details

property	value
status	complete
benchmark	gcd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.537 seconds
cpu usage	638.246
user time	633.565
system time	4.68054
max virtual memory	3.8191036E7
max residence set size	5530124.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 292 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), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 221 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 745 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 583 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 574 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 558 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 541 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 467 ms] (28) CdtProblem (29) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (30) BOUNDS(1, 1) (31) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxRelTRS (33) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (34) typed CpxTrs (35) OrderProof [LOWER BOUND(ID), 0 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 1072 ms] (38) BEST (39) proven lower bound (40) LowerBoundPropagationProof [FINISHED, 0 ms] (41) BOUNDS(n^1, INF) (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 39 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 736 ms] (46) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: minus(X, s(Y)) -> pred(minus(X, Y)) minus(X, 0) -> X pred(s(X)) -> X le(s(X), s(Y)) -> le(X, Y) le(s(X), 0) -> false le(0, Y) -> true gcd(0, Y) -> 0 gcd(s(X), 0) -> s(X) gcd(s(X), s(Y)) -> if(le(Y, X), s(X), s(Y)) if(true, s(X), s(Y)) -> gcd(minus(X, Y), s(Y)) if(false, s(X), s(Y)) -> gcd(minus(Y, X), s(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(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(false) -> false encArg(true) -> true encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_pred(x_1)) -> pred(encArg(x_1)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_pred(x_1) -> pred(encArg(x_1)) encode_0 -> 0 encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_false -> false encode_true -> true popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Derivational Complexity: TRS Innermost