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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   2ndspos(s(N), cons(X)) -> rcons(posrecip(Y), 2ndsneg(N, Z))
   2ndsneg(s(N), cons(X)) -> rcons(negrecip(Y), 2ndspos(N, Z))
   from(X) -> cons(X)
   2ndspos(0, Z) -> rnil
   2ndsneg(0, Z) -> rnil
   pi(X) -> 2ndspos(X, from(0))
   plus(0, Y) -> Y
   plus(s(X), Y) -> s(plus(X, Y))
   times(0, Y) -> 0
   times(s(X), Y) -> plus(Y, times(X, Y))
   square(X) -> times(X, X)



Outermost Strategy.

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

   2ndspos(s(N), cons(X)) -> rcons(posrecip(Y), 2ndsneg(N, Z))
   2ndsneg(s(N), cons(X)) -> rcons(negrecip(Y), 2ndspos(N, Z))
   from(X) -> cons(X)
   2ndspos(0, Z) -> rnil
   2ndsneg(0, Z) -> rnil
   pi(X) -> 2ndspos(X, from(0))
   plus(0, Y) -> Y
   plus(s(X), Y) -> s(plus(X, Y))
   times(0, Y) -> 0
   times(s(X), Y) -> plus(Y, times(X, Y))
   square(X) -> times(X, X)



Outermost Strategy.

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

2ndspos(s(N), cons(X)) -> rcons(posrecip(2ndspos(s(N), cons(X))), 2ndsneg(N, 2ndspos(s(N), cons(X)))) with rule 2ndspos(s(N''), cons(X'')) -> rcons(posrecip(Y), 2ndsneg(N'', Z)) at position [] and matcher [N'' / N, X'' / X, Y / 2ndspos(s(N), cons(X)), Z / 2ndspos(s(N), cons(X))]

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

Context: rcons(posrecip([]), 2ndsneg(N, 2ndspos(s(N), cons(X))))

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