details

property	value
status	complete
benchmark	2.39.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.09479 seconds
cpu usage	13.3639
user time	12.6366
system time	0.727314
max virtual memory	5.5943456E7
max residence set size	2040360.0

stage attributes

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

output

WORST_CASE(Omega(n^2), 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 9 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)), 38 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 29 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 262 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 5 ms] (26) proven lower bound (27) LowerBoundPropagationProof [FINISHED, 0 ms] (28) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: rev(nil) -> nil rev(.(x, y)) -> ++(rev(y), .(x, nil)) car(.(x, y)) -> x cdr(.(x, y)) -> y null(nil) -> true null(.(x, y)) -> false ++(nil, y) -> y ++(.(x, y), z) -> .(x, ++(y, 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: rev(nil) -> nil rev(.(z0, z1)) -> ++(rev(z1), .(z0, nil)) car(.(z0, z1)) -> z0 cdr(.(z0, z1)) -> z1 null(nil) -> true null(.(z0, z1)) -> false ++(nil, z0) -> z0 ++(.(z0, z1), z2) -> .(z0, ++(z1, z2)) Tuples: REV(nil) -> c REV(.(z0, z1)) -> c1(++'(rev(z1), .(z0, nil)), REV(z1)) CAR(.(z0, z1)) -> c2 CDR(.(z0, z1)) -> c3 NULL(nil) -> c4 NULL(.(z0, z1)) -> c5 ++'(nil, z0) -> c6 ++'(.(z0, z1), z2) -> c7(++'(z1, z2)) S tuples: REV(nil) -> c REV(.(z0, z1)) -> c1(++'(rev(z1), .(z0, nil)), REV(z1)) CAR(.(z0, z1)) -> c2 CDR(.(z0, z1)) -> c3 NULL(nil) -> c4 NULL(.(z0, z1)) -> c5 ++'(nil, z0) -> c6 ++'(.(z0, z1), z2) -> c7(++'(z1, z2)) K tuples:none Defined Rule Symbols: rev_1, car_1, cdr_1, null_1, ++_2 Defined Pair Symbols: REV_1, CAR_1, CDR_1, NULL_1, ++'_2 popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost