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


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NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   U31(tt) -> N
   U42(tt) -> s(plus(N, M))
   U11(tt) -> U12(isNat)
   U12(tt) -> tt
   U21(tt) -> tt
   U41(tt) -> U42(isNat)
   isNat -> tt
   isNat -> U11(isNat)
   isNat -> U21(isNat)
   plus(N, 0) -> U31(isNat)
   plus(N, s(M)) -> U41(isNat)



Outermost Strategy.

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

   U31(tt) -> N
   U42(tt) -> s(plus(N, M))
   U11(tt) -> U12(isNat)
   U12(tt) -> tt
   U21(tt) -> tt
   U41(tt) -> U42(isNat)
   isNat -> tt
   isNat -> U11(isNat)
   isNat -> U21(isNat)
   plus(N, 0) -> U31(isNat)
   plus(N, s(M)) -> U41(isNat)



Outermost Strategy.

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

U31(tt) -> U31(tt) with rule U31(tt) -> N at position [] and matcher [N / U31(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