3.28/1.49	WORST_CASE(?, O(1))
3.28/1.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.28/1.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.50	
3.28/1.50	
3.28/1.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.28/1.50	
3.28/1.50	(0) CpxTRS
3.28/1.50	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.28/1.50	(2) BOUNDS(1, 1)
3.28/1.50	
3.28/1.50	
3.28/1.50	----------------------------------------
3.28/1.50	
3.28/1.50	(0)
3.28/1.50	Obligation:
3.28/1.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.28/1.50	
3.28/1.50	
3.28/1.50	The TRS R consists of the following rules:
3.28/1.50	
3.28/1.50	   gcd(x, 0) -> x
3.28/1.50	   gcd(0, y) -> y
3.28/1.50	   gcd(s(x), s(y)) -> if(<(x, y), gcd(s(x), -(y, x)), gcd(-(x, y), s(y)))
3.28/1.50	
3.28/1.50	S is empty.
3.28/1.50	Rewrite Strategy: FULL
3.28/1.50	----------------------------------------
3.28/1.50	
3.28/1.50	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.28/1.50	Constant runtime complexity proven by termination of constructor-based narrowing.
3.28/1.50	
3.28/1.50	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.28/1.50	
3.28/1.50	gcd(s(x0), s(x1)) ->^* if(<(x0, x1), gcd(s(x0), -(x1, x0)), gcd(-(x0, x1), s(x1)))
3.28/1.50	
3.28/1.50	
3.28/1.50	
3.28/1.50	
3.28/1.50	----------------------------------------
3.28/1.50	
3.28/1.50	(2)
3.28/1.50	BOUNDS(1, 1)
3.48/1.58	EOF