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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   tail(cons(X)) -> Y
   if(true) -> X
   if(false) -> Y
   primes -> sieve(from(s(s(0))))
   from(X) -> cons(X)
   head(cons(X)) -> X
   filter(s(s(X)), cons(Y)) -> if(divides(s(s(X)), Y))
   sieve(cons(X)) -> cons(X)



Outermost Strategy.

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

   tail(cons(X)) -> Y
   if(true) -> X
   if(false) -> Y
   primes -> sieve(from(s(s(0))))
   from(X) -> cons(X)
   head(cons(X)) -> X
   filter(s(s(X)), cons(Y)) -> if(divides(s(s(X)), Y))
   sieve(cons(X)) -> cons(X)



Outermost Strategy.

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

tail(cons(X)) -> tail(cons(X)) with rule tail(cons(X'')) -> Y at position [] and matcher [X'' / X, Y / tail(cons(X))]

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