details

property	value
status	complete
benchmark	IJCAR_1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.54444 seconds
cpu usage	21.7218
user time	19.826
system time	1.89586
max virtual memory	1.9008584E7
max residence set size	4885932.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 7 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 74 ms] (8) CdtProblem (9) CdtKnowledgeProof [FINISHED, 0 ms] (10) BOUNDS(1, 1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 352 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(0, s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(z))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: div(0, z0) -> 0 div(z0, z1) -> quot(z0, z1, z1) quot(0, s(z0), z1) -> 0 quot(s(z0), s(z1), z2) -> quot(z0, z1, z2) quot(z0, 0, s(z1)) -> s(div(z0, s(z1))) Tuples: DIV(0, z0) -> c DIV(z0, z1) -> c1(QUOT(z0, z1, z1)) QUOT(0, s(z0), z1) -> c2 QUOT(s(z0), s(z1), z2) -> c3(QUOT(z0, z1, z2)) QUOT(z0, 0, s(z1)) -> c4(DIV(z0, s(z1))) S tuples: DIV(0, z0) -> c DIV(z0, z1) -> c1(QUOT(z0, z1, z1)) QUOT(0, s(z0), z1) -> c2 QUOT(s(z0), s(z1), z2) -> c3(QUOT(z0, z1, z2)) QUOT(z0, 0, s(z1)) -> c4(DIV(z0, s(z1))) K tuples:none Defined Rule Symbols: div_2, quot_3 Defined Pair Symbols: DIV_2, QUOT_3 Compound Symbols: c, c1_1, c2, c3_1, c4_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: DIV(0, z0) -> c QUOT(0, s(z0), z1) -> c2 ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: div(0, z0) -> 0 popout

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all output return to Runtime Complexity: TRS Innermost