Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308153

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n130.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.2266 seconds
cpu usage	40.6989
user time	38.8067
system time	1.89221
max virtual memory	3.778182E7
max residence set size	4079632.0

stage attributes

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

output

40.09/11.13	WORST_CASE(Omega(n^1), O(n^1))
40.53/11.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
40.53/11.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
40.53/11.14	
40.53/11.14	
40.53/11.14	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
40.53/11.14	
40.53/11.14	(0) CpxTRS
40.53/11.14	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
40.53/11.14	(2) CpxTRS
40.53/11.14	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 73 ms]
40.53/11.14	    (4) CpxTRS
40.53/11.14	    (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
40.53/11.14	    (6) CdtProblem
40.53/11.14	    (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
40.53/11.14	    (8) CdtProblem
40.53/11.14	    (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
40.53/11.14	    (10) CdtProblem
40.53/11.14	    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
40.53/11.14	    (12) CdtProblem
40.53/11.14	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 221 ms]
40.53/11.14	    (14) CdtProblem
40.53/11.14	    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 62 ms]
40.53/11.14	    (16) CdtProblem
40.53/11.14	    (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
40.53/11.14	    (18) BOUNDS(1, 1)
40.53/11.14	(19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
40.53/11.14	(20) TRS for Loop Detection
40.53/11.14	    (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
40.53/11.14	    (22) BEST
40.53/11.14	        (23) proven lower bound
40.53/11.14	            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
40.53/11.14	            (25) BOUNDS(n^1, INF)
40.53/11.14	        (26) TRS for Loop Detection
40.53/11.14	
40.53/11.14	
40.53/11.14	----------------------------------------
40.53/11.14	
40.53/11.14	(0)
40.53/11.14	Obligation:
40.53/11.14	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
40.53/11.14	
40.53/11.14	
40.53/11.14	The TRS R consists of the following rules:
40.53/11.14	
40.53/11.14	   active(U11(tt, N, XS)) -> mark(U12(tt, N, XS))
40.53/11.14	   active(U12(tt, N, XS)) -> mark(snd(splitAt(N, XS)))
40.53/11.14	   active(U21(tt, X)) -> mark(U22(tt, X))
40.53/11.14	   active(U22(tt, X)) -> mark(X)
40.53/11.14	   active(U31(tt, N)) -> mark(U32(tt, N))
40.53/11.14	   active(U32(tt, N)) -> mark(N)
40.53/11.14	   active(U41(tt, N, XS)) -> mark(U42(tt, N, XS))
40.53/11.14	   active(U42(tt, N, XS)) -> mark(head(afterNth(N, XS)))
40.53/11.14	   active(U51(tt, Y)) -> mark(U52(tt, Y))
40.53/11.14	   active(U52(tt, Y)) -> mark(Y)
40.53/11.14	   active(U61(tt, N, X, XS)) -> mark(U62(tt, N, X, XS))
40.53/11.14	   active(U62(tt, N, X, XS)) -> mark(U63(tt, N, X, XS))
40.53/11.14	   active(U63(tt, N, X, XS)) -> mark(U64(splitAt(N, XS), X))
40.53/11.14	   active(U64(pair(YS, ZS), X)) -> mark(pair(cons(X, YS), ZS))
40.53/11.14	   active(U71(tt, XS)) -> mark(U72(tt, XS))
40.53/11.14	   active(U72(tt, XS)) -> mark(XS)
40.53/11.14	   active(U81(tt, N, XS)) -> mark(U82(tt, N, XS))
40.53/11.14	   active(U82(tt, N, XS)) -> mark(fst(splitAt(N, XS)))
40.53/11.14	   active(afterNth(N, XS)) -> mark(U11(tt, N, XS))
40.53/11.14	   active(fst(pair(X, Y))) -> mark(U21(tt, X))
40.53/11.14	   active(head(cons(N, XS))) -> mark(U31(tt, N))
40.53/11.14	   active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
40.53/11.14	   active(sel(N, XS)) -> mark(U41(tt, N, XS))
40.53/11.14	   active(snd(pair(X, Y))) -> mark(U51(tt, Y))
40.53/11.14	   active(splitAt(0, XS)) -> mark(pair(nil, XS))
40.53/11.14	   active(splitAt(s(N), cons(X, XS))) -> mark(U61(tt, N, X, XS))
40.53/11.14	   active(tail(cons(N, XS))) -> mark(U71(tt, XS))
40.53/11.14	   active(take(N, XS)) -> mark(U81(tt, N, XS))
40.53/11.14	   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
40.53/11.14	   active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
40.53/11.14	   active(snd(X)) -> snd(active(X))
40.53/11.14	   active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
40.53/11.14	   active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
40.53/11.14	   active(U21(X1, X2)) -> U21(active(X1), X2)
40.53/11.14	   active(U22(X1, X2)) -> U22(active(X1), X2)
40.53/11.14	   active(U31(X1, X2)) -> U31(active(X1), X2)
40.53/11.14	   active(U32(X1, X2)) -> U32(active(X1), X2)
40.53/11.14	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
40.53/11.14	   active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
40.53/11.14	   active(head(X)) -> head(active(X))
40.53/11.14	   active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
40.53/11.14	   active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
40.53/11.14	   active(U51(X1, X2)) -> U51(active(X1), X2)
40.53/11.14	   active(U52(X1, X2)) -> U52(active(X1), X2)
40.53/11.14	   active(U61(X1, X2, X3, X4)) -> U61(active(X1), X2, X3, X4)
40.53/11.14	   active(U62(X1, X2, X3, X4)) -> U62(active(X1), X2, X3, X4)
40.53/11.14	   active(U63(X1, X2, X3, X4)) -> U63(active(X1), X2, X3, X4)
40.53/11.14	   active(U64(X1, X2)) -> U64(active(X1), X2)
40.53/11.14	   active(pair(X1, X2)) -> pair(active(X1), X2)
40.53/11.14	   active(pair(X1, X2)) -> pair(X1, active(X2))
40.53/11.14	   active(cons(X1, X2)) -> cons(active(X1), X2)
40.53/11.14	   active(U71(X1, X2)) -> U71(active(X1), X2)
40.53/11.14	   active(U72(X1, X2)) -> U72(active(X1), X2)
40.53/11.14	   active(U81(X1, X2, X3)) -> U81(active(X1), X2, X3)
40.53/11.14	   active(U82(X1, X2, X3)) -> U82(active(X1), X2, X3)

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job log

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11