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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   nats -> cons(0, n__incr(nats))
   pairs -> cons(0, n__incr(odds))
   odds -> incr(pairs)
   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
   head(cons(X, XS)) -> X
   tail(cons(X, XS)) -> activate(XS)
   incr(X) -> n__incr(X)
   activate(n__incr(X)) -> incr(X)
   activate(X) -> X



Outermost Strategy.

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

   nats -> cons(0, n__incr(nats))
   pairs -> cons(0, n__incr(odds))
   odds -> incr(pairs)
   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
   head(cons(X, XS)) -> X
   tail(cons(X, XS)) -> activate(XS)
   incr(X) -> n__incr(X)
   activate(n__incr(X)) -> incr(X)
   activate(X) -> X



Outermost Strategy.

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

nats -> cons(0, n__incr(nats)) with rule nats -> cons(0, n__incr(nats)) at position [] and matcher [ ]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [1,0].

Context: cons(0, n__incr([]))

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