3.35/1.66	WORST_CASE(NON_POLY, ?)
3.35/1.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.68	
3.35/1.68	
3.35/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.35/1.68	
3.35/1.68	(0) CpxTRS
3.35/1.68	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.35/1.68	(2) TRS for Loop Detection
3.35/1.68	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.35/1.68	(4) BEST
3.35/1.68	    (5) proven lower bound
3.35/1.68	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.35/1.68	        (7) BOUNDS(n^1, INF)
3.35/1.68	    (8) TRS for Loop Detection
3.35/1.68	        (9) InfiniteLowerBoundProof [FINISHED, 29 ms]
3.35/1.68	        (10) BOUNDS(INF, INF)
3.35/1.68	
3.35/1.68	
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(0)
3.35/1.68	Obligation:
3.35/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.35/1.68	
3.35/1.68	
3.35/1.68	The TRS R consists of the following rules:
3.35/1.68	
3.35/1.68	   immatcopy(Cons(x, xs)) -> Cons(Nil, immatcopy(xs))
3.35/1.68	   nestimeql(Nil) -> number42(Nil)
3.35/1.68	   nestimeql(Cons(x, xs)) -> nestimeql(immatcopy(Cons(x, xs)))
3.35/1.68	   immatcopy(Nil) -> Nil
3.35/1.68	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.35/1.68	   goal(x) -> nestimeql(x)
3.35/1.68	
3.35/1.68	S is empty.
3.35/1.68	Rewrite Strategy: INNERMOST
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.35/1.68	Transformed a relative TRS into a decreasing-loop problem.
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(2)
3.35/1.68	Obligation:
3.35/1.68	Analyzing the following TRS for decreasing loops:
3.35/1.68	
3.35/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.35/1.68	
3.35/1.68	
3.35/1.68	The TRS R consists of the following rules:
3.35/1.68	
3.35/1.68	   immatcopy(Cons(x, xs)) -> Cons(Nil, immatcopy(xs))
3.35/1.68	   nestimeql(Nil) -> number42(Nil)
3.35/1.68	   nestimeql(Cons(x, xs)) -> nestimeql(immatcopy(Cons(x, xs)))
3.35/1.68	   immatcopy(Nil) -> Nil
3.35/1.68	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.35/1.68	   goal(x) -> nestimeql(x)
3.35/1.68	
3.35/1.68	S is empty.
3.35/1.68	Rewrite Strategy: INNERMOST
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.35/1.68	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.35/1.68	
3.35/1.68	The rewrite sequence
3.35/1.68	
3.35/1.68	immatcopy(Cons(x, xs)) ->^+ Cons(Nil, immatcopy(xs))
3.35/1.68	
3.35/1.68	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.35/1.68	
3.35/1.68	The pumping substitution is [xs / Cons(x, xs)].
3.35/1.68	
3.35/1.68	The result substitution is [ ].
3.35/1.68	
3.35/1.68	
3.35/1.68	
3.35/1.68	
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(4)
3.35/1.68	Complex Obligation (BEST)
3.35/1.68	
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(5)
3.35/1.68	Obligation:
3.35/1.68	Proved the lower bound n^1 for the following obligation:
3.35/1.68	
3.35/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.35/1.68	
3.35/1.68	
3.35/1.68	The TRS R consists of the following rules:
3.35/1.68	
3.35/1.68	   immatcopy(Cons(x, xs)) -> Cons(Nil, immatcopy(xs))
3.35/1.68	   nestimeql(Nil) -> number42(Nil)
3.35/1.68	   nestimeql(Cons(x, xs)) -> nestimeql(immatcopy(Cons(x, xs)))
3.35/1.68	   immatcopy(Nil) -> Nil
3.35/1.68	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.35/1.68	   goal(x) -> nestimeql(x)
3.35/1.68	
3.35/1.68	S is empty.
3.35/1.68	Rewrite Strategy: INNERMOST
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(6) LowerBoundPropagationProof (FINISHED)
3.35/1.68	Propagated lower bound.
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(7)
3.35/1.68	BOUNDS(n^1, INF)
3.35/1.68	
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(8)
3.35/1.68	Obligation:
3.35/1.68	Analyzing the following TRS for decreasing loops:
3.35/1.68	
3.35/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.35/1.68	
3.35/1.68	
3.35/1.68	The TRS R consists of the following rules:
3.35/1.68	
3.35/1.68	   immatcopy(Cons(x, xs)) -> Cons(Nil, immatcopy(xs))
3.35/1.68	   nestimeql(Nil) -> number42(Nil)
3.35/1.68	   nestimeql(Cons(x, xs)) -> nestimeql(immatcopy(Cons(x, xs)))
3.35/1.68	   immatcopy(Nil) -> Nil
3.35/1.68	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.35/1.68	   goal(x) -> nestimeql(x)
3.35/1.68	
3.35/1.68	S is empty.
3.35/1.68	Rewrite Strategy: INNERMOST
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(9) InfiniteLowerBoundProof (FINISHED)
3.35/1.68	The following loop proves infinite runtime complexity:
3.35/1.68	
3.35/1.68	The rewrite sequence
3.35/1.68	
3.35/1.68	nestimeql(Cons(x, xs)) ->^+ nestimeql(Cons(Nil, immatcopy(xs)))
3.35/1.68	
3.35/1.68	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.35/1.68	
3.35/1.68	The pumping substitution is [ ].
3.35/1.68	
3.35/1.68	The result substitution is [x / Nil, xs / immatcopy(xs)].
3.35/1.68	
3.35/1.68	
3.35/1.68	
3.35/1.68	
3.35/1.68	----------------------------------------
3.35/1.68	
3.35/1.68	(10)
3.35/1.68	BOUNDS(INF, INF)
3.48/1.71	EOF