/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 filter(cons(X),0,M) -> cons(0)
 filter(cons(X),s(N),M) -> cons(X)
 nats(N) -> cons(N)
 sieve(cons(0)) -> cons(0)
 sieve(cons(s(N))) -> cons(s(N))
 zprimes -> sieve(nats(s(s(0))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ZPRIMES -> NATS(s(s(0)))
 ZPRIMES -> SIEVE(nats(s(s(0))))
-> Rules:
 filter(cons(X),0,M) -> cons(0)
 filter(cons(X),s(N),M) -> cons(X)
 nats(N) -> cons(N)
 sieve(cons(0)) -> cons(0)
 sieve(cons(s(N))) -> cons(s(N))
 zprimes -> sieve(nats(s(s(0))))

Problem 1: 

SCC Processor:
-> Pairs:
 ZPRIMES -> NATS(s(s(0)))
 ZPRIMES -> SIEVE(nats(s(s(0))))
-> Rules:
 filter(cons(X),0,M) -> cons(0)
 filter(cons(X),s(N),M) -> cons(X)
 nats(N) -> cons(N)
 sieve(cons(0)) -> cons(0)
 sieve(cons(s(N))) -> cons(s(N))
 zprimes -> sieve(nats(s(s(0))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.