details

property	value
status	complete
benchmark	Ex5_Zan97_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.488 seconds
cpu usage	328.601
user time	326.112
system time	2.4886
max virtual memory	3.7917768E7
max residence set size	5407080.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 169 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 257 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 459 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 396 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 383 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 393 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 365 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), 455 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), 116 ms] (42) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: f(X) -> if(X, c, n__f(n__true)) if(true, X, Y) -> X if(false, X, Y) -> activate(Y) f(X) -> n__f(X) true -> n__true activate(n__f(X)) -> f(activate(X)) activate(n__true) -> true activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(c) -> c encArg(n__f(x_1)) -> n__f(encArg(x_1)) encArg(n__true) -> n__true encArg(false) -> false encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_true) -> true encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_c -> c encode_n__f(x_1) -> n__f(encArg(x_1)) encode_n__true -> n__true encode_true -> true encode_false -> false encode_activate(x_1) -> activate(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). popout

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actions

all output return to Derivational Complexity: TRS Innermost