3.04/1.62	WORST_CASE(NON_POLY, ?)
3.40/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.40/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.40/1.63	
3.40/1.63	
3.40/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.40/1.63	
3.40/1.63	(0) CpxTRS
3.40/1.63	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.40/1.63	(2) TRS for Loop Detection
3.40/1.63	(3) InfiniteLowerBoundProof [FINISHED, 8 ms]
3.40/1.63	(4) BOUNDS(INF, INF)
3.40/1.63	
3.40/1.63	
3.40/1.63	----------------------------------------
3.40/1.63	
3.40/1.63	(0)
3.40/1.63	Obligation:
3.40/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.40/1.63	
3.40/1.63	
3.40/1.63	The TRS R consists of the following rules:
3.40/1.63	
3.40/1.63	   f -> f
3.40/1.63	   g(b) -> c
3.40/1.63	   b -> c
3.40/1.63	
3.40/1.63	S is empty.
3.40/1.63	Rewrite Strategy: FULL
3.40/1.63	----------------------------------------
3.40/1.63	
3.40/1.63	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.40/1.63	Transformed a relative TRS into a decreasing-loop problem.
3.40/1.63	----------------------------------------
3.40/1.63	
3.40/1.63	(2)
3.40/1.63	Obligation:
3.40/1.63	Analyzing the following TRS for decreasing loops:
3.40/1.63	
3.40/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.40/1.63	
3.40/1.63	
3.40/1.63	The TRS R consists of the following rules:
3.40/1.63	
3.40/1.63	   f -> f
3.40/1.63	   g(b) -> c
3.40/1.63	   b -> c
3.40/1.63	
3.40/1.63	S is empty.
3.40/1.63	Rewrite Strategy: FULL
3.40/1.63	----------------------------------------
3.40/1.63	
3.40/1.63	(3) InfiniteLowerBoundProof (FINISHED)
3.40/1.63	The following loop proves infinite runtime complexity:
3.40/1.63	
3.40/1.63	The rewrite sequence
3.40/1.63	
3.40/1.63	f ->^+ f
3.40/1.63	
3.40/1.63	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.40/1.63	
3.40/1.63	The pumping substitution is [ ].
3.40/1.63	
3.40/1.63	The result substitution is [ ].
3.40/1.63	
3.40/1.63	
3.40/1.63	
3.40/1.63	
3.40/1.63	----------------------------------------
3.40/1.63	
3.40/1.63	(4)
3.40/1.63	BOUNDS(INF, INF)
3.40/1.66	EOF