3.35/1.59	WORST_CASE(NON_POLY, ?)
3.35/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.59	
3.35/1.59	
3.35/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.59	
3.35/1.59	(0) CpxTRS
3.35/1.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.35/1.59	(2) TRS for Loop Detection
3.35/1.59	(3) DecreasingLoopProof [FINISHED, 0 ms]
3.35/1.59	(4) BOUNDS(EXP, INF)
3.35/1.59	
3.35/1.59	
3.35/1.59	----------------------------------------
3.35/1.59	
3.35/1.59	(0)
3.35/1.59	Obligation:
3.35/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.59	
3.35/1.59	
3.35/1.59	The TRS R consists of the following rules:
3.35/1.59	
3.35/1.59	   purge(nil) -> nil
3.35/1.59	   purge(.(x, y)) -> .(x, purge(remove(x, y)))
3.35/1.59	   remove(x, nil) -> nil
3.35/1.59	   remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))
3.35/1.59	
3.35/1.59	S is empty.
3.35/1.59	Rewrite Strategy: INNERMOST
3.35/1.59	----------------------------------------
3.35/1.59	
3.35/1.59	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.35/1.59	Transformed a relative TRS into a decreasing-loop problem.
3.35/1.59	----------------------------------------
3.35/1.59	
3.35/1.59	(2)
3.35/1.59	Obligation:
3.35/1.59	Analyzing the following TRS for decreasing loops:
3.35/1.59	
3.35/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.59	
3.35/1.59	
3.35/1.59	The TRS R consists of the following rules:
3.35/1.59	
3.35/1.59	   purge(nil) -> nil
3.35/1.59	   purge(.(x, y)) -> .(x, purge(remove(x, y)))
3.35/1.59	   remove(x, nil) -> nil
3.35/1.59	   remove(x, .(y, z)) -> if(=(x, y), remove(x, z), .(y, remove(x, z)))
3.35/1.59	
3.35/1.59	S is empty.
3.35/1.59	Rewrite Strategy: INNERMOST
3.35/1.59	----------------------------------------
3.35/1.59	
3.35/1.59	(3) DecreasingLoopProof (FINISHED)
3.35/1.59	The following loop(s) give(s) rise to the lower bound EXP:
3.35/1.59	
3.35/1.59	The rewrite sequence
3.35/1.59	
3.35/1.59	remove(x, .(y, z)) ->^+ if(=(x, y), remove(x, z), .(y, remove(x, z)))
3.35/1.59	
3.35/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.35/1.59	
3.35/1.59	The pumping substitution is [z / .(y, z)].
3.35/1.59	
3.35/1.59	The result substitution is [ ].
3.35/1.59	
3.35/1.59	
3.35/1.59	
3.35/1.59	The rewrite sequence
3.35/1.59	
3.35/1.59	remove(x, .(y, z)) ->^+ if(=(x, y), remove(x, z), .(y, remove(x, z)))
3.35/1.59	
3.35/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
3.35/1.59	
3.35/1.59	The pumping substitution is [z / .(y, z)].
3.35/1.59	
3.35/1.59	The result substitution is [ ].
3.35/1.59	
3.35/1.59	
3.35/1.59	
3.35/1.59	
3.35/1.59	----------------------------------------
3.35/1.59	
3.35/1.59	(4)
3.35/1.59	BOUNDS(EXP, INF)
3.35/1.64	EOF