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Runti Compl Inner Rewri 22807 pair #381903982
details
property
value
status
complete
benchmark
IJCAR_1.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
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.69042086601 seconds
cpu usage
13.082975156
max memory
2.85503488E9
stage attributes
key
value
output-size
9893
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 40 ms] (8) CdtProblem (9) CdtKnowledgeProof [FINISHED, 0 ms] (10) BOUNDS(1, 1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 437 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs ---------------------------------------- (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: div(0, y) -> 0 div(x, y) -> quot(x, y, y) quot(0, s(y), z) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(div(x, s(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: div(0, z0) -> 0 div(z0, z1) -> quot(z0, z1, z1) quot(0, s(z0), z1) -> 0 quot(s(z0), s(z1), z2) -> quot(z0, z1, z2) quot(z0, 0, s(z1)) -> s(div(z0, s(z1))) Tuples: DIV(0, z0) -> c DIV(z0, z1) -> c1(QUOT(z0, z1, z1)) QUOT(0, s(z0), z1) -> c2 QUOT(s(z0), s(z1), z2) -> c3(QUOT(z0, z1, z2)) QUOT(z0, 0, s(z1)) -> c4(DIV(z0, s(z1))) S tuples: DIV(0, z0) -> c DIV(z0, z1) -> c1(QUOT(z0, z1, z1)) QUOT(0, s(z0), z1) -> c2 QUOT(s(z0), s(z1), z2) -> c3(QUOT(z0, z1, z2)) QUOT(z0, 0, s(z1)) -> c4(DIV(z0, s(z1))) K tuples:none Defined Rule Symbols: div_2, quot_3 Defined Pair Symbols: DIV_2, QUOT_3 Compound Symbols: c, c1_1, c2, c3_1, c4_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: QUOT(0, s(z0), z1) -> c2 DIV(0, z0) -> c ----------------------------------------
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