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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307675
details
property
value
status
complete
benchmark
IJCAR_12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.1886 seconds
cpu usage
30.9318
user time
29.1193
system time
1.81245
max virtual memory
3.7642632E7
max residence set size
3934004.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
30.72/10.13 WORST_CASE(Omega(n^2), O(n^2)) 30.72/10.14 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.72/10.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.72/10.14 30.72/10.14 30.72/10.14 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 30.72/10.14 30.72/10.14 (0) CpxTRS 30.72/10.14 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 30.72/10.14 (2) CpxTRS 30.72/10.14 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (4) CpxTRS 30.72/10.14 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 4 ms] 30.72/10.14 (6) CdtProblem 30.72/10.14 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (8) CdtProblem 30.72/10.14 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (10) CdtProblem 30.72/10.14 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 72 ms] 30.72/10.14 (12) CdtProblem 30.72/10.14 (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (14) CdtProblem 30.72/10.14 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 45 ms] 30.72/10.14 (16) CdtProblem 30.72/10.14 (17) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (18) BOUNDS(1, 1) 30.72/10.14 (19) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (20) CpxTRS 30.72/10.14 (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 30.72/10.14 (22) typed CpxTrs 30.72/10.14 (23) OrderProof [LOWER BOUND(ID), 0 ms] 30.72/10.14 (24) typed CpxTrs 30.72/10.14 (25) RewriteLemmaProof [LOWER BOUND(ID), 297 ms] 30.72/10.14 (26) BEST 30.72/10.14 (27) proven lower bound 30.72/10.14 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 30.72/10.14 (29) BOUNDS(n^1, INF) 30.72/10.14 (30) typed CpxTrs 30.72/10.14 (31) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] 30.72/10.14 (32) BEST 30.72/10.14 (33) proven lower bound 30.72/10.14 (34) LowerBoundPropagationProof [FINISHED, 0 ms] 30.72/10.14 (35) BOUNDS(n^2, INF) 30.72/10.14 (36) typed CpxTrs 30.72/10.14 (37) RewriteLemmaProof [LOWER BOUND(ID), 28 ms] 30.72/10.14 (38) typed CpxTrs 30.72/10.14 30.72/10.14 30.72/10.14 ---------------------------------------- 30.72/10.14 30.72/10.14 (0) 30.72/10.14 Obligation: 30.72/10.14 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 30.72/10.14 30.72/10.14 30.72/10.14 The TRS R consists of the following rules: 30.72/10.14 30.72/10.14 plus(x, 0) -> x 30.72/10.14 plus(0, y) -> y 30.72/10.14 plus(s(x), y) -> s(plus(x, y)) 30.72/10.14 times(0, y) -> 0 30.72/10.14 times(s(0), y) -> y 30.72/10.14 times(s(x), y) -> plus(y, times(x, y)) 30.72/10.14 div(0, y) -> 0 30.72/10.14 div(x, y) -> quot(x, y, y) 30.72/10.14 quot(0, s(y), z) -> 0 30.72/10.14 quot(s(x), s(y), z) -> quot(x, y, z) 30.72/10.14 quot(x, 0, s(z)) -> s(div(x, s(z))) 30.72/10.14 div(div(x, y), z) -> div(x, times(y, z)) 30.72/10.14 30.72/10.14 S is empty. 30.72/10.14 Rewrite Strategy: FULL 30.72/10.14 ---------------------------------------- 30.72/10.14 30.72/10.14 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 30.72/10.14 The following defined symbols can occur below the 1th argument of plus: plus, times 30.72/10.14 30.72/10.14 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 30.72/10.14 div(div(x, y), z) -> div(x, times(y, z)) 30.72/10.14 30.72/10.14 ---------------------------------------- 30.72/10.14 30.72/10.14 (2) 30.72/10.14 Obligation: 30.72/10.14 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 30.72/10.14 30.72/10.14 30.72/10.14 The TRS R consists of the following rules: 30.72/10.14 30.72/10.14 plus(x, 0) -> x 30.72/10.14 plus(0, y) -> y 30.72/10.14 plus(s(x), y) -> s(plus(x, y)) 30.72/10.14 times(0, y) -> 0 30.72/10.14 times(s(0), y) -> y 30.72/10.14 times(s(x), y) -> plus(y, times(x, y)) 30.72/10.14 div(0, y) -> 0 30.72/10.14 div(x, y) -> quot(x, y, y) 30.72/10.14 quot(0, s(y), z) -> 0 30.72/10.14 quot(s(x), s(y), z) -> quot(x, y, z) 30.72/10.14 quot(x, 0, s(z)) -> s(div(x, s(z)))
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