details

property	value
status	complete
benchmark	intersect.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.459876776 seconds
cpu usage	396.054345506
max memory	7.442497536E9

stage attributes

key	value
output-size	37453
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 107 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 94 ms] (16) CdtProblem (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 115 ms] (20) CdtProblem (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (22) BOUNDS(1, 1) (23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTRS (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) typed CpxTrs (27) OrderProof [LOWER BOUND(ID), 0 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 77 ms] (36) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: if(true, x, y) -> x if(false, x, y) -> y eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) app(nil, l) -> l app(cons(x, l1), l2) -> cons(x, app(l1, l2)) app(app(l1, l2), l3) -> app(l1, app(l2, l3)) mem(x, nil) -> false mem(x, cons(y, l)) -> ifmem(eq(x, y), x, l) ifmem(true, x, l) -> true ifmem(false, x, l) -> mem(x, l) inter(x, nil) -> nil inter(nil, x) -> nil inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) inter(cons(x, l1), l2) -> ifinter(mem(x, l2), x, l1, l2) inter(l1, cons(x, l2)) -> ifinter(mem(x, l1), x, l2, l1) ifinter(true, x, l1, l2) -> cons(x, inter(l1, l2)) ifinter(false, x, l1, l2) -> inter(l1, l2) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of ifinter: ifmem, eq, mem The following defined symbols can occur below the 0th argument of ifmem: eq Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: app(app(l1, l2), l3) -> app(l1, app(l2, l3)) inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) ---------------------------------------- (2) Obligation: popout

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

job log

popout

actions

all output return to Runti Compl Full Rewri 10127