/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(),N) -> activate(N)
    2: U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
    3: and(tt(),X) -> activate(X)
    4: isNat(n__0()) -> tt()
    5: isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
    6: isNat(n__s(V1)) -> isNat(activate(V1))
    7: plus(N,0()) -> U11(isNat(N),N)
    8: plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
    9: 0() -> n__0()
    10: plus(X1,X2) -> n__plus(X1,X2)
    11: isNat(X) -> n__isNat(X)
    12: s(X) -> n__s(X)
    13: activate(n__0()) -> 0()
    14: activate(n__plus(X1,X2)) -> plus(X1,X2)
    15: activate(n__isNat(X)) -> isNat(X)
    16: activate(n__s(X)) -> s(X)
    17: activate(X) -> X
Number of strict rules: 17
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: #isNat(n__s(V1)) -> #isNat(activate(V1))
   #6: #isNat(n__s(V1)) -> #activate(V1)
   #7: #activate(n__0()) -> #0()
   #8: #activate(n__plus(X1,X2)) -> #plus(X1,X2)
   #9: #plus(N,0()) -> #U11(isNat(N),N)
   #10: #plus(N,0()) -> #isNat(N)
   #11: #isNat(n__plus(V1,V2)) -> #and(isNat(activate(V1)),n__isNat(activate(V2)))
   #12: #isNat(n__plus(V1,V2)) -> #isNat(activate(V1))
   #13: #isNat(n__plus(V1,V2)) -> #activate(V1)
   #14: #isNat(n__plus(V1,V2)) -> #activate(V2)
   #15: #activate(n__s(X)) -> #s(X)
   #16: #and(tt(),X) -> #activate(X)
   #17: #U11(tt(),N) -> #activate(N)
   #18: #plus(N,s(M)) -> #U21(and(isNat(M),n__isNat(N)),M,N)
   #19: #plus(N,s(M)) -> #and(isNat(M),n__isNat(N))
   #20: #plus(N,s(M)) -> #isNat(M)
   #21: #activate(n__isNat(X)) -> #isNat(X)
Number of SCCs: 1, DPs: 18
	SCC { #2..6 #8..14 #16..21 }
Sum... succeeded.
  #0()		w: (0)
  U21(x1,x2,x3)		w: (5 + x3 + x2)
  U11(x1,x2)		w: (x2)
  s(x1)		w: (2 + x1)
  #isNat(x1)		w: (20982 + x1)
  activate(x1)		w: (x1)
  and(x1,x2)		w: (1 + x2 + x1)
  #plus(x1,x2)		w: (20983 + x2 + x1)
  #activate(x1)		w: (20982 + x1)
  n__s(x1)		w: (2 + x1)
  0()		w: (1)
  #s(x1)		w: (0)
  n__isNat(x1)		w: (1 + x1)
  n__plus(x1,x2)		w: (3 + x2 + x1)
  n__0()		w: (1)
  isNat(x1)		w: (1 + x1)
  plus(x1,x2)		w: (3 + x2 + x1)
  #U11(x1,x2)		w: (20983 + x2)
  #U21(x1,x2,x3)		w: (20984 + x3 + x2)
  tt()		w: (1)
  #and(x1,x2)		w: (20982 + x2 + x1)
    USABLE RULES: { 1..17 }
    Removed DPs: #2..6 #8..14 #16..21
Number of SCCs: 0, DPs: 0