/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 48 ms]
(2) NO


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(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

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



Outermost Strategy.

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

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



Outermost Strategy.

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

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

Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].

Context: cons(X, [])

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