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	n149.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.506 seconds
cpu usage	347.978
user time	344.428
system time	3.54985
max virtual memory	1.9113816E7
max residence set size	6355448.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 171 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 13 ms] (6) CpxRelTRS (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (8) CdtProblem (9) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 125 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 551 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 110 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 76 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 72 ms] (26) CdtProblem (27) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (28) BOUNDS(1, 1) (29) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRelTRS (31) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (32) typed CpxTrs (33) OrderProof [LOWER BOUND(ID), 0 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 7090 ms] (36) BEST (37) proven lower bound (38) LowerBoundPropagationProof [FINISHED, 0 ms] (39) BOUNDS(n^1, INF) (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (42) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). 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) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(a) -> a encArg(b) -> b encArg(f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__f(x_1, x_2, x_3)) -> a__f(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__b) -> a__b encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__f(x_1, x_2, x_3) -> a__f(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_a__b -> a__b encode_b -> b encode_mark(x_1) -> mark(encArg(x_1)) encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) popout

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job log

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actions

all output return to Derivational Complexity: TRS