/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
(2) NO


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(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   uTake2(tt) -> cons(N)
   uLength(tt) -> s(length(L))
   and(tt, T) -> T
   isNatIList -> isNatList
   isNat -> tt
   isNat -> isNat
   isNat -> isNatList
   isNatIList -> tt
   isNatIList -> and(isNat, isNatIList)
   isNatList -> tt
   isNatList -> and(isNat, isNatList)
   isNatList -> and(isNat, isNatIList)
   zeros -> cons(0)
   take(0, IL) -> uTake1(isNatIList)
   uTake1(tt) -> nil
   take(s(M), cons(N)) -> uTake2(and(isNat, and(isNat, isNatIList)))
   length(cons(N)) -> uLength(and(isNat, isNatList))



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   uTake2(tt) -> cons(N)
   uLength(tt) -> s(length(L))
   and(tt, T) -> T
   isNatIList -> isNatList
   isNat -> tt
   isNat -> isNat
   isNat -> isNatList
   isNatIList -> tt
   isNatIList -> and(isNat, isNatIList)
   isNatList -> tt
   isNatList -> and(isNat, isNatList)
   isNatList -> and(isNat, isNatIList)
   zeros -> cons(0)
   take(0, IL) -> uTake1(isNatIList)
   uTake1(tt) -> nil
   take(s(M), cons(N)) -> uTake2(and(isNat, and(isNat, isNatIList)))
   length(cons(N)) -> uLength(and(isNat, isNatList))



Outermost Strategy.

---------- Loop: ----------

uTake2(tt) -> cons(uTake2(tt)) with rule uTake2(tt) -> cons(N) at position [] and matcher [N / uTake2(tt)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].

Context: cons([])

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO