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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307623
details
property
value
status
complete
benchmark
intersect.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n169.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.578 seconds
cpu usage
378.871
user time
373.56
system time
5.31106
max virtual memory
1.9173536E7
max residence set size
7423076.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
378.69/291.52 WORST_CASE(Omega(n^1), O(n^2)) 378.69/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 378.69/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 378.69/291.53 378.69/291.53 378.69/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 378.69/291.53 378.69/291.53 (0) CpxTRS 378.69/291.53 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 378.69/291.53 (2) CpxTRS 378.69/291.53 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (4) CpxTRS 378.69/291.53 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 378.69/291.53 (6) CdtProblem 378.69/291.53 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (8) CdtProblem 378.69/291.53 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (10) CdtProblem 378.69/291.53 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 102 ms] 378.69/291.53 (12) CdtProblem 378.69/291.53 (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (14) CdtProblem 378.69/291.53 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 124 ms] 378.69/291.53 (16) CdtProblem 378.69/291.53 (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (18) CdtProblem 378.69/291.53 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 84 ms] 378.69/291.53 (20) CdtProblem 378.69/291.53 (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (22) BOUNDS(1, 1) 378.69/291.53 (23) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (24) CpxTRS 378.69/291.53 (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 378.69/291.53 (26) typed CpxTrs 378.69/291.53 (27) OrderProof [LOWER BOUND(ID), 0 ms] 378.69/291.53 (28) typed CpxTrs 378.69/291.53 (29) RewriteLemmaProof [LOWER BOUND(ID), 314 ms] 378.69/291.53 (30) BEST 378.69/291.53 (31) proven lower bound 378.69/291.53 (32) LowerBoundPropagationProof [FINISHED, 0 ms] 378.69/291.53 (33) BOUNDS(n^1, INF) 378.69/291.53 (34) typed CpxTrs 378.69/291.53 (35) RewriteLemmaProof [LOWER BOUND(ID), 18 ms] 378.69/291.53 (36) typed CpxTrs 378.69/291.53 378.69/291.53 378.69/291.53 ---------------------------------------- 378.69/291.53 378.69/291.53 (0) 378.69/291.53 Obligation: 378.69/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 378.69/291.53 378.69/291.53 378.69/291.53 The TRS R consists of the following rules: 378.69/291.53 378.69/291.53 if(true, x, y) -> x 378.69/291.53 if(false, x, y) -> y 378.69/291.53 eq(0, 0) -> true 378.69/291.53 eq(0, s(x)) -> false 378.69/291.53 eq(s(x), 0) -> false 378.69/291.53 eq(s(x), s(y)) -> eq(x, y) 378.69/291.53 app(nil, l) -> l 378.69/291.53 app(cons(x, l1), l2) -> cons(x, app(l1, l2)) 378.69/291.53 app(app(l1, l2), l3) -> app(l1, app(l2, l3)) 378.69/291.53 mem(x, nil) -> false 378.69/291.53 mem(x, cons(y, l)) -> ifmem(eq(x, y), x, l) 378.69/291.53 ifmem(true, x, l) -> true 378.69/291.53 ifmem(false, x, l) -> mem(x, l) 378.69/291.53 inter(x, nil) -> nil 378.69/291.53 inter(nil, x) -> nil 378.69/291.53 inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) 378.69/291.53 inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) 378.69/291.53 inter(cons(x, l1), l2) -> ifinter(mem(x, l2), x, l1, l2) 378.69/291.53 inter(l1, cons(x, l2)) -> ifinter(mem(x, l1), x, l2, l1) 378.69/291.53 ifinter(true, x, l1, l2) -> cons(x, inter(l1, l2)) 378.69/291.53 ifinter(false, x, l1, l2) -> inter(l1, l2) 378.69/291.53 378.69/291.53 S is empty. 378.69/291.53 Rewrite Strategy: FULL 378.69/291.53 ---------------------------------------- 378.69/291.53 378.69/291.53 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 378.69/291.53 The following defined symbols can occur below the 0th argument of ifinter: ifmem, eq, mem 378.69/291.53 The following defined symbols can occur below the 0th argument of ifmem: eq 378.69/291.53 378.69/291.53 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 378.69/291.53 app(app(l1, l2), l3) -> app(l1, app(l2, l3)) 378.69/291.53 inter(app(l1, l2), l3) -> app(inter(l1, l3), inter(l2, l3)) 378.69/291.53 inter(l1, app(l2, l3)) -> app(inter(l1, l2), inter(l1, l3)) 378.69/291.53 378.69/291.53 ---------------------------------------- 378.69/291.53 378.69/291.53 (2) 378.69/291.53 Obligation: 378.69/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 378.69/291.53 378.69/291.53 378.69/291.53 The TRS R consists of the following rules: 378.69/291.53 378.69/291.53 if(true, x, y) -> x
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