2.98/1.61	WORST_CASE(?, O(1))
2.98/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.98/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.98/1.63	
2.98/1.63	
2.98/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.98/1.63	
2.98/1.63	(0) CpxTRS
2.98/1.63	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.98/1.63	(2) BOUNDS(1, 1)
2.98/1.63	
2.98/1.63	
2.98/1.63	----------------------------------------
2.98/1.63	
2.98/1.63	(0)
2.98/1.63	Obligation:
2.98/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.98/1.63	
2.98/1.63	
2.98/1.63	The TRS R consists of the following rules:
2.98/1.63	
2.98/1.63	   f(0) -> cons(0)
2.98/1.63	   f(s(0)) -> f(p(s(0)))
2.98/1.63	   p(s(X)) -> X
2.98/1.63	
2.98/1.63	S is empty.
2.98/1.63	Rewrite Strategy: INNERMOST
2.98/1.63	----------------------------------------
2.98/1.63	
2.98/1.63	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.98/1.63	Constant runtime complexity proven by termination of constructor-based narrowing.
2.98/1.63	
2.98/1.63	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.98/1.63	
2.98/1.63	f(s(0)) ->^* cons(0)
2.98/1.63	
2.98/1.63	f(0) ->^* cons(0)
2.98/1.63	
2.98/1.63	p(x0) ->^* p(x0)
2.98/1.63	
2.98/1.63	
2.98/1.63	
2.98/1.63	
2.98/1.63	----------------------------------------
2.98/1.63	
2.98/1.63	(2)
2.98/1.63	BOUNDS(1, 1)
3.27/1.67	EOF