2.95/1.66	WORST_CASE(NON_POLY, ?)
2.95/1.66	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.95/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.95/1.66	
2.95/1.66	
2.95/1.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.95/1.66	
2.95/1.66	(0) CpxTRS
2.95/1.66	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.95/1.66	(2) TRS for Loop Detection
2.95/1.66	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.95/1.66	(4) BOUNDS(INF, INF)
2.95/1.66	
2.95/1.66	
2.95/1.66	----------------------------------------
2.95/1.66	
2.95/1.66	(0)
2.95/1.66	Obligation:
2.95/1.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.95/1.66	
2.95/1.66	
2.95/1.66	The TRS R consists of the following rules:
2.95/1.66	
2.95/1.66	   *(X, +(Y, 1)) -> +(*(X, +(Y, *(1, 0))), X)
2.95/1.66	   *(X, 1) -> X
2.95/1.66	   *(X, 0) -> X
2.95/1.66	   *(X, 0) -> 0
2.95/1.66	
2.95/1.66	S is empty.
2.95/1.66	Rewrite Strategy: INNERMOST
2.95/1.66	----------------------------------------
2.95/1.66	
2.95/1.66	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.95/1.66	Transformed a relative TRS into a decreasing-loop problem.
2.95/1.66	----------------------------------------
2.95/1.66	
2.95/1.66	(2)
2.95/1.66	Obligation:
2.95/1.66	Analyzing the following TRS for decreasing loops:
2.95/1.66	
2.95/1.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.95/1.66	
2.95/1.66	
2.95/1.66	The TRS R consists of the following rules:
2.95/1.66	
2.95/1.66	   *(X, +(Y, 1)) -> +(*(X, +(Y, *(1, 0))), X)
2.95/1.66	   *(X, 1) -> X
2.95/1.66	   *(X, 0) -> X
2.95/1.66	   *(X, 0) -> 0
2.95/1.66	
2.95/1.66	S is empty.
2.95/1.66	Rewrite Strategy: INNERMOST
2.95/1.66	----------------------------------------
2.95/1.66	
2.95/1.66	(3) InfiniteLowerBoundProof (FINISHED)
2.95/1.66	The following loop proves infinite runtime complexity:
2.95/1.66	
2.95/1.66	The rewrite sequence
2.95/1.66	
2.95/1.66	*(X, +(Y, 1)) ->^+ +(*(X, +(Y, 1)), X)
2.95/1.66	
2.95/1.66	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
2.95/1.66	
2.95/1.66	The pumping substitution is [ ].
2.95/1.66	
2.95/1.66	The result substitution is [ ].
2.95/1.66	
2.95/1.66	
2.95/1.66	
2.95/1.66	
2.95/1.66	----------------------------------------
2.95/1.66	
2.95/1.66	(4)
2.95/1.66	BOUNDS(INF, INF)
3.27/1.70	EOF