activate(M)),activate(N))
   #34: #U41(tt(),M,N) -> #x(activate(N),activate(M))
   #35: #U41(tt(),M,N) -> #activate(N)
   #36: #U41(tt(),M,N) -> #activate(M)
   #37: #U41(tt(),M,N) -> #activate(N)
Number of SCCs: 1, DPs: 32
	SCC { #2..15 #17..25 #28 #30..37 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 1859 + x2, 0})
  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{x2, x1})
  #activate(x1)		w: (x1)
  x(x1,x2)		w: (max{1857 + x2, 5147 + x1})
  n__s(x1)		w: (x1)
  0()		w: (3289)
  #x(x1,x2)		w: (max{1857 + x2, 5147 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{1859 + x2, x1})
  n__0()		w: (3289)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{1857 + x2, 5147 + x1})
  plus(x1,x2)		w: (max{1859 + x2, x1})
  #U11(x1,x2)		w: (max{x2, x1})
  U31(x1)		w: (5147)
  #U41(x1,x2,x3)		w: (max{5147 + x3, 1857 + x2, 5147 + x1})
  #U21(x1,x2,x3)		w: (max{x3, x2, x1})
  tt()		w: (3289)
  U41(x1,x2,x3)		w: (max{5147 + x3, 1857 + x2, x1})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{x2, x1})
    USABLE RULES: { 1..24 }
    Removed DPs: #6..11 #17 #22 #35..37
Number of SCCs: 1, DPs: 21
	SCC { #2..5 #12..15 #18..21 #23..25 #28 #30..34 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 3 + x2, 0})
  U11(x1,x2)		w: (max{x2, 0})
  s(x1)		w: (x1)
  #isNat(x1)		w: (5 + x1)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (max{x2, 0})
  #plus(x1,x2)		w: (max{7 + x2, 5 + x1})
  #activate(x1)		w: (5 + x1)
  x(x1,x2)		w: (max{1 + x2, 4 + x1})
  n__s(x1)		w: (x1)
  0()		w: (5)
  #x(x1,x2)		w: (max{6 + x2, 9 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (x1)
  n__plus(x1,x2)		w: (max{3 + x2, x1})
  n__0()		w: (5)
  isNat(x1)		w: (x1)
  n__x(x1,x2)		w: (max{1 + x2, 4 + x1})
  plus(x1,x2)		w: (max{3 + x2, x1})
  #U11(x1,x2)		w: (max{5 + x2, 5 + x1})
  U31(x1)		w: (5)
  #U41(x1,x2,x3)		w: (max{9 + x3, 6 + x2, 1 + x1})
  #U21(x1,x2,x3)		w: (max{5 + x3, 7 + x2, 3 + x1})
  tt()		w: (3)
  U41(x1,x2,x3)		w: (max{4 + x3, 1 + x2, x1})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{5 + x2, 1 + x1})
    USABLE RULES: { 1..24 }
    Removed DPs: #4 #14 #19
Number of SCCs: 1, DPs: 18
	SCC { #2 #3 #5 #12 #13 #15 #18 #20 #21 #23..25 #28 #30..34 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  U21(x1,x2,x3)	4[x3,x2,x1]
  U11(x1,x2)	3[x2]
  s(x1)	0[x1]
  #isNat(x1)	x1
  activate(x1)	x1
  and(x1,x2)	x2
  #plus(x1,x2)	x1
  #activate(x1)	x1
  x(x1,x2)	5[x1,x2]
  n__s(x1)	0[x1]
  0()	2
  #x(x1,x2)	5[x1,x2]
  #s(x1)	0[]
  n__isNat(x1)	x1
  n__plus(x1,x2)	4[x1,x2]
  n__0()	2
  isNat(x1)	x1
  n__x(x1,x2)	5[x1,x2]
  plus(x1,x2)	4[x1,x2]
  #U11(x1,x2)	x2
  U31(x1)	3[]
  #U41(x1,x2,x3)	5[x3,x2]
  #U21(x1,x2,x3)	x3
  tt()	1
  U41(x1,x2,x3)	5[x3,x2,x1]
  #U31(x1)	0[]
  #and(x1,x2)	x2
    USABLE RULES: { 1..24 }
    Removed DPs: #18 #20 #21 #31 #32
Number of SCCs: 1, DPs: 11
	SCC { #2 #3 #5 #12 #13 #15 #23 #25 #30 #33 #34 }
Sum... Max... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (max{x3, 30341 + x2, 9245 + x1})
  U11(x1,x2)		w: (max{x2, 2 + 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{106497 + x2, 58585 + x1})
  #activate(x1)		w: (58585 + x1)
  x(x1,x2)		w: (max{69009 + x2, 47914 + x1})
  n__s(x1)		w: (x1)
  0()		w: (25051)
  #x(x1,x2)		w: (max{127594 + x2, 106499 + x1})
  #s(x1)		w: (0)
  n__isNat(x1)		w: (21096)
  n__plus(x1,x2)		w: (max{30341 + x2, x1})
  n__0()		w: (25051)
  isNat(x1)		w: (21096)
  n__x(x1,x2)		w: (max{69009 + x2, 47914 + x1})
  plus(x1,x2)		w: (max{30341 + x2, x1})
  #U11(x1,x2)		w: (max{58585 + x2, 27846 + x1})
  U31(x1)		w: (26819 + x1)
  #U41(x1,x2,x3)		w: (max{106499 + x3, 127594 + x2, 106498 + x1})
  #U21(x1,x2,x3)		w: (max{58585 + x3, 106497 + x2, 85400 + x1})
  tt()		w: (0)
  U41(x1,x2,x3)		w: (max{47914 + x3, 69009 + x2, 0})
  #U31(x1)		w: (0)
  #and(x1,x2)		w: (max{58586 + x2, 58586 + x1})
    USABLE RULES: { 1..24 }
    Removed DPs: #13 #25
Number of SCCs: 1, DPs: 9
	SCC { #2 #3 #5 #12 #15 #23 #30 #33 #34 }
Sum... Max... QLPOpS... succeeded.
  #0()	0
  U21(x1,x2,x3)	4[x3,x2,x1]
  U11(x1,x2)	4[x2]
  s(x1)	1[x1]
  #isNat(x1)	x1
  activate(x1)	x1
  and(x1,x2)	x2
  #plus(x1,x2)	x1
  #activate(x1)	x1
  x(x1,x2)	5[x1,x2]
  n__s(x1)	1[x1]
  0()	3
  #x(x1,x2)	5[x1,x2]
  #s(x1)	0[]
  n__isNat(x1)	x1
  n__plus(x1,x2)	4[x1,x2]
  n__0()	3
  isNat(x1)	x1
  n__x(x1,x2)	5[x1,x2]
  plus(x1,x2)	4[x1,x2]
  #U11(x1,x2)	x2
  U31(x1)	4[]
  #U41(x1,x2,x3)	5[x3,x2]
  #U21(x1,x2,x3)	x3
  tt()	2
  U41(x1,x2,x3)	5[x3,x2,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)	7[x3,x2,x1]
  U11(x1,x2)	7[x2]
  s(x1)	5[x1]
  #isNat(x1)	x1
  activate(x1)	x1
  and(x1,x2)	x2
  #plus(x1,x2)	6[x1,x2]
  #activate(x1)	x1
  x(x1,x2)	8[x1,x2]
  n__s(x1)	5[x1]
  0()	4
  #x(x1,x2)	5[x1,x2]
  #s(x1)	0[]
  n__isNat(x1)	5[x1]
  n__plus(x1,x2)	7[x1,x2]
  n__0()	4
  isNat(x1)	5[x1]
  n__x(x1,x2)	8[x1,x2]
  plus(x1,x2)	7[x1,x2]
  #U11(x1,x2)	x2
  U31(x1)	5[]
  #U41(x1,x2,x3)	5[x3,x2]
  #U21(x1,x2,x3)	6[x3,x2]
  tt()	3
  U41(x1,x2,x3)	8[x3,x2,x1]
  #U31(x1)	0[]
  #and(x1,x2)	x2
    USABLE RULES: { 1..24 }
    Removed DPs: #12
Number of SCCs: 0, DPs: 0