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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313619
details
property
value
status
complete
benchmark
2.18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.548 seconds
cpu usage
314.959
user time
312.179
system time
2.77935
max virtual memory
1.9207756E7
max residence set size
5491824.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
314.82/291.50 WORST_CASE(Omega(n^1), O(n^2)) 314.87/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 314.87/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 314.87/291.51 314.87/291.51 314.87/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 314.87/291.51 314.87/291.51 (0) CpxTRS 314.87/291.51 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 314.87/291.51 (2) CdtProblem 314.87/291.51 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 314.87/291.51 (4) CdtProblem 314.87/291.51 (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 89 ms] 314.87/291.51 (6) CdtProblem 314.87/291.51 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 29 ms] 314.87/291.51 (8) CdtProblem 314.87/291.51 (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 314.87/291.51 (10) BOUNDS(1, 1) 314.87/291.51 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 314.87/291.51 (12) CpxTRS 314.87/291.51 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 314.87/291.51 (14) typed CpxTrs 314.87/291.51 (15) OrderProof [LOWER BOUND(ID), 0 ms] 314.87/291.51 (16) typed CpxTrs 314.87/291.51 (17) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] 314.87/291.51 (18) BEST 314.87/291.51 (19) proven lower bound 314.87/291.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 314.87/291.51 (21) BOUNDS(n^1, INF) 314.87/291.51 (22) typed CpxTrs 314.87/291.51 (23) RewriteLemmaProof [LOWER BOUND(ID), 778 ms] 314.87/291.51 (24) BOUNDS(1, INF) 314.87/291.51 314.87/291.51 314.87/291.51 ---------------------------------------- 314.87/291.51 314.87/291.51 (0) 314.87/291.51 Obligation: 314.87/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 314.87/291.51 314.87/291.51 314.87/291.51 The TRS R consists of the following rules: 314.87/291.51 314.87/291.51 sum(0) -> 0 314.87/291.51 sum(s(x)) -> +(sum(x), s(x)) 314.87/291.51 +(x, 0) -> x 314.87/291.51 +(x, s(y)) -> s(+(x, y)) 314.87/291.51 314.87/291.51 S is empty. 314.87/291.51 Rewrite Strategy: INNERMOST 314.87/291.51 ---------------------------------------- 314.87/291.51 314.87/291.51 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 314.87/291.51 Converted Cpx (relative) TRS to CDT 314.87/291.51 ---------------------------------------- 314.87/291.51 314.87/291.51 (2) 314.87/291.51 Obligation: 314.87/291.51 Complexity Dependency Tuples Problem 314.87/291.51 314.87/291.51 Rules: 314.87/291.51 sum(0) -> 0 314.87/291.51 sum(s(z0)) -> +(sum(z0), s(z0)) 314.87/291.51 +(z0, 0) -> z0 314.87/291.51 +(z0, s(z1)) -> s(+(z0, z1)) 314.87/291.51 Tuples: 314.87/291.51 SUM(0) -> c 314.87/291.51 SUM(s(z0)) -> c1(+'(sum(z0), s(z0)), SUM(z0)) 314.87/291.51 +'(z0, 0) -> c2 314.87/291.51 +'(z0, s(z1)) -> c3(+'(z0, z1)) 314.87/291.51 S tuples: 314.87/291.51 SUM(0) -> c 314.87/291.51 SUM(s(z0)) -> c1(+'(sum(z0), s(z0)), SUM(z0)) 314.87/291.51 +'(z0, 0) -> c2 314.87/291.51 +'(z0, s(z1)) -> c3(+'(z0, z1)) 314.87/291.51 K tuples:none 314.87/291.51 Defined Rule Symbols: sum_1, +_2 314.87/291.51 314.87/291.51 Defined Pair Symbols: SUM_1, +'_2 314.87/291.51 314.87/291.51 Compound Symbols: c, c1_2, c2, c3_1 314.87/291.51 314.87/291.51 314.87/291.51 ---------------------------------------- 314.87/291.51 314.87/291.51 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 314.87/291.51 Removed 2 trailing nodes: 314.87/291.51 +'(z0, 0) -> c2 314.87/291.51 SUM(0) -> c 314.87/291.51 314.87/291.51 ---------------------------------------- 314.87/291.51 314.87/291.51 (4) 314.87/291.51 Obligation: 314.87/291.51 Complexity Dependency Tuples Problem 314.87/291.51 314.87/291.51 Rules: 314.87/291.51 sum(0) -> 0 314.87/291.51 sum(s(z0)) -> +(sum(z0), s(z0)) 314.87/291.51 +(z0, 0) -> z0
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