3.89/1.72	WORST_CASE(NON_POLY, ?)
3.89/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.89/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.89/1.74	
3.89/1.74	
3.89/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.89/1.74	
3.89/1.74	(0) CpxTRS
3.89/1.74	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.89/1.74	(2) TRS for Loop Detection
3.89/1.74	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.89/1.74	(4) BEST
3.89/1.74	    (5) proven lower bound
3.89/1.74	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.89/1.74	        (7) BOUNDS(n^1, INF)
3.89/1.74	    (8) TRS for Loop Detection
3.89/1.74	        (9) InfiniteLowerBoundProof [FINISHED, 28 ms]
3.89/1.74	        (10) BOUNDS(INF, INF)
3.89/1.74	
3.89/1.74	
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(0)
3.89/1.74	Obligation:
3.89/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.89/1.74	
3.89/1.74	
3.89/1.74	The TRS R consists of the following rules:
3.89/1.74	
3.89/1.74	   zeros -> cons(0, n__zeros)
3.89/1.74	   and(tt, X) -> activate(X)
3.89/1.74	   length(nil) -> 0
3.89/1.74	   length(cons(N, L)) -> s(length(activate(L)))
3.89/1.74	   take(0, IL) -> nil
3.89/1.74	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
3.89/1.74	   zeros -> n__zeros
3.89/1.74	   take(X1, X2) -> n__take(X1, X2)
3.89/1.74	   activate(n__zeros) -> zeros
3.89/1.74	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
3.89/1.74	   activate(X) -> X
3.89/1.74	
3.89/1.74	S is empty.
3.89/1.74	Rewrite Strategy: INNERMOST
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.89/1.74	Transformed a relative TRS into a decreasing-loop problem.
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(2)
3.89/1.74	Obligation:
3.89/1.74	Analyzing the following TRS for decreasing loops:
3.89/1.74	
3.89/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.89/1.74	
3.89/1.74	
3.89/1.74	The TRS R consists of the following rules:
3.89/1.74	
3.89/1.74	   zeros -> cons(0, n__zeros)
3.89/1.74	   and(tt, X) -> activate(X)
3.89/1.74	   length(nil) -> 0
3.89/1.74	   length(cons(N, L)) -> s(length(activate(L)))
3.89/1.74	   take(0, IL) -> nil
3.89/1.74	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
3.89/1.74	   zeros -> n__zeros
3.89/1.74	   take(X1, X2) -> n__take(X1, X2)
3.89/1.74	   activate(n__zeros) -> zeros
3.89/1.74	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
3.89/1.74	   activate(X) -> X
3.89/1.74	
3.89/1.74	S is empty.
3.89/1.74	Rewrite Strategy: INNERMOST
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.89/1.74	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.89/1.74	
3.89/1.74	The rewrite sequence
3.89/1.74	
3.89/1.74	activate(n__take(X1, X2)) ->^+ take(activate(X1), activate(X2))
3.89/1.74	
3.89/1.74	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.89/1.74	
3.89/1.74	The pumping substitution is [X1 / n__take(X1, X2)].
3.89/1.74	
3.89/1.74	The result substitution is [ ].
3.89/1.74	
3.89/1.74	
3.89/1.74	
3.89/1.74	
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(4)
3.89/1.74	Complex Obligation (BEST)
3.89/1.74	
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(5)
3.89/1.74	Obligation:
3.89/1.74	Proved the lower bound n^1 for the following obligation:
3.89/1.74	
3.89/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.89/1.74	
3.89/1.74	
3.89/1.74	The TRS R consists of the following rules:
3.89/1.74	
3.89/1.74	   zeros -> cons(0, n__zeros)
3.89/1.74	   and(tt, X) -> activate(X)
3.89/1.74	   length(nil) -> 0
3.89/1.74	   length(cons(N, L)) -> s(length(activate(L)))
3.89/1.74	   take(0, IL) -> nil
3.89/1.74	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
3.89/1.74	   zeros -> n__zeros
3.89/1.74	   take(X1, X2) -> n__take(X1, X2)
3.89/1.74	   activate(n__zeros) -> zeros
3.89/1.74	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
3.89/1.74	   activate(X) -> X
3.89/1.74	
3.89/1.74	S is empty.
3.89/1.74	Rewrite Strategy: INNERMOST
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(6) LowerBoundPropagationProof (FINISHED)
3.89/1.74	Propagated lower bound.
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(7)
3.89/1.74	BOUNDS(n^1, INF)
3.89/1.74	
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(8)
3.89/1.74	Obligation:
3.89/1.74	Analyzing the following TRS for decreasing loops:
3.89/1.74	
3.89/1.74	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.89/1.74	
3.89/1.74	
3.89/1.74	The TRS R consists of the following rules:
3.89/1.74	
3.89/1.74	   zeros -> cons(0, n__zeros)
3.89/1.74	   and(tt, X) -> activate(X)
3.89/1.74	   length(nil) -> 0
3.89/1.74	   length(cons(N, L)) -> s(length(activate(L)))
3.89/1.74	   take(0, IL) -> nil
3.89/1.74	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
3.89/1.74	   zeros -> n__zeros
3.89/1.74	   take(X1, X2) -> n__take(X1, X2)
3.89/1.74	   activate(n__zeros) -> zeros
3.89/1.74	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
3.89/1.74	   activate(X) -> X
3.89/1.74	
3.89/1.74	S is empty.
3.89/1.74	Rewrite Strategy: INNERMOST
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(9) InfiniteLowerBoundProof (FINISHED)
3.89/1.74	The following loop proves infinite runtime complexity:
3.89/1.74	
3.89/1.74	The rewrite sequence
3.89/1.74	
3.89/1.74	length(cons(N, n__zeros)) ->^+ s(length(cons(0, n__zeros)))
3.89/1.74	
3.89/1.74	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.89/1.74	
3.89/1.74	The pumping substitution is [ ].
3.89/1.74	
3.89/1.74	The result substitution is [N / 0].
3.89/1.74	
3.89/1.74	
3.89/1.74	
3.89/1.74	
3.89/1.74	----------------------------------------
3.89/1.74	
3.89/1.74	(10)
3.89/1.74	BOUNDS(INF, INF)
4.07/1.77	EOF