Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313441

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.698 seconds
cpu usage	806.438
user time	773.696
system time	32.7423
max virtual memory	3.8318456E7
max residence set size	5625552.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

806.25/291.60	WORST_CASE(Omega(n^1), O(n^1))
806.25/291.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
806.25/291.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
806.25/291.61	
806.25/291.61	
806.25/291.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
806.25/291.61	
806.25/291.61	(0) CpxTRS
806.25/291.61	(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
806.25/291.61	(2) CdtProblem
806.25/291.61	    (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
806.25/291.61	    (4) CdtProblem
806.25/291.61	    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
806.25/291.61	    (6) CdtProblem
806.25/291.61	    (7) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
806.25/291.61	    (8) CdtProblem
806.25/291.61	    (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
806.25/291.61	    (10) CdtProblem
806.25/291.61	    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 130 ms]
806.25/291.61	    (12) CdtProblem
806.25/291.61	    (13) CdtKnowledgeProof [FINISHED, 0 ms]
806.25/291.61	    (14) BOUNDS(1, 1)
806.25/291.61	(15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
806.25/291.61	(16) TRS for Loop Detection
806.25/291.61	    (17) DecreasingLoopProof [LOWER BOUND(ID), 18.9 s]
806.25/291.61	    (18) BEST
806.25/291.61	        (19) proven lower bound
806.25/291.61	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
806.25/291.61	            (21) BOUNDS(n^1, INF)
806.25/291.61	        (22) TRS for Loop Detection
806.25/291.61	
806.25/291.61	
806.25/291.61	----------------------------------------
806.25/291.61	
806.25/291.61	(0)
806.25/291.61	Obligation:
806.25/291.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
806.25/291.61	
806.25/291.61	
806.25/291.61	The TRS R consists of the following rules:
806.25/291.61	
806.25/291.61	   U11(tt, N, XS) -> U12(tt, activate(N), activate(XS))
806.25/291.61	   U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS)))
806.25/291.61	   U21(tt, X) -> U22(tt, activate(X))
806.25/291.61	   U22(tt, X) -> activate(X)
806.25/291.61	   U31(tt, N) -> U32(tt, activate(N))
806.25/291.61	   U32(tt, N) -> activate(N)
806.25/291.61	   U41(tt, N, XS) -> U42(tt, activate(N), activate(XS))
806.25/291.61	   U42(tt, N, XS) -> head(afterNth(activate(N), activate(XS)))
806.25/291.61	   U51(tt, Y) -> U52(tt, activate(Y))
806.25/291.61	   U52(tt, Y) -> activate(Y)
806.25/291.61	   U61(tt, N, X, XS) -> U62(tt, activate(N), activate(X), activate(XS))
806.25/291.61	   U62(tt, N, X, XS) -> U63(tt, activate(N), activate(X), activate(XS))
806.25/291.61	   U63(tt, N, X, XS) -> U64(splitAt(activate(N), activate(XS)), activate(X))
806.25/291.61	   U64(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
806.25/291.61	   U71(tt, XS) -> U72(tt, activate(XS))
806.25/291.61	   U72(tt, XS) -> activate(XS)
806.25/291.61	   U81(tt, N, XS) -> U82(tt, activate(N), activate(XS))
806.25/291.61	   U82(tt, N, XS) -> fst(splitAt(activate(N), activate(XS)))
806.25/291.61	   afterNth(N, XS) -> U11(tt, N, XS)
806.25/291.61	   fst(pair(X, Y)) -> U21(tt, X)
806.25/291.61	   head(cons(N, XS)) -> U31(tt, N)
806.25/291.61	   natsFrom(N) -> cons(N, n__natsFrom(s(N)))
806.25/291.61	   sel(N, XS) -> U41(tt, N, XS)
806.25/291.61	   snd(pair(X, Y)) -> U51(tt, Y)
806.25/291.61	   splitAt(0, XS) -> pair(nil, XS)
806.25/291.61	   splitAt(s(N), cons(X, XS)) -> U61(tt, N, X, activate(XS))
806.25/291.61	   tail(cons(N, XS)) -> U71(tt, activate(XS))
806.25/291.61	   take(N, XS) -> U81(tt, N, XS)
806.25/291.61	   natsFrom(X) -> n__natsFrom(X)
806.25/291.61	   activate(n__natsFrom(X)) -> natsFrom(X)
806.25/291.61	   activate(X) -> X
806.25/291.61	
806.25/291.61	S is empty.
806.25/291.61	Rewrite Strategy: INNERMOST
806.25/291.61	----------------------------------------
806.25/291.61	
806.25/291.61	(1) CpxTrsToCdtProof (UPPER BOUND(ID))
806.25/291.61	Converted Cpx (relative) TRS to CDT
806.25/291.61	----------------------------------------
806.25/291.61	
806.25/291.61	(2)
806.25/291.61	Obligation:
806.25/291.61	Complexity Dependency Tuples Problem
806.25/291.61	
806.25/291.61	Rules:
806.25/291.61	   U11(tt, z0, z1) -> U12(tt, activate(z0), activate(z1))
806.25/291.61	   U12(tt, z0, z1) -> snd(splitAt(activate(z0), activate(z1)))
806.25/291.61	   U21(tt, z0) -> U22(tt, activate(z0))
806.25/291.61	   U22(tt, z0) -> activate(z0)
806.25/291.61	   U31(tt, z0) -> U32(tt, activate(z0))
806.25/291.61	   U32(tt, z0) -> activate(z0)
806.25/291.61	   U41(tt, z0, z1) -> U42(tt, activate(z0), activate(z1))
806.25/291.61	   U42(tt, z0, z1) -> head(afterNth(activate(z0), activate(z1)))
806.25/291.61	   U51(tt, z0) -> U52(tt, activate(z0))
806.25/291.61	   U52(tt, z0) -> activate(z0)
806.25/291.61	   U61(tt, z0, z1, z2) -> U62(tt, activate(z0), activate(z1), activate(z2))
806.25/291.61	   U62(tt, z0, z1, z2) -> U63(tt, activate(z0), activate(z1), activate(z2))
806.25/291.61	   U63(tt, z0, z1, z2) -> U64(splitAt(activate(z0), activate(z2)), activate(z1))
806.25/291.61	   U64(pair(z0, z1), z2) -> pair(cons(activate(z2), z0), z1)

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40