2.90/1.78	WORST_CASE(?, O(1))
2.90/1.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.90/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.90/1.79	
2.90/1.79	
2.90/1.79	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.90/1.79	
2.90/1.79	(0) CpxTRS
2.90/1.79	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.90/1.79	(2) BOUNDS(1, 1)
2.90/1.79	
2.90/1.79	
2.90/1.79	----------------------------------------
2.90/1.79	
2.90/1.79	(0)
2.90/1.79	Obligation:
2.90/1.79	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.90/1.79	
2.90/1.79	
2.90/1.79	The TRS R consists of the following rules:
2.90/1.79	
2.90/1.79	   f(0) -> cons(0)
2.90/1.79	   f(s(0)) -> f(p(s(0)))
2.90/1.79	   p(s(0)) -> 0
2.90/1.79	
2.90/1.79	S is empty.
2.90/1.79	Rewrite Strategy: FULL
2.90/1.79	----------------------------------------
2.90/1.79	
2.90/1.79	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.90/1.79	Constant runtime complexity proven by termination of constructor-based narrowing.
2.90/1.79	
2.90/1.79	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.90/1.79	
2.90/1.79	f(s(0)) ->^* cons(0)
2.90/1.79	
2.90/1.79	f(0) ->^* cons(0)
2.90/1.79	
2.90/1.79	p(s(0)) ->^* 0
2.90/1.79	
2.90/1.79	
2.90/1.79	
2.90/1.79	
2.90/1.79	----------------------------------------
2.90/1.79	
2.90/1.79	(2)
2.90/1.79	BOUNDS(1, 1)
3.31/1.84	EOF