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Runti Compl Inner Rewri 22807 pair #381904536
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
n045.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.467308044 seconds
cpu usage
323.328287634
max memory
5.770694656E9
stage attributes
key
value
output-size
24656
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 81 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 131 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 76 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 95 ms] (14) CdtProblem (15) CdtKnowledgeProof [FINISHED, 0 ms] (16) BOUNDS(1, 1) (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxTRS (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) typed CpxTrs (21) OrderProof [LOWER BOUND(ID), 0 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 315 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] (30) typed CpxTrs ---------------------------------------- (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))
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