3.13/1.62	WORST_CASE(?, O(1))
3.13/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.13/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.13/1.63	
3.13/1.63	
3.13/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.13/1.63	
3.13/1.63	(0) CpxTRS
3.13/1.63	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.13/1.63	(2) BOUNDS(1, 1)
3.13/1.63	
3.13/1.63	
3.13/1.63	----------------------------------------
3.13/1.63	
3.13/1.63	(0)
3.13/1.63	Obligation:
3.13/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.13/1.63	
3.13/1.63	
3.13/1.63	The TRS R consists of the following rules:
3.13/1.63	
3.13/1.63	   f(0, 1, x) -> f(h(x), h(x), x)
3.13/1.63	   h(0) -> 0
3.13/1.63	   h(g(x, y)) -> y
3.13/1.63	
3.13/1.63	S is empty.
3.13/1.63	Rewrite Strategy: INNERMOST
3.13/1.63	----------------------------------------
3.13/1.63	
3.13/1.63	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.13/1.63	Constant runtime complexity proven by termination of constructor-based narrowing.
3.13/1.63	
3.13/1.63	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.13/1.63	
3.13/1.63	h(0) ->^* 0
3.13/1.63	
3.13/1.63	f(0, 1, g(x0, x1)) ->^* f(x1, x1, g(x0, x1))
3.13/1.63	
3.13/1.63	f(0, 1, 0) ->^* f(0, 0, 0)
3.13/1.63	
3.13/1.63	f(0, 1, g(x0, x1)) ->^* f(x1, x1, g(x0, x1))
3.13/1.63	
3.13/1.63	f(0, 1, 0) ->^* f(0, 0, 0)
3.13/1.63	
3.13/1.63	
3.13/1.63	
3.13/1.63	
3.13/1.63	----------------------------------------
3.13/1.63	
3.13/1.63	(2)
3.13/1.63	BOUNDS(1, 1)
3.32/1.68	EOF