details

property	value
status	complete
benchmark	elimdupl.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	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.508 seconds
cpu usage	320.635
user time	317.41
system time	3.22523
max virtual memory	1.9016064E7
max residence set size	5615320.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 13 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)), 64 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 155 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 101 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 67 ms] (14) CdtProblem (15) CdtKnowledgeProof [FINISHED, 0 ms] (16) BOUNDS(1, 1) (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) 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: eq(0, 0) -> true eq(0, s(X)) -> false eq(s(X), 0) -> false eq(s(X), s(Y)) -> eq(X, Y) rm(N, nil) -> nil rm(N, add(M, X)) -> ifrm(eq(N, M), N, add(M, X)) ifrm(true, N, add(M, X)) -> rm(N, X) ifrm(false, N, add(M, X)) -> add(M, rm(N, X)) purge(nil) -> nil purge(add(N, X)) -> add(N, purge(rm(N, X))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: eq(0, 0) -> true eq(0, s(z0)) -> false eq(s(z0), 0) -> false eq(s(z0), s(z1)) -> eq(z0, z1) rm(z0, nil) -> nil rm(z0, add(z1, z2)) -> ifrm(eq(z0, z1), z0, add(z1, z2)) ifrm(true, z0, add(z1, z2)) -> rm(z0, z2) ifrm(false, z0, add(z1, z2)) -> add(z1, rm(z0, z2)) purge(nil) -> nil purge(add(z0, z1)) -> add(z0, purge(rm(z0, z1))) Tuples: EQ(0, 0) -> c EQ(0, s(z0)) -> c1 EQ(s(z0), 0) -> c2 EQ(s(z0), s(z1)) -> c3(EQ(z0, z1)) RM(z0, nil) -> c4 RM(z0, add(z1, z2)) -> c5(IFRM(eq(z0, z1), z0, add(z1, z2)), EQ(z0, z1)) IFRM(true, z0, add(z1, z2)) -> c6(RM(z0, z2)) IFRM(false, z0, add(z1, z2)) -> c7(RM(z0, z2)) PURGE(nil) -> c8 PURGE(add(z0, z1)) -> c9(PURGE(rm(z0, z1)), RM(z0, z1)) S tuples: EQ(0, 0) -> c EQ(0, s(z0)) -> c1 EQ(s(z0), 0) -> c2 EQ(s(z0), s(z1)) -> c3(EQ(z0, z1)) RM(z0, nil) -> c4 RM(z0, add(z1, z2)) -> c5(IFRM(eq(z0, z1), z0, add(z1, z2)), EQ(z0, z1)) IFRM(true, z0, add(z1, z2)) -> c6(RM(z0, z2)) IFRM(false, z0, add(z1, z2)) -> c7(RM(z0, z2)) PURGE(nil) -> c8 PURGE(add(z0, z1)) -> c9(PURGE(rm(z0, z1)), RM(z0, z1)) K tuples:none 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