3.11/1.54	WORST_CASE(?, O(1))
3.11/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.11/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.11/1.56	
3.11/1.56	
3.11/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.11/1.56	
3.11/1.56	(0) CpxTRS
3.11/1.56	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.11/1.56	(2) BOUNDS(1, 1)
3.11/1.56	
3.11/1.56	
3.11/1.56	----------------------------------------
3.11/1.56	
3.11/1.56	(0)
3.11/1.56	Obligation:
3.11/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.11/1.56	
3.11/1.56	
3.11/1.56	The TRS R consists of the following rules:
3.11/1.56	
3.11/1.56	   f(0) -> cons(0)
3.11/1.56	   f(s(0)) -> f(p(s(0)))
3.11/1.56	   p(s(0)) -> 0
3.11/1.56	
3.11/1.56	S is empty.
3.11/1.56	Rewrite Strategy: INNERMOST
3.11/1.56	----------------------------------------
3.11/1.56	
3.11/1.56	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.11/1.56	Constant runtime complexity proven by termination of constructor-based narrowing.
3.11/1.56	
3.11/1.56	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.11/1.56	
3.11/1.56	f(s(0)) ->^* cons(0)
3.11/1.56	
3.11/1.56	f(0) ->^* cons(0)
3.11/1.56	
3.11/1.56	p(s(0)) ->^* 0
3.11/1.56	
3.11/1.56	
3.11/1.56	
3.11/1.56	
3.11/1.56	----------------------------------------
3.11/1.56	
3.11/1.56	(2)
3.11/1.56	BOUNDS(1, 1)
3.11/1.59	EOF