details

property	value
status	complete
benchmark	4.05.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	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.528 seconds
cpu usage	414.038
user time	408.617
system time	5.42078
max virtual memory	1.8812028E7
max residence set size	8681740.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (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^2)), 40 ms] (8) CdtProblem (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (10) BOUNDS(1, 1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: *(x, +(y, z)) -> +(*(x, y), *(x, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, 1) -> x *(1, y) -> y S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) *(z0, 1) -> z0 *(1, z0) -> z0 Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) *'(z0, 1) -> c2 *'(1, z0) -> c3 S tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) *'(z0, 1) -> c2 *'(1, z0) -> c3 K tuples:none Defined Rule Symbols: *_2 Defined Pair Symbols: *'_2 Compound Symbols: c_2, c1_2, c2, c3 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: *'(1, z0) -> c3 *'(z0, 1) -> c2 ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) *(z0, 1) -> z0 *(1, z0) -> z0 Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) S tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) popout

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actions

all output return to Runtime Complexity: TRS Innermost