Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308196

details

property	value
status	complete
benchmark	OvConsOS_nosorts-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	21.4194 seconds
cpu usage	79.9873
user time	78.1654
system time	1.82189
max virtual memory	3.7726156E7
max residence set size	4223812.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

79.74/21.36	WORST_CASE(NON_POLY, ?)
79.74/21.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
79.74/21.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
79.74/21.37	
79.74/21.37	
79.74/21.37	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
79.74/21.37	
79.74/21.37	(0) CpxTRS
79.74/21.37	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
79.74/21.37	(2) TRS for Loop Detection
79.74/21.37	(3) DecreasingLoopProof [LOWER BOUND(ID), 59 ms]
79.74/21.37	(4) BEST
79.74/21.37	    (5) proven lower bound
79.74/21.37	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
79.74/21.37	        (7) BOUNDS(n^1, INF)
79.74/21.37	    (8) TRS for Loop Detection
79.74/21.37	        (9) InfiniteLowerBoundProof [FINISHED, 13.7 s]
79.74/21.37	        (10) BOUNDS(INF, INF)
79.74/21.37	
79.74/21.37	
79.74/21.37	----------------------------------------
79.74/21.37	
79.74/21.37	(0)
79.74/21.37	Obligation:
79.74/21.37	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
79.74/21.37	
79.74/21.37	
79.74/21.37	The TRS R consists of the following rules:
79.74/21.37	
79.74/21.37	   zeros -> cons(0, n__zeros)
79.74/21.37	   U11(tt, L) -> U12(tt, activate(L))
79.74/21.37	   U12(tt, L) -> s(length(activate(L)))
79.74/21.37	   U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N))
79.74/21.37	   U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N))
79.74/21.37	   U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
79.74/21.37	   length(nil) -> 0
79.74/21.37	   length(cons(N, L)) -> U11(tt, activate(L))
79.74/21.37	   take(0, IL) -> nil
79.74/21.37	   take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N)
79.74/21.37	   zeros -> n__zeros
79.74/21.37	   take(X1, X2) -> n__take(X1, X2)
79.74/21.37	   activate(n__zeros) -> zeros
79.74/21.37	   activate(n__take(X1, X2)) -> take(X1, X2)
79.74/21.37	   activate(X) -> X
79.74/21.37	
79.74/21.37	S is empty.
79.74/21.37	Rewrite Strategy: FULL
79.74/21.37	----------------------------------------
79.74/21.37	
79.74/21.37	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
79.74/21.37	Transformed a relative TRS into a decreasing-loop problem.
79.74/21.37	----------------------------------------
79.74/21.37	
79.74/21.37	(2)
79.74/21.37	Obligation:
79.74/21.37	Analyzing the following TRS for decreasing loops:
79.74/21.37	
79.74/21.37	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
79.74/21.37	
79.74/21.37	
79.74/21.37	The TRS R consists of the following rules:
79.74/21.37	
79.74/21.37	   zeros -> cons(0, n__zeros)
79.74/21.37	   U11(tt, L) -> U12(tt, activate(L))
79.74/21.37	   U12(tt, L) -> s(length(activate(L)))
79.74/21.37	   U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N))
79.74/21.37	   U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N))
79.74/21.37	   U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
79.74/21.37	   length(nil) -> 0
79.74/21.37	   length(cons(N, L)) -> U11(tt, activate(L))
79.74/21.37	   take(0, IL) -> nil
79.74/21.37	   take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N)
79.74/21.37	   zeros -> n__zeros
79.74/21.37	   take(X1, X2) -> n__take(X1, X2)
79.74/21.37	   activate(n__zeros) -> zeros
79.74/21.37	   activate(n__take(X1, X2)) -> take(X1, X2)
79.74/21.37	   activate(X) -> X
79.74/21.37	
79.74/21.37	S is empty.
79.74/21.37	Rewrite Strategy: FULL
79.74/21.37	----------------------------------------
79.74/21.37	
79.74/21.37	(3) DecreasingLoopProof (LOWER BOUND(ID))
79.74/21.37	The following loop(s) give(s) rise to the lower bound Omega(n^1):
79.74/21.37	
79.74/21.37	The rewrite sequence
79.74/21.37	
79.74/21.37	activate(n__take(s(M1_0), cons(N2_0, IL3_0))) ->^+ U21(tt, activate(IL3_0), M1_0, N2_0)
79.74/21.37	
79.74/21.37	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
79.74/21.37	
79.74/21.37	The pumping substitution is [IL3_0 / n__take(s(M1_0), cons(N2_0, IL3_0))].
79.74/21.37	
79.74/21.37	The result substitution is [ ].
79.74/21.37	
79.74/21.37	
79.74/21.37	
79.74/21.37	
79.74/21.37	----------------------------------------
79.74/21.37

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