3.17/1.54	WORST_CASE(NON_POLY, ?)
3.17/1.55	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.17/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.17/1.55	
3.17/1.55	
3.17/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.17/1.55	
3.17/1.55	(0) CpxTRS
3.17/1.55	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.17/1.55	(2) TRS for Loop Detection
3.17/1.55	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.17/1.55	(4) BOUNDS(INF, INF)
3.17/1.55	
3.17/1.55	
3.17/1.55	----------------------------------------
3.17/1.55	
3.17/1.55	(0)
3.17/1.55	Obligation:
3.17/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.17/1.55	
3.17/1.55	
3.17/1.55	The TRS R consists of the following rules:
3.17/1.55	
3.17/1.55	   f(a, X) -> f(X, X)
3.17/1.55	   c -> a
3.17/1.55	   c -> b
3.17/1.55	
3.17/1.55	S is empty.
3.17/1.55	Rewrite Strategy: INNERMOST
3.17/1.55	----------------------------------------
3.17/1.55	
3.17/1.55	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.17/1.55	Transformed a relative TRS into a decreasing-loop problem.
3.17/1.55	----------------------------------------
3.17/1.55	
3.17/1.55	(2)
3.17/1.55	Obligation:
3.17/1.55	Analyzing the following TRS for decreasing loops:
3.17/1.55	
3.17/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.17/1.55	
3.17/1.55	
3.17/1.55	The TRS R consists of the following rules:
3.17/1.55	
3.17/1.55	   f(a, X) -> f(X, X)
3.17/1.55	   c -> a
3.17/1.55	   c -> b
3.17/1.55	
3.17/1.55	S is empty.
3.17/1.55	Rewrite Strategy: INNERMOST
3.17/1.55	----------------------------------------
3.17/1.55	
3.17/1.55	(3) InfiniteLowerBoundProof (FINISHED)
3.17/1.55	The following loop proves infinite runtime complexity:
3.17/1.55	
3.17/1.55	The rewrite sequence
3.17/1.55	
3.17/1.55	f(a, a) ->^+ f(a, a)
3.17/1.55	
3.17/1.55	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.17/1.55	
3.17/1.55	The pumping substitution is [ ].
3.17/1.55	
3.17/1.55	The result substitution is [ ].
3.17/1.55	
3.17/1.55	
3.17/1.55	
3.17/1.55	
3.17/1.55	----------------------------------------
3.17/1.55	
3.17/1.55	(4)
3.17/1.55	BOUNDS(INF, INF)
3.30/1.58	EOF