details

property	value
status	complete
benchmark	Ex9_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.95298 seconds
cpu usage	27.3398
user time	25.9406
system time	1.39928
max virtual memory	1.9046796E7
max residence set size	3880132.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 54 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(b) -> a__b mark(a) -> a a__f(X1, X2, X3) -> f(X1, X2, X3) a__b -> b S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS is a non-duplicating overlay system, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(b) -> a__b mark(a) -> a a__f(X1, X2, X3) -> f(X1, X2, X3) a__b -> b S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, z0, z0) -> a__f(z0, a__b, b) a__f(z0, z1, z2) -> f(z0, z1, z2) a__b -> a a__b -> b mark(f(z0, z1, z2)) -> a__f(z0, mark(z1), z2) mark(b) -> a__b mark(a) -> a Tuples: A__F(a, z0, z0) -> c(A__F(z0, a__b, b), A__B) A__F(z0, z1, z2) -> c1 A__B -> c2 A__B -> c3 MARK(f(z0, z1, z2)) -> c4(A__F(z0, mark(z1), z2), MARK(z1)) popout

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job log

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actions

all output return to Runtime Complexity: TRS