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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313690
details
property
value
status
complete
benchmark
thiemann40_modified.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n125.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
16.4484 seconds
cpu usage
58.7228
user time
55.9515
system time
2.7713
max virtual memory
1.9326792E7
max residence set size
4177424.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
58.50/16.39 WORST_CASE(Omega(n^2), O(n^2)) 58.50/16.40 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 58.50/16.40 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 58.50/16.40 58.50/16.40 58.50/16.40 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 58.50/16.40 58.50/16.40 (0) CpxTRS 58.50/16.40 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 58.50/16.40 (2) CpxWeightedTrs 58.50/16.40 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 58.50/16.40 (4) CpxTypedWeightedTrs 58.50/16.40 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 58.50/16.40 (6) CpxTypedWeightedCompleteTrs 58.50/16.40 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 58.50/16.40 (8) CpxRNTS 58.50/16.40 (9) CompleteCoflocoProof [FINISHED, 390 ms] 58.50/16.40 (10) BOUNDS(1, n^2) 58.50/16.40 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 58.50/16.40 (12) CpxTRS 58.50/16.40 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 58.50/16.40 (14) typed CpxTrs 58.50/16.40 (15) OrderProof [LOWER BOUND(ID), 0 ms] 58.50/16.40 (16) typed CpxTrs 58.50/16.40 (17) RewriteLemmaProof [LOWER BOUND(ID), 255 ms] 58.50/16.40 (18) BEST 58.50/16.40 (19) proven lower bound 58.50/16.40 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 58.50/16.40 (21) BOUNDS(n^1, INF) 58.50/16.40 (22) typed CpxTrs 58.50/16.40 (23) RewriteLemmaProof [LOWER BOUND(ID), 51 ms] 58.50/16.40 (24) proven lower bound 58.50/16.40 (25) LowerBoundPropagationProof [FINISHED, 0 ms] 58.50/16.40 (26) BOUNDS(n^2, INF) 58.50/16.40 58.50/16.40 58.50/16.40 ---------------------------------------- 58.50/16.40 58.50/16.40 (0) 58.50/16.40 Obligation: 58.50/16.40 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 58.50/16.40 58.50/16.40 58.50/16.40 The TRS R consists of the following rules: 58.50/16.40 58.50/16.40 nonZero(0) -> false 58.50/16.40 nonZero(s(x)) -> true 58.50/16.40 p(s(0)) -> 0 58.50/16.40 p(s(s(x))) -> s(p(s(x))) 58.50/16.40 id_inc(x) -> x 58.50/16.40 id_inc(x) -> s(x) 58.50/16.40 random(x) -> rand(x, 0) 58.50/16.40 rand(x, y) -> if(nonZero(x), x, y) 58.50/16.40 if(false, x, y) -> y 58.50/16.40 if(true, x, y) -> rand(p(x), id_inc(y)) 58.50/16.40 58.50/16.40 S is empty. 58.50/16.40 Rewrite Strategy: INNERMOST 58.50/16.40 ---------------------------------------- 58.50/16.40 58.50/16.40 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 58.50/16.40 Transformed relative TRS to weighted TRS 58.50/16.40 ---------------------------------------- 58.50/16.40 58.50/16.40 (2) 58.50/16.40 Obligation: 58.50/16.40 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 58.50/16.40 58.50/16.40 58.50/16.40 The TRS R consists of the following rules: 58.50/16.40 58.50/16.40 nonZero(0) -> false [1] 58.50/16.40 nonZero(s(x)) -> true [1] 58.50/16.40 p(s(0)) -> 0 [1] 58.50/16.40 p(s(s(x))) -> s(p(s(x))) [1] 58.50/16.40 id_inc(x) -> x [1] 58.50/16.40 id_inc(x) -> s(x) [1] 58.50/16.40 random(x) -> rand(x, 0) [1] 58.50/16.40 rand(x, y) -> if(nonZero(x), x, y) [1] 58.50/16.40 if(false, x, y) -> y [1] 58.50/16.40 if(true, x, y) -> rand(p(x), id_inc(y)) [1] 58.50/16.40 58.50/16.40 Rewrite Strategy: INNERMOST 58.50/16.40 ---------------------------------------- 58.50/16.40 58.50/16.40 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 58.50/16.40 Infered types. 58.50/16.40 ---------------------------------------- 58.50/16.40 58.50/16.40 (4) 58.50/16.40 Obligation: 58.50/16.40 Runtime Complexity Weighted TRS with Types. 58.50/16.40 The TRS R consists of the following rules: 58.50/16.40 58.50/16.40 nonZero(0) -> false [1] 58.50/16.40 nonZero(s(x)) -> true [1] 58.50/16.40 p(s(0)) -> 0 [1] 58.50/16.40 p(s(s(x))) -> s(p(s(x))) [1] 58.50/16.40 id_inc(x) -> x [1] 58.50/16.40 id_inc(x) -> s(x) [1]
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