1069.83/291.49	WORST_CASE(Omega(n^1), ?)
1069.83/291.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1069.83/291.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1069.83/291.50	
1069.83/291.50	(0) CpxTRS
1069.83/291.50	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1069.83/291.50	(2) TRS for Loop Detection
1069.83/291.50	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1069.83/291.50	(4) BEST
1069.83/291.50	    (5) proven lower bound
1069.83/291.50	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1069.83/291.50	        (7) BOUNDS(n^1, INF)
1069.83/291.50	    (8) TRS for Loop Detection
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(0)
1069.83/291.50	Obligation:
1069.83/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	The TRS R consists of the following rules:
1069.83/291.50	
1069.83/291.50	   not(not(x)) -> x
1069.83/291.50	   not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))
1069.83/291.50	   not(and(x, y)) -> or(not(not(not(x))), not(not(not(y))))
1069.83/291.50	
1069.83/291.50	S is empty.
1069.83/291.50	Rewrite Strategy: FULL
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1069.83/291.50	Transformed a relative TRS into a decreasing-loop problem.
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(2)
1069.83/291.50	Obligation:
1069.83/291.50	Analyzing the following TRS for decreasing loops:
1069.83/291.50	
1069.83/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	The TRS R consists of the following rules:
1069.83/291.50	
1069.83/291.50	   not(not(x)) -> x
1069.83/291.50	   not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))
1069.83/291.50	   not(and(x, y)) -> or(not(not(not(x))), not(not(not(y))))
1069.83/291.50	
1069.83/291.50	S is empty.
1069.83/291.50	Rewrite Strategy: FULL
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(3) DecreasingLoopProof (LOWER BOUND(ID))
1069.83/291.50	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1069.83/291.50	
1069.83/291.50	The rewrite sequence
1069.83/291.50	
1069.83/291.50	not(or(x, y)) ->^+ and(not(not(not(x))), not(not(not(y))))
1069.83/291.50	
1069.83/291.50	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0].
1069.83/291.50	
1069.83/291.50	The pumping substitution is [x / or(x, y)].
1069.83/291.50	
1069.83/291.50	The result substitution is [ ].
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(4)
1069.83/291.50	Complex Obligation (BEST)
1069.83/291.50	
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(5)
1069.83/291.50	Obligation:
1069.83/291.50	Proved the lower bound n^1 for the following obligation:
1069.83/291.50	
1069.83/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	The TRS R consists of the following rules:
1069.83/291.50	
1069.83/291.50	   not(not(x)) -> x
1069.83/291.50	   not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))
1069.83/291.50	   not(and(x, y)) -> or(not(not(not(x))), not(not(not(y))))
1069.83/291.50	
1069.83/291.50	S is empty.
1069.83/291.50	Rewrite Strategy: FULL
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(6) LowerBoundPropagationProof (FINISHED)
1069.83/291.50	Propagated lower bound.
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(7)
1069.83/291.50	BOUNDS(n^1, INF)
1069.83/291.50	
1069.83/291.50	----------------------------------------
1069.83/291.50	
1069.83/291.50	(8)
1069.83/291.50	Obligation:
1069.83/291.50	Analyzing the following TRS for decreasing loops:
1069.83/291.50	
1069.83/291.50	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1069.83/291.50	
1069.83/291.50	
1069.83/291.50	The TRS R consists of the following rules:
1069.83/291.50	
1069.83/291.50	   not(not(x)) -> x
1069.83/291.50	   not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))
1069.83/291.50	   not(and(x, y)) -> or(not(not(not(x))), not(not(not(y))))
1069.83/291.50	
1069.83/291.50	S is empty.
1069.83/291.50	Rewrite Strategy: FULL
1070.32/291.64	EOF