1065.76/295.01	WORST_CASE(Omega(n^1), ?)
1065.76/295.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1065.76/295.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1065.76/295.03	
1065.76/295.03	(0) CpxTRS
1065.76/295.03	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1065.76/295.03	(2) TRS for Loop Detection
1065.76/295.03	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1065.76/295.03	(4) BEST
1065.76/295.03	    (5) proven lower bound
1065.76/295.03	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1065.76/295.03	        (7) BOUNDS(n^1, INF)
1065.76/295.03	    (8) TRS for Loop Detection
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(0)
1065.76/295.03	Obligation:
1065.76/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	The TRS R consists of the following rules:
1065.76/295.03	
1065.76/295.03	   f(x, a(a(b(b(y))))) -> f(a(a(a(b(b(b(x)))))), y)
1065.76/295.03	   f(a(x), y) -> f(x, a(y))
1065.76/295.03	   f(b(x), y) -> f(x, b(y))
1065.76/295.03	
1065.76/295.03	S is empty.
1065.76/295.03	Rewrite Strategy: FULL
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1065.76/295.03	Transformed a relative TRS into a decreasing-loop problem.
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(2)
1065.76/295.03	Obligation:
1065.76/295.03	Analyzing the following TRS for decreasing loops:
1065.76/295.03	
1065.76/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	The TRS R consists of the following rules:
1065.76/295.03	
1065.76/295.03	   f(x, a(a(b(b(y))))) -> f(a(a(a(b(b(b(x)))))), y)
1065.76/295.03	   f(a(x), y) -> f(x, a(y))
1065.76/295.03	   f(b(x), y) -> f(x, b(y))
1065.76/295.03	
1065.76/295.03	S is empty.
1065.76/295.03	Rewrite Strategy: FULL
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(3) DecreasingLoopProof (LOWER BOUND(ID))
1065.76/295.03	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1065.76/295.03	
1065.76/295.03	The rewrite sequence
1065.76/295.03	
1065.76/295.03	f(x, a(a(b(b(y))))) ->^+ f(a(a(a(b(b(b(x)))))), y)
1065.76/295.03	
1065.76/295.03	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
1065.76/295.03	
1065.76/295.03	The pumping substitution is [y / a(a(b(b(y))))].
1065.76/295.03	
1065.76/295.03	The result substitution is [x / a(a(a(b(b(b(x))))))].
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(4)
1065.76/295.03	Complex Obligation (BEST)
1065.76/295.03	
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(5)
1065.76/295.03	Obligation:
1065.76/295.03	Proved the lower bound n^1 for the following obligation:
1065.76/295.03	
1065.76/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	The TRS R consists of the following rules:
1065.76/295.03	
1065.76/295.03	   f(x, a(a(b(b(y))))) -> f(a(a(a(b(b(b(x)))))), y)
1065.76/295.03	   f(a(x), y) -> f(x, a(y))
1065.76/295.03	   f(b(x), y) -> f(x, b(y))
1065.76/295.03	
1065.76/295.03	S is empty.
1065.76/295.03	Rewrite Strategy: FULL
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(6) LowerBoundPropagationProof (FINISHED)
1065.76/295.03	Propagated lower bound.
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(7)
1065.76/295.03	BOUNDS(n^1, INF)
1065.76/295.03	
1065.76/295.03	----------------------------------------
1065.76/295.03	
1065.76/295.03	(8)
1065.76/295.03	Obligation:
1065.76/295.03	Analyzing the following TRS for decreasing loops:
1065.76/295.03	
1065.76/295.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1065.76/295.03	
1065.76/295.03	
1065.76/295.03	The TRS R consists of the following rules:
1065.76/295.03	
1065.76/295.03	   f(x, a(a(b(b(y))))) -> f(a(a(a(b(b(b(x)))))), y)
1065.76/295.03	   f(a(x), y) -> f(x, a(y))
1065.76/295.03	   f(b(x), y) -> f(x, b(y))
1065.76/295.03	
1065.76/295.03	S is empty.
1065.76/295.03	Rewrite Strategy: FULL
1065.92/295.09	EOF