/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem:
 and(tt(),T) -> T
 isNatIList(IL) -> isNatList(activate(IL))
 isNat(n__0()) -> tt()
 isNat(n__s(N)) -> isNat(activate(N))
 isNat(n__length(L)) -> isNatList(activate(L))
 isNatIList(n__zeros()) -> tt()
 isNatIList(n__cons(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
 isNatList(n__nil()) -> tt()
 isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L)))
 isNatList(n__take(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
 zeros() -> cons(0(),n__zeros())
 take(0(),IL) -> uTake1(isNatIList(IL))
 uTake1(tt()) -> nil()
 take(s(M),cons(N,IL)) ->
 uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL))
 uTake2(tt(),M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL)))
 length(cons(N,L)) -> uLength(and(isNat(N),isNatList(activate(L))),activate(L))
 uLength(tt(),L) -> s(length(activate(L)))
 0() -> n__0()
 s(X) -> n__s(X)
 length(X) -> n__length(X)
 zeros() -> n__zeros()
 cons(X1,X2) -> n__cons(X1,X2)
 nil() -> n__nil()
 take(X1,X2) -> n__take(X1,X2)
 activate(n__0()) -> 0()
 activate(n__s(X)) -> s(activate(X))
 activate(n__length(X)) -> length(activate(X))
 activate(n__zeros()) -> zeros()
 activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
 activate(n__nil()) -> nil()
 activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
 activate(X) -> X

Proof:
 Unfolding Processor:
  loop length: 4
  terms:
   isNatIList(activate(n__zeros()))
   isNatIList(zeros())
   isNatIList(cons(0(),n__zeros()))
   isNatIList(n__cons(0(),n__zeros()))
  context: and(isNat(activate(0())),[])
  substitution:
   
  Qed