/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(),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(),N) -> activate(N)
    7: U41(tt(),M,N) -> s(plus(activate(N),activate(M)))
    8: and(tt(),X) -> activate(X)
    9: isNat(n__0()) -> tt()
    10: isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
    11: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
    12: isNatKind(n__0()) -> tt()
    13: isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
    14: isNatKind(n__s(V1)) -> isNatKind(activate(V1))
    15: plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N)
    16: plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N)
    17: 0() -> n__0()
    18: plus(X1,X2) -> n__plus(X1,X2)
    19: isNatKind(X) -> n__isNatKind(X)
    20: s(X) -> n__s(X)
    21: and(X1,X2) -> n__and(X1,X2)
    22: activate(n__0()) -> 0()
    23: activate(n__plus(X1,X2)) -> plus(X1,X2)
    24: activate(n__isNatKind(X)) -> isNatKind(X)
    25: activate(n__s(X)) -> s(X)
    26: activate(n__and(X1,X2)) -> and(X1,X2)
    27: activate(X) -> X
Number of strict rules: 27
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: #U31(tt(),N) -> #activate(N)
   #5: #isNatKind(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #6: #isNatKind(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #7: #isNatKind(n__plus(V1,V2)) -> #activate(V1)
   #8: #isNatKind(n__plus(V1,V2)) -> #activate(V2)
   #9: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1))
   #10: #isNat(n__s(V1)) -> #isNatKind(activate(V1))
   #11: #isNat(n__s(V1)) -> #activate(V1)
   #12: #isNat(n__s(V1)) -> #activate(V1)
   #13: #activate(n__isNatKind(X)) -> #isNatKind(X)
   #14: #activate(n__plus(X1,X2)) -> #plus(X1,X2)
   #15: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
   #16: #isNatKind(n__s(V1)) -> #activate(V1)
   #17: #activate(n__s(X)) -> #s(X)
   #18: #U41(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #19: #U41(tt(),M,N) -> #plus(activate(N),activate(M))
   #20: #U41(tt(),M,N) -> #activate(N)
   #21: #U41(tt(),M,N) -> #activate(M)
   #22: #isNat(n__plus(V1,V2)) -> #U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2))
   #23: #isNat(n__plus(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
   #24: #isNat(n__plus(V1,V2)) -> #isNatKind(activate(V1))
   #25: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #26: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #27: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #28: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #29: #activate(n__0()) -> #0()
   #30: #activate(n__and(X1,X2)) -> #and(X1,X2)
   #31: #plus(N,s(M)) -> #U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N)
   #32: #plus(N,s(M)) -> #and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N)))
   #33: #plus(N,s(M)) -> #and(isNat(M),n__isNatKind(M))
   #34: #plus(N,s(M)) -> #isNat(M)
   #35: #plus(N,s(M)) -> #isNat(N)
   #36: #U11(tt(),V1,V2) -> #U12(isNat(activate(V1)),activate(V2))
   #37: #U11(tt(),V1,V2) -> #isNat(activate(V1))
   #38: #U11(tt(),V1,V2) -> #activate(V1)
   #39: #U11(tt(),V1,V2) -> #activate(V2)
   #40: #and(tt(),X) -> #activate(X)
   #41: #plus(N,0()) -> #U31(and(isNat(N),n__isNatKind(N)),N)
   #42: #plus(N,0()) -> #and(isNat(N),n__isNatKind(N))
   #43: #plus(N,0()) -> #isNat(N)
   #44: #U21(tt(),V1) -> #U22(isNat(activate(V1)))
   #45: #U21(tt(),V1) -> #isNat(activate(V1))
   #46: #U21(tt(),V1) -> #activate(V1)
Number of SCCs: 1, DPs: 41
	SCC { #2..16 #19..28 #30..43 #45 #46 }
Sum... succeeded.
  #0()		w: (0)
  isNatKind(x1)		w: (1 + x1)
  U21(x1,x2)		w: (591 + x1)
  U11(x1,x2,x3)		w: (2 + x3 + x2)
  s(x1)		w: (2452 + x1)
  #isNat(x1)		w: (x1)
  activate(x1)		w: (x1)
  n__isNatKind(x1)		w: (1 + x1)
  and(x1,x2)		w: (2 + x2)
  #plus(x1,x2)		w: (2 + x2 + x1)
  #activate(x1)		w: (x1)
  #U13(x1)		w: (0)
  U12(x1,x2)		w: (32281)
  n__s(x1)		w: (2452 + x1)
  #U12(x1,x2)		w: (1 + x2)
  0()		w: (32282)
  #s(x1)		w: (0)
  n__plus(x1,x2)		w: (3 + x2 + x1)
  n__0()		w: (32282)
  isNat(x1)		w: (1)
  plus(x1,x2)		w: (3 + x2 + x1)
  #U11(x1,x2,x3)		w: (2 + x3 + x2)
  U31(x1,x2)		w: (x2)
  #U41(x1,x2,x3)		w: (6 + x3 + x2)
  #U21(x1,x2)		w: (2447 + x2)
  #U22(x1)		w: (0)
  tt()		w: (32283)
  n__and(x1,x2)		w: (2 + x2)
  U13(x1)		w: (32282)
  U22(x1)		w: (32874 + x1)
  #isNatKind(x1)		w: (x1)
  U41(x1,x2,x3)		w: (2455 + x3 + x2)
  #U31(x1,x2)		w: (1 + x2)
  #and(x1,x2)		w: (1 + x2)
    USABLE RULES: { 6..8 12..27 }
    Removed DPs: #2..16 #19..28 #30..43 #45 #46
Number of SCCs: 0, DPs: 0