Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313473

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n165.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.61269 seconds
cpu usage	13.4806
user time	12.4355
system time	1.04502
max virtual memory	1.8711052E7
max residence set size	3564256.0

stage attributes

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

output

12.90/4.55	WORST_CASE(Omega(n^1), O(n^1))
12.90/4.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
12.90/4.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.90/4.57	
12.90/4.57	
12.90/4.57	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.90/4.57	
12.90/4.57	(0) CpxTRS
12.90/4.57	(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
12.90/4.57	(2) CdtProblem
12.90/4.57	    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
12.90/4.57	    (4) CdtProblem
12.90/4.57	    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
12.90/4.57	    (6) CdtProblem
12.90/4.57	    (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
12.90/4.57	    (8) CdtProblem
12.90/4.57	    (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
12.90/4.57	    (10) CdtProblem
12.90/4.57	    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 69 ms]
12.90/4.57	    (12) CdtProblem
12.90/4.57	    (13) CdtKnowledgeProof [FINISHED, 0 ms]
12.90/4.57	    (14) BOUNDS(1, 1)
12.90/4.57	(15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
12.90/4.57	(16) TRS for Loop Detection
12.90/4.57	    (17) DecreasingLoopProof [LOWER BOUND(ID), 152 ms]
12.90/4.57	    (18) BEST
12.90/4.57	        (19) proven lower bound
12.90/4.57	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
12.90/4.57	            (21) BOUNDS(n^1, INF)
12.90/4.57	        (22) TRS for Loop Detection
12.90/4.57	
12.90/4.57	
12.90/4.57	----------------------------------------
12.90/4.57	
12.90/4.57	(0)
12.90/4.57	Obligation:
12.90/4.57	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
12.90/4.57	
12.90/4.57	
12.90/4.57	The TRS R consists of the following rules:
12.90/4.57	
12.90/4.57	   U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X))
12.90/4.57	   U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
12.90/4.57	   afterNth(N, XS) -> snd(splitAt(N, XS))
12.90/4.57	   and(tt, X) -> activate(X)
12.90/4.57	   fst(pair(X, Y)) -> X
12.90/4.57	   head(cons(N, XS)) -> N
12.90/4.57	   natsFrom(N) -> cons(N, n__natsFrom(s(N)))
12.90/4.57	   sel(N, XS) -> head(afterNth(N, XS))
12.90/4.57	   snd(pair(X, Y)) -> Y
12.90/4.57	   splitAt(0, XS) -> pair(nil, XS)
12.90/4.57	   splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, activate(XS))
12.90/4.57	   tail(cons(N, XS)) -> activate(XS)
12.90/4.57	   take(N, XS) -> fst(splitAt(N, XS))
12.90/4.57	   natsFrom(X) -> n__natsFrom(X)
12.90/4.57	   activate(n__natsFrom(X)) -> natsFrom(X)
12.90/4.57	   activate(X) -> X
12.90/4.57	
12.90/4.57	S is empty.
12.90/4.57	Rewrite Strategy: INNERMOST
12.90/4.57	----------------------------------------
12.90/4.57	
12.90/4.57	(1) CpxTrsToCdtProof (UPPER BOUND(ID))
12.90/4.57	Converted Cpx (relative) TRS to CDT
12.90/4.57	----------------------------------------
12.90/4.57	
12.90/4.57	(2)
12.90/4.57	Obligation:
12.90/4.57	Complexity Dependency Tuples Problem
12.90/4.57	
12.90/4.57	Rules:
12.90/4.57	   U11(tt, z0, z1, z2) -> U12(splitAt(activate(z0), activate(z2)), activate(z1))
12.90/4.57	   U12(pair(z0, z1), z2) -> pair(cons(activate(z2), z0), z1)
12.90/4.57	   afterNth(z0, z1) -> snd(splitAt(z0, z1))
12.90/4.57	   and(tt, z0) -> activate(z0)
12.90/4.57	   fst(pair(z0, z1)) -> z0
12.90/4.57	   head(cons(z0, z1)) -> z0
12.90/4.57	   natsFrom(z0) -> cons(z0, n__natsFrom(s(z0)))
12.90/4.57	   natsFrom(z0) -> n__natsFrom(z0)
12.90/4.57	   sel(z0, z1) -> head(afterNth(z0, z1))
12.90/4.57	   snd(pair(z0, z1)) -> z1
12.90/4.57	   splitAt(0, z0) -> pair(nil, z0)
12.90/4.57	   splitAt(s(z0), cons(z1, z2)) -> U11(tt, z0, z1, activate(z2))
12.90/4.57	   tail(cons(z0, z1)) -> activate(z1)
12.90/4.57	   take(z0, z1) -> fst(splitAt(z0, z1))
12.90/4.57	   activate(n__natsFrom(z0)) -> natsFrom(z0)
12.90/4.57	   activate(z0) -> z0
12.90/4.57	Tuples:
12.90/4.57	   U11'(tt, z0, z1, z2) -> c(U12'(splitAt(activate(z0), activate(z2)), activate(z1)), SPLITAT(activate(z0), activate(z2)), ACTIVATE(z0), ACTIVATE(z2), ACTIVATE(z1))
12.90/4.57	   U12'(pair(z0, z1), z2) -> c1(ACTIVATE(z2))
12.90/4.57	   AFTERNTH(z0, z1) -> c2(SND(splitAt(z0, z1)), SPLITAT(z0, z1))
12.90/4.57	   AND(tt, z0) -> c3(ACTIVATE(z0))
12.90/4.57	   FST(pair(z0, z1)) -> c4
12.90/4.57	   HEAD(cons(z0, z1)) -> c5
12.90/4.57	   NATSFROM(z0) -> c6
12.90/4.57	   NATSFROM(z0) -> c7
12.90/4.57	   SEL(z0, z1) -> c8(HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
12.90/4.57	   SND(pair(z0, z1)) -> c9
12.90/4.57	   SPLITAT(0, z0) -> c10
12.90/4.57	   SPLITAT(s(z0), cons(z1, z2)) -> c11(U11'(tt, z0, z1, activate(z2)), ACTIVATE(z2))

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