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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313584
details
property
value
status
complete
benchmark
2.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n012.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.80734 seconds
cpu usage
19.6985
user time
18.1552
system time
1.54324
max virtual memory
3.7899304E7
max residence set size
4147724.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
19.50/5.71 WORST_CASE(Omega(n^1), O(n^1)) 19.54/5.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.54/5.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.54/5.73 19.54/5.73 19.54/5.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.54/5.73 19.54/5.73 (0) CpxTRS 19.54/5.73 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 19.54/5.73 (2) CdtProblem 19.54/5.73 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 19.54/5.73 (4) CdtProblem 19.54/5.73 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 19.54/5.73 (6) CdtProblem 19.54/5.73 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 61 ms] 19.54/5.73 (8) CdtProblem 19.54/5.73 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 1 ms] 19.54/5.73 (10) CdtProblem 19.54/5.73 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 19.54/5.73 (12) BOUNDS(1, 1) 19.54/5.73 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.54/5.73 (14) CpxTRS 19.54/5.73 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 19.54/5.73 (16) CpxTRS 19.54/5.73 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.54/5.73 (18) typed CpxTrs 19.54/5.73 (19) OrderProof [LOWER BOUND(ID), 0 ms] 19.54/5.73 (20) typed CpxTrs 19.54/5.73 (21) RewriteLemmaProof [LOWER BOUND(ID), 1875 ms] 19.54/5.73 (22) BEST 19.54/5.73 (23) proven lower bound 19.54/5.73 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 19.54/5.73 (25) BOUNDS(n^1, INF) 19.54/5.73 (26) typed CpxTrs 19.54/5.73 19.54/5.73 19.54/5.73 ---------------------------------------- 19.54/5.73 19.54/5.73 (0) 19.54/5.73 Obligation: 19.54/5.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 19.54/5.73 19.54/5.73 19.54/5.73 The TRS R consists of the following rules: 19.54/5.73 19.54/5.73 sum(0) -> 0 19.54/5.73 sum(s(x)) -> +(sum(x), s(x)) 19.54/5.73 sum1(0) -> 0 19.54/5.73 sum1(s(x)) -> s(+(sum1(x), +(x, x))) 19.54/5.73 19.54/5.73 S is empty. 19.54/5.73 Rewrite Strategy: INNERMOST 19.54/5.73 ---------------------------------------- 19.54/5.73 19.54/5.73 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 19.54/5.73 Converted Cpx (relative) TRS to CDT 19.54/5.73 ---------------------------------------- 19.54/5.73 19.54/5.73 (2) 19.54/5.73 Obligation: 19.54/5.73 Complexity Dependency Tuples Problem 19.54/5.73 19.54/5.73 Rules: 19.54/5.73 sum(0) -> 0 19.54/5.73 sum(s(z0)) -> +(sum(z0), s(z0)) 19.54/5.73 sum1(0) -> 0 19.54/5.73 sum1(s(z0)) -> s(+(sum1(z0), +(z0, z0))) 19.54/5.73 Tuples: 19.54/5.73 SUM(0) -> c 19.54/5.73 SUM(s(z0)) -> c1(SUM(z0)) 19.54/5.73 SUM1(0) -> c2 19.54/5.73 SUM1(s(z0)) -> c3(SUM1(z0)) 19.54/5.73 S tuples: 19.54/5.73 SUM(0) -> c 19.54/5.73 SUM(s(z0)) -> c1(SUM(z0)) 19.54/5.73 SUM1(0) -> c2 19.54/5.73 SUM1(s(z0)) -> c3(SUM1(z0)) 19.54/5.73 K tuples:none 19.54/5.73 Defined Rule Symbols: sum_1, sum1_1 19.54/5.73 19.54/5.73 Defined Pair Symbols: SUM_1, SUM1_1 19.54/5.73 19.54/5.73 Compound Symbols: c, c1_1, c2, c3_1 19.54/5.73 19.54/5.73 19.54/5.73 ---------------------------------------- 19.54/5.73 19.54/5.73 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 19.54/5.73 Removed 2 trailing nodes: 19.54/5.73 SUM(0) -> c 19.54/5.73 SUM1(0) -> c2 19.54/5.73 19.54/5.73 ---------------------------------------- 19.54/5.73 19.54/5.73 (4) 19.54/5.73 Obligation: 19.54/5.73 Complexity Dependency Tuples Problem 19.54/5.73 19.54/5.73 Rules: 19.54/5.73 sum(0) -> 0
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