4.35/1.84	WORST_CASE(NON_POLY, ?)
4.35/1.85	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.35/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.35/1.85	
4.35/1.85	
4.35/1.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
4.35/1.85	
4.35/1.85	(0) CpxTRS
4.35/1.85	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
4.35/1.85	(2) TRS for Loop Detection
4.35/1.85	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
4.35/1.85	(4) BEST
4.35/1.85	    (5) proven lower bound
4.35/1.85	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
4.35/1.85	        (7) BOUNDS(n^1, INF)
4.35/1.85	    (8) TRS for Loop Detection
4.35/1.85	        (9) DecreasingLoopProof [FINISHED, 172 ms]
4.35/1.85	        (10) BOUNDS(EXP, INF)
4.35/1.85	
4.35/1.85	
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(0)
4.35/1.85	Obligation:
4.35/1.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
4.35/1.85	
4.35/1.85	
4.35/1.85	The TRS R consists of the following rules:
4.35/1.85	
4.35/1.85	   pairNs -> cons(0, n__incr(n__oddNs))
4.35/1.85	   oddNs -> incr(pairNs)
4.35/1.85	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
4.35/1.85	   take(0, XS) -> nil
4.35/1.85	   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
4.35/1.85	   zip(nil, XS) -> nil
4.35/1.85	   zip(X, nil) -> nil
4.35/1.85	   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
4.35/1.85	   tail(cons(X, XS)) -> activate(XS)
4.35/1.85	   repItems(nil) -> nil
4.35/1.85	   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
4.35/1.85	   incr(X) -> n__incr(X)
4.35/1.85	   oddNs -> n__oddNs
4.35/1.85	   take(X1, X2) -> n__take(X1, X2)
4.35/1.85	   zip(X1, X2) -> n__zip(X1, X2)
4.35/1.85	   cons(X1, X2) -> n__cons(X1, X2)
4.35/1.85	   repItems(X) -> n__repItems(X)
4.35/1.85	   activate(n__incr(X)) -> incr(activate(X))
4.35/1.85	   activate(n__oddNs) -> oddNs
4.35/1.85	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
4.35/1.85	   activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2))
4.35/1.85	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
4.35/1.85	   activate(n__repItems(X)) -> repItems(activate(X))
4.35/1.85	   activate(X) -> X
4.35/1.85	
4.35/1.85	S is empty.
4.35/1.85	Rewrite Strategy: FULL
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
4.35/1.85	Transformed a relative TRS into a decreasing-loop problem.
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(2)
4.35/1.85	Obligation:
4.35/1.85	Analyzing the following TRS for decreasing loops:
4.35/1.85	
4.35/1.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
4.35/1.85	
4.35/1.85	
4.35/1.85	The TRS R consists of the following rules:
4.35/1.85	
4.35/1.85	   pairNs -> cons(0, n__incr(n__oddNs))
4.35/1.85	   oddNs -> incr(pairNs)
4.35/1.85	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
4.35/1.85	   take(0, XS) -> nil
4.35/1.85	   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
4.35/1.85	   zip(nil, XS) -> nil
4.35/1.85	   zip(X, nil) -> nil
4.35/1.85	   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
4.35/1.85	   tail(cons(X, XS)) -> activate(XS)
4.35/1.85	   repItems(nil) -> nil
4.35/1.85	   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
4.35/1.85	   incr(X) -> n__incr(X)
4.35/1.85	   oddNs -> n__oddNs
4.35/1.85	   take(X1, X2) -> n__take(X1, X2)
4.35/1.85	   zip(X1, X2) -> n__zip(X1, X2)
4.35/1.85	   cons(X1, X2) -> n__cons(X1, X2)
4.35/1.85	   repItems(X) -> n__repItems(X)
4.35/1.85	   activate(n__incr(X)) -> incr(activate(X))
4.35/1.85	   activate(n__oddNs) -> oddNs
4.35/1.85	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
4.35/1.85	   activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2))
4.35/1.85	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
4.35/1.85	   activate(n__repItems(X)) -> repItems(activate(X))
4.35/1.85	   activate(X) -> X
4.35/1.85	
4.35/1.85	S is empty.
4.35/1.85	Rewrite Strategy: FULL
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(3) DecreasingLoopProof (LOWER BOUND(ID))
4.35/1.85	The following loop(s) give(s) rise to the lower bound Omega(n^1):
4.35/1.85	
4.35/1.85	The rewrite sequence
4.35/1.85	
4.35/1.85	activate(n__cons(X1, X2)) ->^+ cons(activate(X1), X2)
4.35/1.85	
4.35/1.85	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
4.35/1.85	
4.35/1.85	The pumping substitution is [X1 / n__cons(X1, X2)].
4.35/1.85	
4.35/1.85	The result substitution is [ ].
4.35/1.85	
4.35/1.85	
4.35/1.85	
4.35/1.85	
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(4)
4.35/1.85	Complex Obligation (BEST)
4.35/1.85	
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(5)
4.35/1.85	Obligation:
4.35/1.85	Proved the lower bound n^1 for the following obligation:
4.35/1.85	
4.35/1.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
4.35/1.85	
4.35/1.85	
4.35/1.85	The TRS R consists of the following rules:
4.35/1.85	
4.35/1.85	   pairNs -> cons(0, n__incr(n__oddNs))
4.35/1.85	   oddNs -> incr(pairNs)
4.35/1.85	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
4.35/1.85	   take(0, XS) -> nil
4.35/1.85	   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
4.35/1.85	   zip(nil, XS) -> nil
4.35/1.85	   zip(X, nil) -> nil
4.35/1.85	   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
4.35/1.85	   tail(cons(X, XS)) -> activate(XS)
4.35/1.85	   repItems(nil) -> nil
4.35/1.85	   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
4.35/1.85	   incr(X) -> n__incr(X)
4.35/1.85	   oddNs -> n__oddNs
4.35/1.85	   take(X1, X2) -> n__take(X1, X2)
4.35/1.85	   zip(X1, X2) -> n__zip(X1, X2)
4.35/1.85	   cons(X1, X2) -> n__cons(X1, X2)
4.35/1.85	   repItems(X) -> n__repItems(X)
4.35/1.85	   activate(n__incr(X)) -> incr(activate(X))
4.35/1.85	   activate(n__oddNs) -> oddNs
4.35/1.85	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
4.35/1.85	   activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2))
4.35/1.85	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
4.35/1.85	   activate(n__repItems(X)) -> repItems(activate(X))
4.35/1.85	   activate(X) -> X
4.35/1.85	
4.35/1.85	S is empty.
4.35/1.85	Rewrite Strategy: FULL
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(6) LowerBoundPropagationProof (FINISHED)
4.35/1.85	Propagated lower bound.
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(7)
4.35/1.85	BOUNDS(n^1, INF)
4.35/1.85	
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(8)
4.35/1.85	Obligation:
4.35/1.85	Analyzing the following TRS for decreasing loops:
4.35/1.85	
4.35/1.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
4.35/1.85	
4.35/1.85	
4.35/1.85	The TRS R consists of the following rules:
4.35/1.85	
4.35/1.85	   pairNs -> cons(0, n__incr(n__oddNs))
4.35/1.85	   oddNs -> incr(pairNs)
4.35/1.85	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
4.35/1.85	   take(0, XS) -> nil
4.35/1.85	   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
4.35/1.85	   zip(nil, XS) -> nil
4.35/1.85	   zip(X, nil) -> nil
4.35/1.85	   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
4.35/1.85	   tail(cons(X, XS)) -> activate(XS)
4.35/1.85	   repItems(nil) -> nil
4.35/1.85	   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
4.35/1.85	   incr(X) -> n__incr(X)
4.35/1.85	   oddNs -> n__oddNs
4.35/1.85	   take(X1, X2) -> n__take(X1, X2)
4.35/1.85	   zip(X1, X2) -> n__zip(X1, X2)
4.35/1.85	   cons(X1, X2) -> n__cons(X1, X2)
4.35/1.85	   repItems(X) -> n__repItems(X)
4.35/1.85	   activate(n__incr(X)) -> incr(activate(X))
4.35/1.85	   activate(n__oddNs) -> oddNs
4.35/1.85	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
4.35/1.85	   activate(n__zip(X1, X2)) -> zip(activate(X1), activate(X2))
4.35/1.85	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
4.35/1.85	   activate(n__repItems(X)) -> repItems(activate(X))
4.35/1.85	   activate(X) -> X
4.35/1.85	
4.35/1.85	S is empty.
4.35/1.85	Rewrite Strategy: FULL
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(9) DecreasingLoopProof (FINISHED)
4.35/1.85	The following loop(s) give(s) rise to the lower bound EXP:
4.35/1.85	
4.35/1.85	The rewrite sequence
4.35/1.85	
4.35/1.85	activate(n__repItems(n__cons(X11_0, X22_0))) ->^+ cons(activate(X11_0), n__cons(activate(X11_0), n__repItems(activate(X22_0))))
4.35/1.85	
4.35/1.85	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
4.35/1.85	
4.35/1.85	The pumping substitution is [X11_0 / n__repItems(n__cons(X11_0, X22_0))].
4.35/1.85	
4.35/1.85	The result substitution is [ ].
4.35/1.85	
4.35/1.85	
4.35/1.85	
4.35/1.85	The rewrite sequence
4.35/1.85	
4.35/1.85	activate(n__repItems(n__cons(X11_0, X22_0))) ->^+ cons(activate(X11_0), n__cons(activate(X11_0), n__repItems(activate(X22_0))))
4.35/1.85	
4.35/1.85	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0].
4.35/1.85	
4.35/1.85	The pumping substitution is [X11_0 / n__repItems(n__cons(X11_0, X22_0))].
4.35/1.85	
4.35/1.85	The result substitution is [ ].
4.35/1.85	
4.35/1.85	
4.35/1.85	
4.35/1.85	
4.35/1.85	----------------------------------------
4.35/1.85	
4.35/1.85	(10)
4.35/1.85	BOUNDS(EXP, INF)
4.35/1.89	EOF