3.01/1.49	WORST_CASE(NON_POLY, ?)
3.01/1.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.01/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.01/1.49	
3.01/1.49	
3.01/1.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.01/1.49	
3.01/1.49	(0) CpxTRS
3.01/1.49	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.01/1.49	(2) TRS for Loop Detection
3.01/1.49	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.01/1.49	(4) BOUNDS(INF, INF)
3.01/1.49	
3.01/1.49	
3.01/1.49	----------------------------------------
3.01/1.49	
3.01/1.49	(0)
3.01/1.49	Obligation:
3.01/1.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.01/1.49	
3.01/1.49	
3.01/1.49	The TRS R consists of the following rules:
3.01/1.49	
3.01/1.49	   f(x, y) -> f(x, x)
3.01/1.49	   f(s(x), y) -> f(y, x)
3.01/1.49	
3.01/1.49	S is empty.
3.01/1.49	Rewrite Strategy: INNERMOST
3.01/1.49	----------------------------------------
3.01/1.49	
3.01/1.49	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.01/1.49	Transformed a relative TRS into a decreasing-loop problem.
3.01/1.49	----------------------------------------
3.01/1.49	
3.01/1.49	(2)
3.01/1.49	Obligation:
3.01/1.49	Analyzing the following TRS for decreasing loops:
3.01/1.49	
3.01/1.49	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.01/1.49	
3.01/1.49	
3.01/1.49	The TRS R consists of the following rules:
3.01/1.49	
3.01/1.49	   f(x, y) -> f(x, x)
3.01/1.49	   f(s(x), y) -> f(y, x)
3.01/1.49	
3.01/1.49	S is empty.
3.01/1.49	Rewrite Strategy: INNERMOST
3.01/1.49	----------------------------------------
3.01/1.49	
3.01/1.49	(3) InfiniteLowerBoundProof (FINISHED)
3.01/1.49	The following loop proves infinite runtime complexity:
3.01/1.49	
3.01/1.49	The rewrite sequence
3.01/1.49	
3.01/1.49	f(x, y) ->^+ f(x, x)
3.01/1.49	
3.01/1.49	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.01/1.49	
3.01/1.49	The pumping substitution is [ ].
3.01/1.49	
3.01/1.49	The result substitution is [y / x].
3.01/1.49	
3.01/1.49	
3.01/1.49	
3.01/1.49	
3.01/1.49	----------------------------------------
3.01/1.49	
3.01/1.49	(4)
3.01/1.49	BOUNDS(INF, INF)
3.11/1.52	EOF