3.09/1.57	WORST_CASE(?, O(1))
3.09/1.57	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.09/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.09/1.57	
3.09/1.57	
3.09/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.09/1.57	
3.09/1.57	(0) CpxTRS
3.09/1.57	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.09/1.57	(2) BOUNDS(1, 1)
3.09/1.57	
3.09/1.57	
3.09/1.57	----------------------------------------
3.09/1.57	
3.09/1.57	(0)
3.09/1.57	Obligation:
3.09/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.09/1.57	
3.09/1.57	
3.09/1.57	The TRS R consists of the following rules:
3.09/1.57	
3.09/1.57	   g(x, y) -> x
3.09/1.57	   g(x, y) -> y
3.09/1.57	   f(s(x), y, y) -> f(y, x, s(x))
3.09/1.57	
3.09/1.57	S is empty.
3.09/1.57	Rewrite Strategy: FULL
3.09/1.57	----------------------------------------
3.09/1.57	
3.09/1.57	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.09/1.57	Constant runtime complexity proven by termination of constructor-based narrowing.
3.09/1.57	
3.09/1.57	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.09/1.57	
3.09/1.57	g(x0, x1) ->^* g(x0, x1)
3.09/1.57	
3.09/1.57	f(s(x0), x1, x1) ->^* f(x1, x0, s(x0))
3.09/1.57	
3.09/1.57	
3.09/1.57	
3.09/1.57	
3.09/1.57	----------------------------------------
3.09/1.57	
3.09/1.57	(2)
3.09/1.57	BOUNDS(1, 1)
3.09/1.61	EOF