3.19/1.68	WORST_CASE(NON_POLY, ?)
3.19/1.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.19/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.19/1.68	
3.19/1.68	
3.19/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.68	
3.19/1.68	(0) CpxTRS
3.19/1.68	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.19/1.68	(2) TRS for Loop Detection
3.19/1.68	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.19/1.68	(4) BOUNDS(INF, INF)
3.19/1.68	
3.19/1.68	
3.19/1.68	----------------------------------------
3.19/1.68	
3.19/1.68	(0)
3.19/1.68	Obligation:
3.19/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.68	
3.19/1.68	
3.19/1.68	The TRS R consists of the following rules:
3.19/1.68	
3.19/1.68	   c -> f(n__g(n__c))
3.19/1.68	   f(n__g(X)) -> g(activate(X))
3.19/1.68	   g(X) -> n__g(X)
3.19/1.68	   c -> n__c
3.19/1.68	   activate(n__g(X)) -> g(X)
3.19/1.68	   activate(n__c) -> c
3.19/1.68	   activate(X) -> X
3.19/1.68	
3.19/1.68	S is empty.
3.19/1.68	Rewrite Strategy: INNERMOST
3.19/1.68	----------------------------------------
3.19/1.68	
3.19/1.68	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.19/1.68	Transformed a relative TRS into a decreasing-loop problem.
3.19/1.68	----------------------------------------
3.19/1.68	
3.19/1.68	(2)
3.19/1.68	Obligation:
3.19/1.68	Analyzing the following TRS for decreasing loops:
3.19/1.68	
3.19/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.68	
3.19/1.68	
3.19/1.68	The TRS R consists of the following rules:
3.19/1.68	
3.19/1.68	   c -> f(n__g(n__c))
3.19/1.68	   f(n__g(X)) -> g(activate(X))
3.19/1.68	   g(X) -> n__g(X)
3.19/1.68	   c -> n__c
3.19/1.68	   activate(n__g(X)) -> g(X)
3.19/1.68	   activate(n__c) -> c
3.19/1.68	   activate(X) -> X
3.19/1.68	
3.19/1.68	S is empty.
3.19/1.68	Rewrite Strategy: INNERMOST
3.19/1.68	----------------------------------------
3.19/1.68	
3.19/1.68	(3) InfiniteLowerBoundProof (FINISHED)
3.19/1.68	The following loop proves infinite runtime complexity:
3.19/1.68	
3.19/1.68	The rewrite sequence
3.19/1.68	
3.19/1.68	c ->^+ g(c)
3.19/1.68	
3.19/1.68	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.19/1.68	
3.19/1.68	The pumping substitution is [ ].
3.19/1.68	
3.19/1.68	The result substitution is [ ].
3.19/1.68	
3.19/1.68	
3.19/1.68	
3.19/1.68	
3.19/1.68	----------------------------------------
3.19/1.68	
3.19/1.68	(4)
3.19/1.68	BOUNDS(INF, INF)
3.50/1.72	EOF