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Runti Compl Inner Rewri 22807 pair #381904335
details
property
value
status
complete
benchmark
Ex24_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.29400491714 seconds
cpu usage
15.354256409
max memory
2.22369792E9
stage attributes
key
value
output-size
8033
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 12 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: a__f(b, X, c) -> a__f(X, a__c, X) a__c -> b mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(c) -> a__c mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: a__f(b, z0, c) -> a__f(z0, a__c, z0) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(z0, mark(z1), z2) mark(c) -> a__c mark(b) -> b Tuples: A__F(b, z0, c) -> c1(A__F(z0, a__c, z0), A__C) A__F(z0, z1, z2) -> c2 A__C -> c3 A__C -> c4 MARK(f(z0, z1, z2)) -> c5(A__F(z0, mark(z1), z2), MARK(z1)) MARK(c) -> c6(A__C) MARK(b) -> c7 S tuples: A__F(b, z0, c) -> c1(A__F(z0, a__c, z0), A__C) A__F(z0, z1, z2) -> c2 A__C -> c3 A__C -> c4 MARK(f(z0, z1, z2)) -> c5(A__F(z0, mark(z1), z2), MARK(z1)) MARK(c) -> c6(A__C) MARK(b) -> c7 K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, A__C, MARK_1 Compound Symbols: c1_2, c2, c3, c4, c5_2, c6_1, c7 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
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