details

property	value
status	complete
benchmark	32.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.536 seconds
cpu usage	334.225
user time	331.052
system time	3.1721
max virtual memory	1.9217104E7
max residence set size	5897296.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 77 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 75 ms] (8) CdtProblem (9) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 61 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) 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: sort(nil) -> nil sort(cons(x, y)) -> insert(x, sort(y)) insert(x, nil) -> cons(x, nil) insert(x, cons(v, w)) -> choose(x, cons(v, w), x, v) choose(x, cons(v, w), y, 0) -> cons(x, cons(v, w)) choose(x, cons(v, w), 0, s(z)) -> cons(v, insert(x, w)) choose(x, cons(v, w), s(y), s(z)) -> choose(x, cons(v, w), 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: sort(nil) -> nil sort(cons(z0, z1)) -> insert(z0, sort(z1)) insert(z0, nil) -> cons(z0, nil) insert(z0, cons(z1, z2)) -> choose(z0, cons(z1, z2), z0, z1) choose(z0, cons(z1, z2), z3, 0) -> cons(z0, cons(z1, z2)) choose(z0, cons(z1, z2), 0, s(z3)) -> cons(z1, insert(z0, z2)) choose(z0, cons(z1, z2), s(z3), s(z4)) -> choose(z0, cons(z1, z2), z3, z4) Tuples: SORT(nil) -> c SORT(cons(z0, z1)) -> c1(INSERT(z0, sort(z1)), SORT(z1)) INSERT(z0, nil) -> c2 INSERT(z0, cons(z1, z2)) -> c3(CHOOSE(z0, cons(z1, z2), z0, z1)) CHOOSE(z0, cons(z1, z2), z3, 0) -> c4 CHOOSE(z0, cons(z1, z2), 0, s(z3)) -> c5(INSERT(z0, z2)) CHOOSE(z0, cons(z1, z2), s(z3), s(z4)) -> c6(CHOOSE(z0, cons(z1, z2), z3, z4)) S tuples: SORT(nil) -> c SORT(cons(z0, z1)) -> c1(INSERT(z0, sort(z1)), SORT(z1)) INSERT(z0, nil) -> c2 INSERT(z0, cons(z1, z2)) -> c3(CHOOSE(z0, cons(z1, z2), z0, z1)) CHOOSE(z0, cons(z1, z2), z3, 0) -> c4 CHOOSE(z0, cons(z1, z2), 0, s(z3)) -> c5(INSERT(z0, z2)) CHOOSE(z0, cons(z1, z2), s(z3), s(z4)) -> c6(CHOOSE(z0, cons(z1, z2), z3, z4)) K tuples:none Defined Rule Symbols: sort_1, insert_2, choose_4 Defined Pair Symbols: SORT_1, INSERT_2, CHOOSE_4 Compound Symbols: c, c1_2, c2, c3_1, c4, c5_1, c6_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: CHOOSE(z0, cons(z1, z2), z3, 0) -> c4 INSERT(z0, nil) -> c2 SORT(nil) -> c popout

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

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actions

all output return to Runtime Complexity: TRS Innermost