2.96/1.59	WORST_CASE(?, O(1))
2.96/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.96/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.96/1.60	
2.96/1.60	
2.96/1.60	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.96/1.60	
2.96/1.60	(0) CpxTRS
2.96/1.60	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.96/1.60	(2) BOUNDS(1, 1)
2.96/1.60	
2.96/1.60	
2.96/1.60	----------------------------------------
2.96/1.60	
2.96/1.60	(0)
2.96/1.60	Obligation:
2.96/1.60	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.96/1.60	
2.96/1.60	
2.96/1.60	The TRS R consists of the following rules:
2.96/1.60	
2.96/1.60	   filter(cons(X), 0, M) -> cons(0)
2.96/1.60	   filter(cons(X), s(N), M) -> cons(X)
2.96/1.60	   sieve(cons(0)) -> cons(0)
2.96/1.60	   sieve(cons(s(N))) -> cons(s(N))
2.96/1.60	   nats(N) -> cons(N)
2.96/1.60	   zprimes -> sieve(nats(s(s(0))))
2.96/1.60	
2.96/1.60	S is empty.
2.96/1.60	Rewrite Strategy: FULL
2.96/1.60	----------------------------------------
2.96/1.60	
2.96/1.60	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.96/1.60	Constant runtime complexity proven by termination of constructor-based narrowing.
2.96/1.60	
2.96/1.60	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.96/1.60	
2.96/1.60	sieve(cons(s(x0))) ->^* cons(s(x0))
2.96/1.60	
2.96/1.60	sieve(cons(0)) ->^* cons(0)
2.96/1.60	
2.96/1.60	zprimes ->^* cons(s(s(0)))
2.96/1.60	
2.96/1.60	filter(cons(x0), s(x1), x2) ->^* cons(x0)
2.96/1.60	
2.96/1.60	filter(cons(x0), 0, x1) ->^* cons(0)
2.96/1.60	
2.96/1.60	nats(x0) ->^* cons(x0)
2.96/1.60	
2.96/1.60	
2.96/1.60	
2.96/1.60	
2.96/1.60	----------------------------------------
2.96/1.60	
2.96/1.60	(2)
2.96/1.60	BOUNDS(1, 1)
3.18/1.63	EOF