/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(),V2) -> U12(isNat(activate(V2)))
    2: U12(tt()) -> tt()
    3: U21(tt()) -> tt()
    4: U31(tt(),N) -> activate(N)
    5: U41(tt(),M,N) -> U42(isNat(activate(N)),activate(M),activate(N))
    6: U42(tt(),M,N) -> s(plus(activate(N),activate(M)))
    7: isNat(n__0()) -> tt()
    8: isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
    9: isNat(n__s(V1)) -> U21(isNat(activate(V1)))
    10: plus(N,0()) -> U31(isNat(N),N)
    11: plus(N,s(M)) -> U41(isNat(M),M,N)
    12: 0() -> n__0()
    13: plus(X1,X2) -> n__plus(X1,X2)
    14: s(X) -> n__s(X)
    15: activate(n__0()) -> 0()
    16: activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
    17: activate(n__s(X)) -> s(activate(X))
    18: activate(X) -> X
Number of strict rules: 18
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #U42(tt(),M,N) -> #s(plus(activate(N),activate(M)))
   #2: #U42(tt(),M,N) -> #plus(activate(N),activate(M))
   #3: #U42(tt(),M,N) -> #activate(N)
   #4: #U42(tt(),M,N) -> #activate(M)
   #5: #isNat(n__s(V1)) -> #U21(isNat(activate(V1)))
   #6: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #7: #isNat(n__s(V1)) -> #activate(V1)
   #8: #plus(N,s(M)) -> #U41(isNat(M),M,N)
   #9: #plus(N,s(M)) -> #isNat(M)
   #10: #plus(N,0()) -> #U31(isNat(N),N)
   #11: #plus(N,0()) -> #isNat(N)
   #12: #U41(tt(),M,N) -> #U42(isNat(activate(N)),activate(M),activate(N))
   #13: #U41(tt(),M,N) -> #isNat(activate(N))
   #14: #U41(tt(),M,N) -> #activate(N)
   #15: #U41(tt(),M,N) -> #activate(M)
   #16: #U41(tt(),M,N) -> #activate(N)
   #17: #activate(n__s(X)) -> #s(activate(X))
   #18: #activate(n__s(X)) -> #activate(X)
   #19: #activate(n__plus(X1,X2)) -> #plus(activate(X1),activate(X2))
   #20: #activate(n__plus(X1,X2)) -> #activate(X1)
   #21: #activate(n__plus(X1,X2)) -> #activate(X2)
   #22: #U11(tt(),V2) -> #U12(isNat(activate(V2)))
   #23: #U11(tt(),V2) -> #isNat(activate(V2))
   #24: #U11(tt(),V2) -> #activate(V2)
   #25: #isNat(n__plus(V1,V2)) -> #U11(isNat(activate(V1)),activate(V2))
   #26: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1))
   #27: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #28: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #29: #activate(n__0()) -> #0()
   #30: #U31(tt(),N) -> #activate(N)
Number of SCCs: 1, DPs: 25
  SCC { #2..4 #6..16 #18..21 #23..28 #30 }
POLO(Sum)... succeeded.
      #0 	w: 0
      U21	w: x1
      U11	w: x1
      s 	w: x1 + 1
      #isNat	w: x1
      U42	w: x2 + x3 + 4
      activate	w: x1
      #plus	w: x1 + x2 + 1
      #activate	w: x1
      U12	w: 2
      n__s	w: x1 + 1
      #U42	w: x2 + x3 + 1
      #U12	w: 0
      0 	w: 1
      #s 	w: 0
      n__plus	w: x1 + x2 + 3
      n__0	w: 1
      isNat	w: x1 + 1
      plus	w: x1 + x2 + 3
      #U11	w: x2 + 1
      U31	w: x2
      #U41	w: x2 + x3 + 1
      #U21	w: 0
      tt	w: 3
      U41	w: x2 + x3 + 4
      #U31	w: x2 + 1
    USABLE RULES: { 4..6 10..18 }
    Removed DPs: #3 #4 #6..11 #13..16 #18..21 #23..28 #30
Number of SCCs: 0, DPs: 0