3.43/1.62	WORST_CASE(NON_POLY, ?)
3.43/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.43/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.43/1.62	
3.43/1.62	
3.43/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.43/1.62	
3.43/1.62	(0) CpxTRS
3.43/1.62	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.43/1.62	(2) TRS for Loop Detection
3.43/1.62	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.43/1.62	(4) BEST
3.43/1.62	    (5) proven lower bound
3.43/1.62	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.43/1.62	        (7) BOUNDS(n^1, INF)
3.43/1.62	    (8) TRS for Loop Detection
3.43/1.62	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.43/1.62	        (10) BOUNDS(EXP, INF)
3.43/1.62	
3.43/1.62	
3.43/1.62	----------------------------------------
3.43/1.62	
3.43/1.62	(0)
3.43/1.62	Obligation:
3.43/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.43/1.62	
3.43/1.62	
3.43/1.62	The TRS R consists of the following rules:
3.43/1.62	
3.43/1.62	   rev(nil) -> nil
3.43/1.62	   rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
3.43/1.62	   rev1(x, nil) -> x
3.43/1.62	   rev1(x, ++(y, z)) -> rev1(y, z)
3.43/1.62	   rev2(x, nil) -> nil
3.43/1.62	   rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))
3.43/1.62	
3.43/1.62	S is empty.
3.43/1.63	Rewrite Strategy: FULL
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.43/1.63	Transformed a relative TRS into a decreasing-loop problem.
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(2)
3.43/1.63	Obligation:
3.43/1.63	Analyzing the following TRS for decreasing loops:
3.43/1.63	
3.43/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.43/1.63	
3.43/1.63	
3.43/1.63	The TRS R consists of the following rules:
3.43/1.63	
3.43/1.63	   rev(nil) -> nil
3.43/1.63	   rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
3.43/1.63	   rev1(x, nil) -> x
3.43/1.63	   rev1(x, ++(y, z)) -> rev1(y, z)
3.43/1.63	   rev2(x, nil) -> nil
3.43/1.63	   rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	S is empty.
3.43/1.63	Rewrite Strategy: FULL
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.43/1.63	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.43/1.63	
3.43/1.63	The rewrite sequence
3.43/1.63	
3.43/1.63	rev2(x, ++(y, z)) ->^+ rev(++(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0].
3.43/1.63	
3.43/1.63	The pumping substitution is [z / ++(y, z)].
3.43/1.63	
3.43/1.63	The result substitution is [x / y].
3.43/1.63	
3.43/1.63	
3.43/1.63	
3.43/1.63	
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(4)
3.43/1.63	Complex Obligation (BEST)
3.43/1.63	
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(5)
3.43/1.63	Obligation:
3.43/1.63	Proved the lower bound n^1 for the following obligation:
3.43/1.63	
3.43/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.43/1.63	
3.43/1.63	
3.43/1.63	The TRS R consists of the following rules:
3.43/1.63	
3.43/1.63	   rev(nil) -> nil
3.43/1.63	   rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
3.43/1.63	   rev1(x, nil) -> x
3.43/1.63	   rev1(x, ++(y, z)) -> rev1(y, z)
3.43/1.63	   rev2(x, nil) -> nil
3.43/1.63	   rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	S is empty.
3.43/1.63	Rewrite Strategy: FULL
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(6) LowerBoundPropagationProof (FINISHED)
3.43/1.63	Propagated lower bound.
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(7)
3.43/1.63	BOUNDS(n^1, INF)
3.43/1.63	
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(8)
3.43/1.63	Obligation:
3.43/1.63	Analyzing the following TRS for decreasing loops:
3.43/1.63	
3.43/1.63	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.43/1.63	
3.43/1.63	
3.43/1.63	The TRS R consists of the following rules:
3.43/1.63	
3.43/1.63	   rev(nil) -> nil
3.43/1.63	   rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
3.43/1.63	   rev1(x, nil) -> x
3.43/1.63	   rev1(x, ++(y, z)) -> rev1(y, z)
3.43/1.63	   rev2(x, nil) -> nil
3.43/1.63	   rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	S is empty.
3.43/1.63	Rewrite Strategy: FULL
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(9) DecreasingLoopProof (FINISHED)
3.43/1.63	The following loop(s) give(s) rise to the lower bound EXP:
3.43/1.63	
3.43/1.63	The rewrite sequence
3.43/1.63	
3.43/1.63	rev2(x, ++(y, z)) ->^+ ++(rev1(x, rev(rev2(y, z))), rev2(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0].
3.43/1.63	
3.43/1.63	The pumping substitution is [z / ++(y, z)].
3.43/1.63	
3.43/1.63	The result substitution is [x / y].
3.43/1.63	
3.43/1.63	
3.43/1.63	
3.43/1.63	The rewrite sequence
3.43/1.63	
3.43/1.63	rev2(x, ++(y, z)) ->^+ ++(rev1(x, rev(rev2(y, z))), rev2(x, rev(rev2(y, z))))
3.43/1.63	
3.43/1.63	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1,0].
3.43/1.63	
3.43/1.63	The pumping substitution is [z / ++(y, z)].
3.43/1.63	
3.43/1.63	The result substitution is [x / y].
3.43/1.63	
3.43/1.63	
3.43/1.63	
3.43/1.63	
3.43/1.63	----------------------------------------
3.43/1.63	
3.43/1.63	(10)
3.43/1.63	BOUNDS(EXP, INF)
3.43/1.66	EOF