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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   U12(tt) -> s(plus(N, M))
   U11(tt) -> U12(tt)
   plus(N, 0) -> N
   plus(N, s(M)) -> U11(tt)



Outermost Strategy.

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

   U12(tt) -> s(plus(N, M))
   U11(tt) -> U12(tt)
   plus(N, 0) -> N
   plus(N, s(M)) -> U11(tt)



Outermost Strategy.

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

plus(N, U12(tt)) -> plus(N, s(plus(U12(tt), U12(tt)))) with rule U12(tt) -> s(plus(N, M)) at position [1] and matcher [N / U12(tt), M / U12(tt)]

plus(N, s(plus(U12(tt), U12(tt)))) -> U11(tt) with rule plus(N', s(M)) -> U11(tt) at position [] and matcher [N' / N, M / plus(U12(tt), U12(tt))]

U11(tt) -> U12(tt) with rule U11(tt) -> U12(tt) at position [] and matcher [ ]

U12(tt) -> s(plus(U12(tt), U12(tt))) with rule U12(tt) -> s(plus(N, M)) at position [] and matcher [N / U12(tt), M / U12(tt)]

Now an instance of the first term with Matcher [N / U12(tt)] occurs in the last term at position [0].

Context: s([])

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