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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307960
details
property
value
status
complete
benchmark
14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n059.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.619 seconds
cpu usage
622.91
user time
619.099
system time
3.81173
max virtual memory
3.7180592E7
max residence set size
6650180.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
622.70/291.53 WORST_CASE(Omega(n^1), O(n^2)) 622.70/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 622.70/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 622.70/291.55 622.70/291.55 622.70/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 622.70/291.55 622.70/291.55 (0) CpxTRS 622.70/291.55 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 622.70/291.55 (2) CpxTRS 622.70/291.55 (3) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] 622.70/291.55 (4) CpxRelTRS 622.70/291.55 (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 48 ms] 622.70/291.55 (6) CpxRelTRS 622.70/291.55 (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 622.70/291.55 (8) CdtProblem 622.70/291.55 (9) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (10) CdtProblem 622.70/291.55 (11) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (12) CdtProblem 622.70/291.55 (13) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (14) CdtProblem 622.70/291.55 (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 622.70/291.55 (16) CdtProblem 622.70/291.55 (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (18) CdtProblem 622.70/291.55 (19) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (20) CdtProblem 622.70/291.55 (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 174 ms] 622.70/291.55 (22) CdtProblem 622.70/291.55 (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 67 ms] 622.70/291.55 (24) CdtProblem 622.70/291.55 (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 38 ms] 622.70/291.55 (26) CdtProblem 622.70/291.55 (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 43 ms] 622.70/291.55 (28) CdtProblem 622.70/291.55 (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 367 ms] 622.70/291.55 (30) CdtProblem 622.70/291.55 (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 372 ms] 622.70/291.55 (32) CdtProblem 622.70/291.55 (33) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (34) BOUNDS(1, 1) 622.70/291.55 (35) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (36) CpxTRS 622.70/291.55 (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 622.70/291.55 (38) typed CpxTrs 622.70/291.55 (39) OrderProof [LOWER BOUND(ID), 0 ms] 622.70/291.55 (40) typed CpxTrs 622.70/291.55 (41) RewriteLemmaProof [LOWER BOUND(ID), 2293 ms] 622.70/291.55 (42) BEST 622.70/291.55 (43) proven lower bound 622.70/291.55 (44) LowerBoundPropagationProof [FINISHED, 0 ms] 622.70/291.55 (45) BOUNDS(n^1, INF) 622.70/291.55 (46) typed CpxTrs 622.70/291.55 (47) RewriteLemmaProof [LOWER BOUND(ID), 65 ms] 622.70/291.55 (48) typed CpxTrs 622.70/291.55 (49) RewriteLemmaProof [LOWER BOUND(ID), 104 ms] 622.70/291.55 (50) typed CpxTrs 622.70/291.55 (51) RewriteLemmaProof [LOWER BOUND(ID), 452 ms] 622.70/291.55 (52) typed CpxTrs 622.70/291.55 622.70/291.55 622.70/291.55 ---------------------------------------- 622.70/291.55 622.70/291.55 (0) 622.70/291.55 Obligation: 622.70/291.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 622.70/291.55 622.70/291.55 622.70/291.55 The TRS R consists of the following rules: 622.70/291.55 622.70/291.55 O(0) -> 0 622.70/291.55 +(0, x) -> x 622.70/291.55 +(x, 0) -> x 622.70/291.55 +(O(x), O(y)) -> O(+(x, y)) 622.70/291.55 +(O(x), I(y)) -> I(+(x, y)) 622.70/291.55 +(I(x), O(y)) -> I(+(x, y)) 622.70/291.55 +(I(x), I(y)) -> O(+(+(x, y), I(0))) 622.70/291.55 +(x, +(y, z)) -> +(+(x, y), z) 622.70/291.55 -(x, 0) -> x 622.70/291.55 -(0, x) -> 0 622.70/291.55 -(O(x), O(y)) -> O(-(x, y)) 622.70/291.55 -(O(x), I(y)) -> I(-(-(x, y), I(1))) 622.70/291.55 -(I(x), O(y)) -> I(-(x, y)) 622.70/291.55 -(I(x), I(y)) -> O(-(x, y)) 622.70/291.55 not(true) -> false 622.70/291.55 not(false) -> true 622.70/291.55 and(x, true) -> x 622.70/291.55 and(x, false) -> false 622.70/291.55 if(true, x, y) -> x 622.70/291.55 if(false, x, y) -> y 622.70/291.55 ge(O(x), O(y)) -> ge(x, y) 622.70/291.55 ge(O(x), I(y)) -> not(ge(y, x)) 622.70/291.55 ge(I(x), O(y)) -> ge(x, y) 622.70/291.55 ge(I(x), I(y)) -> ge(x, y) 622.70/291.55 ge(x, 0) -> true 622.70/291.55 ge(0, O(x)) -> ge(0, x) 622.70/291.55 ge(0, I(x)) -> false 622.70/291.55 Log'(0) -> 0 622.70/291.55 Log'(I(x)) -> +(Log'(x), I(0))
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