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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308477
details
property
value
status
complete
benchmark
secret1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.18584 seconds
cpu usage
16.8794
user time
15.9829
system time
0.896477
max virtual memory
3.683748E7
max residence set size
2879788.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
16.70/5.10 WORST_CASE(Omega(n^1), O(n^1)) 16.70/5.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.70/5.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.70/5.11 16.70/5.11 16.70/5.11 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.70/5.11 16.70/5.11 (0) CpxTRS 16.70/5.11 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 16.70/5.11 (2) CpxTRS 16.70/5.11 (3) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] 16.70/5.11 (4) CpxRelTRS 16.70/5.11 (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (6) CpxRelTRS 16.70/5.11 (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 16.70/5.11 (8) CdtProblem 16.70/5.11 (9) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (10) CdtProblem 16.70/5.11 (11) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (12) CdtProblem 16.70/5.11 (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (14) CdtProblem 16.70/5.11 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 66 ms] 16.70/5.11 (16) CdtProblem 16.70/5.11 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 21 ms] 16.70/5.11 (18) CdtProblem 16.70/5.11 (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (20) BOUNDS(1, 1) 16.70/5.11 (21) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (22) CpxTRS 16.70/5.11 (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 16.70/5.11 (24) typed CpxTrs 16.70/5.11 (25) OrderProof [LOWER BOUND(ID), 0 ms] 16.70/5.11 (26) typed CpxTrs 16.70/5.11 (27) RewriteLemmaProof [LOWER BOUND(ID), 574 ms] 16.70/5.11 (28) BEST 16.70/5.11 (29) proven lower bound 16.70/5.11 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 16.70/5.11 (31) BOUNDS(n^1, INF) 16.70/5.11 (32) typed CpxTrs 16.70/5.11 16.70/5.11 16.70/5.11 ---------------------------------------- 16.70/5.11 16.70/5.11 (0) 16.70/5.11 Obligation: 16.70/5.11 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.70/5.11 16.70/5.11 16.70/5.11 The TRS R consists of the following rules: 16.70/5.11 16.70/5.11 D(t) -> s(h) 16.70/5.11 D(constant) -> h 16.70/5.11 D(b(x, y)) -> b(D(x), D(y)) 16.70/5.11 D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) 16.70/5.11 D(m(x, y)) -> m(D(x), D(y)) 16.70/5.11 D(opp(x)) -> opp(D(x)) 16.70/5.11 D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) 16.70/5.11 D(ln(x)) -> div(D(x), x) 16.70/5.11 D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1))), D(x)), c(c(pow(x, y), ln(x)), D(y))) 16.70/5.11 b(h, x) -> x 16.70/5.11 b(x, h) -> x 16.70/5.11 b(s(x), s(y)) -> s(s(b(x, y))) 16.70/5.11 b(b(x, y), z) -> b(x, b(y, z)) 16.70/5.11 16.70/5.11 S is empty. 16.70/5.11 Rewrite Strategy: FULL 16.70/5.11 ---------------------------------------- 16.70/5.11 16.70/5.11 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 16.70/5.11 The following defined symbols can occur below the 0th argument of b: b, D 16.70/5.11 The following defined symbols can occur below the 1th argument of b: b, D 16.70/5.11 16.70/5.11 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 16.70/5.11 D(b(x, y)) -> b(D(x), D(y)) 16.70/5.11 16.70/5.11 ---------------------------------------- 16.70/5.11 16.70/5.11 (2) 16.70/5.11 Obligation: 16.70/5.11 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 16.70/5.11 16.70/5.11 16.70/5.11 The TRS R consists of the following rules: 16.70/5.11 16.70/5.11 D(t) -> s(h) 16.70/5.11 D(constant) -> h 16.70/5.11 D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) 16.70/5.11 D(m(x, y)) -> m(D(x), D(y)) 16.70/5.11 D(opp(x)) -> opp(D(x)) 16.70/5.11 D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) 16.70/5.11 D(ln(x)) -> div(D(x), x) 16.70/5.11 D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1))), D(x)), c(c(pow(x, y), ln(x)), D(y))) 16.70/5.11 b(h, x) -> x 16.70/5.11 b(x, h) -> x 16.70/5.11 b(s(x), s(y)) -> s(s(b(x, y))) 16.70/5.11 b(b(x, y), z) -> b(x, b(y, z)) 16.70/5.11 16.70/5.11 S is empty. 16.70/5.11 Rewrite Strategy: FULL
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