/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   U11(tt) -> N
   U21(tt) -> s(plus(N, M))
   U41(tt) -> plus(x(N, M), N)
   and(tt) -> X
   U31(tt) -> 0
   isNat -> tt
   isNat -> and(isNat)
   isNat -> isNat
   plus(N, 0) -> U11(isNat)
   plus(N, s(M)) -> U21(and(isNat))
   x(N, 0) -> U31(isNat)
   x(N, s(M)) -> U41(and(isNat))



Outermost Strategy.

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

   U11(tt) -> N
   U21(tt) -> s(plus(N, M))
   U41(tt) -> plus(x(N, M), N)
   and(tt) -> X
   U31(tt) -> 0
   isNat -> tt
   isNat -> and(isNat)
   isNat -> isNat
   plus(N, 0) -> U11(isNat)
   plus(N, s(M)) -> U21(and(isNat))
   x(N, 0) -> U31(isNat)
   x(N, s(M)) -> U41(and(isNat))



Outermost Strategy.

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

U11(tt) -> U11(tt) with rule U11(tt) -> N at position [] and matcher [N / U11(tt)]

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

Context: []

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