3.07/1.69	WORST_CASE(NON_POLY, ?)
3.07/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.07/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.69	
3.07/1.69	
3.07/1.69	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.69	
3.07/1.69	(0) CpxTRS
3.07/1.69	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.07/1.69	(2) TRS for Loop Detection
3.07/1.69	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.07/1.69	(4) BOUNDS(INF, INF)
3.07/1.69	
3.07/1.69	
3.07/1.69	----------------------------------------
3.07/1.69	
3.07/1.69	(0)
3.07/1.69	Obligation:
3.07/1.69	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.69	
3.07/1.69	
3.07/1.69	The TRS R consists of the following rules:
3.07/1.69	
3.07/1.69	   c -> f(g(c))
3.07/1.69	   f(g(X)) -> g(X)
3.07/1.69	
3.07/1.69	S is empty.
3.07/1.69	Rewrite Strategy: INNERMOST
3.07/1.69	----------------------------------------
3.07/1.69	
3.07/1.69	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.07/1.69	Transformed a relative TRS into a decreasing-loop problem.
3.07/1.69	----------------------------------------
3.07/1.69	
3.07/1.69	(2)
3.07/1.69	Obligation:
3.07/1.69	Analyzing the following TRS for decreasing loops:
3.07/1.69	
3.07/1.69	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.07/1.69	
3.07/1.69	
3.07/1.69	The TRS R consists of the following rules:
3.07/1.69	
3.07/1.69	   c -> f(g(c))
3.07/1.69	   f(g(X)) -> g(X)
3.07/1.69	
3.07/1.69	S is empty.
3.07/1.69	Rewrite Strategy: INNERMOST
3.07/1.69	----------------------------------------
3.07/1.69	
3.07/1.69	(3) InfiniteLowerBoundProof (FINISHED)
3.07/1.69	The following loop proves infinite runtime complexity:
3.07/1.69	
3.07/1.69	The rewrite sequence
3.07/1.69	
3.07/1.69	c ->^+ f(g(c))
3.07/1.69	
3.07/1.69	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.07/1.69	
3.07/1.69	The pumping substitution is [ ].
3.07/1.69	
3.07/1.69	The result substitution is [ ].
3.07/1.69	
3.07/1.69	
3.07/1.69	
3.07/1.69	
3.07/1.69	----------------------------------------
3.07/1.69	
3.07/1.69	(4)
3.07/1.69	BOUNDS(INF, INF)
3.27/1.72	EOF