3.07/1.53	WORST_CASE(?, O(1))
3.07/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.07/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.54	
3.07/1.54	
3.07/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.54	
3.07/1.54	(0) CpxTRS
3.07/1.54	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.07/1.54	(2) BOUNDS(1, 1)
3.07/1.54	
3.07/1.54	
3.07/1.54	----------------------------------------
3.07/1.54	
3.07/1.54	(0)
3.07/1.54	Obligation:
3.07/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.54	
3.07/1.54	
3.07/1.54	The TRS R consists of the following rules:
3.07/1.54	
3.07/1.54	   filter(cons(X), 0, M) -> cons(0)
3.07/1.54	   filter(cons(X), s(N), M) -> cons(X)
3.07/1.54	   sieve(cons(0)) -> cons(0)
3.07/1.54	   sieve(cons(s(N))) -> cons(s(N))
3.07/1.54	   nats(N) -> cons(N)
3.07/1.54	   zprimes -> sieve(nats(s(s(0))))
3.07/1.54	
3.07/1.54	S is empty.
3.07/1.54	Rewrite Strategy: INNERMOST
3.07/1.54	----------------------------------------
3.07/1.54	
3.07/1.54	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.07/1.54	Constant runtime complexity proven by termination of constructor-based narrowing.
3.07/1.54	
3.07/1.54	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.07/1.54	
3.07/1.54	sieve(cons(s(x0))) ->^* cons(s(x0))
3.07/1.54	
3.07/1.54	sieve(cons(0)) ->^* cons(0)
3.07/1.54	
3.07/1.54	zprimes ->^* cons(s(s(0)))
3.07/1.54	
3.07/1.54	filter(cons(x0), s(x1), x2) ->^* cons(x0)
3.07/1.54	
3.07/1.54	filter(cons(x0), 0, x1) ->^* cons(0)
3.07/1.54	
3.07/1.54	nats(x0) ->^* cons(x0)
3.07/1.54	
3.07/1.54	
3.07/1.54	
3.07/1.54	
3.07/1.54	----------------------------------------
3.07/1.54	
3.07/1.54	(2)
3.07/1.54	BOUNDS(1, 1)
3.16/4.24	EOF