4.39/1.89	WORST_CASE(NON_POLY, ?)
4.47/1.90	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.47/1.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.47/1.90	
4.47/1.90	
4.47/1.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
4.47/1.90	
4.47/1.90	(0) CpxTRS
4.47/1.90	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
4.47/1.90	(2) TRS for Loop Detection
4.47/1.90	(3) DecreasingLoopProof [LOWER BOUND(ID), 85 ms]
4.47/1.90	(4) BEST
4.47/1.90	    (5) proven lower bound
4.47/1.90	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
4.47/1.90	        (7) BOUNDS(n^1, INF)
4.47/1.90	    (8) TRS for Loop Detection
4.47/1.90	        (9) InfiniteLowerBoundProof [FINISHED, 0 ms]
4.47/1.90	        (10) BOUNDS(INF, INF)
4.47/1.90	
4.47/1.90	
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(0)
4.47/1.90	Obligation:
4.47/1.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
4.47/1.90	
4.47/1.90	
4.47/1.90	The TRS R consists of the following rules:
4.47/1.90	
4.47/1.90	   zeros -> cons(0, n__zeros)
4.47/1.90	   U11(tt, L) -> U12(tt, activate(L))
4.47/1.90	   U12(tt, L) -> s(length(activate(L)))
4.47/1.90	   length(nil) -> 0
4.47/1.90	   length(cons(N, L)) -> U11(tt, activate(L))
4.47/1.90	   zeros -> n__zeros
4.47/1.90	   activate(n__zeros) -> zeros
4.47/1.90	   activate(X) -> X
4.47/1.90	
4.47/1.90	S is empty.
4.47/1.90	Rewrite Strategy: FULL
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
4.47/1.90	Transformed a relative TRS into a decreasing-loop problem.
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(2)
4.47/1.90	Obligation:
4.47/1.90	Analyzing the following TRS for decreasing loops:
4.47/1.90	
4.47/1.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
4.47/1.90	
4.47/1.90	
4.47/1.90	The TRS R consists of the following rules:
4.47/1.90	
4.47/1.90	   zeros -> cons(0, n__zeros)
4.47/1.90	   U11(tt, L) -> U12(tt, activate(L))
4.47/1.90	   U12(tt, L) -> s(length(activate(L)))
4.47/1.90	   length(nil) -> 0
4.47/1.90	   length(cons(N, L)) -> U11(tt, activate(L))
4.47/1.90	   zeros -> n__zeros
4.47/1.90	   activate(n__zeros) -> zeros
4.47/1.90	   activate(X) -> X
4.47/1.90	
4.47/1.90	S is empty.
4.47/1.90	Rewrite Strategy: FULL
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(3) DecreasingLoopProof (LOWER BOUND(ID))
4.47/1.90	The following loop(s) give(s) rise to the lower bound Omega(n^1):
4.47/1.90	
4.47/1.90	The rewrite sequence
4.47/1.90	
4.47/1.90	length(cons(N, L)) ->^+ s(length(L))
4.47/1.90	
4.47/1.90	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
4.47/1.90	
4.47/1.90	The pumping substitution is [L / cons(N, L)].
4.47/1.90	
4.47/1.90	The result substitution is [ ].
4.47/1.90	
4.47/1.90	
4.47/1.90	
4.47/1.90	
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(4)
4.47/1.90	Complex Obligation (BEST)
4.47/1.90	
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(5)
4.47/1.90	Obligation:
4.47/1.90	Proved the lower bound n^1 for the following obligation:
4.47/1.90	
4.47/1.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
4.47/1.90	
4.47/1.90	
4.47/1.90	The TRS R consists of the following rules:
4.47/1.90	
4.47/1.90	   zeros -> cons(0, n__zeros)
4.47/1.90	   U11(tt, L) -> U12(tt, activate(L))
4.47/1.90	   U12(tt, L) -> s(length(activate(L)))
4.47/1.90	   length(nil) -> 0
4.47/1.90	   length(cons(N, L)) -> U11(tt, activate(L))
4.47/1.90	   zeros -> n__zeros
4.47/1.90	   activate(n__zeros) -> zeros
4.47/1.90	   activate(X) -> X
4.47/1.90	
4.47/1.90	S is empty.
4.47/1.90	Rewrite Strategy: FULL
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(6) LowerBoundPropagationProof (FINISHED)
4.47/1.90	Propagated lower bound.
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(7)
4.47/1.90	BOUNDS(n^1, INF)
4.47/1.90	
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(8)
4.47/1.90	Obligation:
4.47/1.90	Analyzing the following TRS for decreasing loops:
4.47/1.90	
4.47/1.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
4.47/1.90	
4.47/1.90	
4.47/1.90	The TRS R consists of the following rules:
4.47/1.90	
4.47/1.90	   zeros -> cons(0, n__zeros)
4.47/1.90	   U11(tt, L) -> U12(tt, activate(L))
4.47/1.90	   U12(tt, L) -> s(length(activate(L)))
4.47/1.90	   length(nil) -> 0
4.47/1.90	   length(cons(N, L)) -> U11(tt, activate(L))
4.47/1.90	   zeros -> n__zeros
4.47/1.90	   activate(n__zeros) -> zeros
4.47/1.90	   activate(X) -> X
4.47/1.90	
4.47/1.90	S is empty.
4.47/1.90	Rewrite Strategy: FULL
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(9) InfiniteLowerBoundProof (FINISHED)
4.47/1.90	The following loop proves infinite runtime complexity:
4.47/1.90	
4.47/1.90	The rewrite sequence
4.47/1.90	
4.47/1.90	length(cons(N, n__zeros)) ->^+ s(length(cons(0, n__zeros)))
4.47/1.90	
4.47/1.90	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
4.47/1.90	
4.47/1.90	The pumping substitution is [ ].
4.47/1.90	
4.47/1.90	The result substitution is [N / 0].
4.47/1.90	
4.47/1.90	
4.47/1.90	
4.47/1.90	
4.47/1.90	----------------------------------------
4.47/1.90	
4.47/1.90	(10)
4.47/1.90	BOUNDS(INF, INF)
4.51/1.93	EOF