3.05/1.61	WORST_CASE(?, O(1))
3.05/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.05/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.05/1.62	
3.05/1.62	
3.05/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.05/1.62	
3.05/1.62	(0) CpxTRS
3.05/1.62	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.05/1.62	(2) BOUNDS(1, 1)
3.05/1.62	
3.05/1.62	
3.05/1.62	----------------------------------------
3.05/1.62	
3.05/1.62	(0)
3.05/1.62	Obligation:
3.05/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.05/1.62	
3.05/1.62	
3.05/1.62	The TRS R consists of the following rules:
3.05/1.62	
3.05/1.62	   f(0, 1, x) -> f(h(x), h(x), x)
3.05/1.62	   h(0) -> 0
3.05/1.62	   h(g(x, y)) -> y
3.05/1.62	
3.05/1.62	S is empty.
3.05/1.62	Rewrite Strategy: FULL
3.05/1.62	----------------------------------------
3.05/1.62	
3.05/1.62	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.05/1.62	Constant runtime complexity proven by termination of constructor-based narrowing.
3.05/1.62	
3.05/1.62	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.05/1.62	
3.05/1.62	h(0) ->^* 0
3.05/1.62	
3.05/1.62	f(0, 1, g(x0, x1)) ->^* f(x1, x1, g(x0, x1))
3.05/1.62	
3.05/1.62	f(0, 1, 0) ->^* f(0, 0, 0)
3.05/1.62	
3.05/1.62	
3.05/1.62	
3.05/1.62	
3.05/1.62	----------------------------------------
3.05/1.62	
3.05/1.62	(2)
3.05/1.62	BOUNDS(1, 1)
3.37/1.66	EOF