/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 36 ms]
(2) NO


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

   filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M))
   filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M))
   sieve(cons(0, Y)) -> cons(0, sieve(Y))
   sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N)))
   nats(N) -> cons(N, nats(s(N)))
   zprimes -> sieve(nats(s(s(0))))



Outermost Strategy.

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

   filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M))
   filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M))
   sieve(cons(0, Y)) -> cons(0, sieve(Y))
   sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N)))
   nats(N) -> cons(N, nats(s(N)))
   zprimes -> sieve(nats(s(s(0))))



Outermost Strategy.

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

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

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

Context: cons(N, [])

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