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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313373
details
property
value
status
complete
benchmark
duplicates.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.778 seconds
cpu usage
404.939
user time
396.298
system time
8.6414
max virtual memory
3.84437E7
max residence set size
1.077302E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
404.78/291.70 WORST_CASE(Omega(n^1), O(n^2)) 404.78/291.71 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 404.78/291.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 404.78/291.71 404.78/291.71 404.78/291.71 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 404.78/291.71 404.78/291.71 (0) CpxRelTRS 404.78/291.71 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 191 ms] 404.78/291.71 (2) CpxRelTRS 404.78/291.71 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 404.78/291.71 (4) CpxWeightedTrs 404.78/291.71 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 404.78/291.71 (6) CpxTypedWeightedTrs 404.78/291.71 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 404.78/291.71 (8) CpxTypedWeightedCompleteTrs 404.78/291.71 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 20 ms] 404.78/291.71 (10) CpxRNTS 404.78/291.71 (11) CompleteCoflocoProof [FINISHED, 3902 ms] 404.78/291.71 (12) BOUNDS(1, n^2) 404.78/291.71 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 404.78/291.71 (14) CpxRelTRS 404.78/291.71 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 404.78/291.71 (16) typed CpxTrs 404.78/291.71 (17) OrderProof [LOWER BOUND(ID), 0 ms] 404.78/291.71 (18) typed CpxTrs 404.78/291.71 (19) RewriteLemmaProof [LOWER BOUND(ID), 25.6 s] 404.78/291.71 (20) typed CpxTrs 404.78/291.71 (21) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] 404.78/291.71 (22) BEST 404.78/291.71 (23) proven lower bound 404.78/291.71 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 404.78/291.71 (25) BOUNDS(n^1, INF) 404.78/291.71 (26) typed CpxTrs 404.78/291.71 (27) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] 404.78/291.71 (28) typed CpxTrs 404.78/291.71 404.78/291.71 404.78/291.71 ---------------------------------------- 404.78/291.71 404.78/291.71 (0) 404.78/291.71 Obligation: 404.78/291.71 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 404.78/291.71 404.78/291.71 404.78/291.71 The TRS R consists of the following rules: 404.78/291.71 404.78/291.71 #equal(@x, @y) -> #eq(@x, @y) 404.78/291.71 and(@x, @y) -> #and(@x, @y) 404.78/291.71 eq(@l1, @l2) -> eq#1(@l1, @l2) 404.78/291.71 eq#1(::(@x, @xs), @l2) -> eq#3(@l2, @x, @xs) 404.78/291.71 eq#1(nil, @l2) -> eq#2(@l2) 404.78/291.71 eq#2(::(@y, @ys)) -> #false 404.78/291.71 eq#2(nil) -> #true 404.78/291.71 eq#3(::(@y, @ys), @x, @xs) -> and(#equal(@x, @y), eq(@xs, @ys)) 404.78/291.71 eq#3(nil, @x, @xs) -> #false 404.78/291.71 nub(@l) -> nub#1(@l) 404.78/291.71 nub#1(::(@x, @xs)) -> ::(@x, nub(remove(@x, @xs))) 404.78/291.71 nub#1(nil) -> nil 404.78/291.71 remove(@x, @l) -> remove#1(@l, @x) 404.78/291.71 remove#1(::(@y, @ys), @x) -> remove#2(eq(@x, @y), @x, @y, @ys) 404.78/291.71 remove#1(nil, @x) -> nil 404.78/291.71 remove#2(#false, @x, @y, @ys) -> ::(@y, remove(@x, @ys)) 404.78/291.71 remove#2(#true, @x, @y, @ys) -> remove(@x, @ys) 404.78/291.71 404.78/291.71 The (relative) TRS S consists of the following rules: 404.78/291.71 404.78/291.71 #and(#false, #false) -> #false 404.78/291.71 #and(#false, #true) -> #false 404.78/291.71 #and(#true, #false) -> #false 404.78/291.71 #and(#true, #true) -> #true 404.78/291.71 #eq(#0, #0) -> #true 404.78/291.71 #eq(#0, #neg(@y)) -> #false 404.78/291.71 #eq(#0, #pos(@y)) -> #false 404.78/291.71 #eq(#0, #s(@y)) -> #false 404.78/291.71 #eq(#neg(@x), #0) -> #false 404.78/291.71 #eq(#neg(@x), #neg(@y)) -> #eq(@x, @y) 404.78/291.71 #eq(#neg(@x), #pos(@y)) -> #false 404.78/291.71 #eq(#pos(@x), #0) -> #false 404.78/291.71 #eq(#pos(@x), #neg(@y)) -> #false 404.78/291.71 #eq(#pos(@x), #pos(@y)) -> #eq(@x, @y) 404.78/291.71 #eq(#s(@x), #0) -> #false 404.78/291.71 #eq(#s(@x), #s(@y)) -> #eq(@x, @y) 404.78/291.71 #eq(::(@x_1, @x_2), ::(@y_1, @y_2)) -> #and(#eq(@x_1, @y_1), #eq(@x_2, @y_2)) 404.78/291.71 #eq(::(@x_1, @x_2), nil) -> #false 404.78/291.71 #eq(nil, ::(@y_1, @y_2)) -> #false 404.78/291.71 #eq(nil, nil) -> #true 404.78/291.71 404.78/291.71 Rewrite Strategy: INNERMOST 404.78/291.71 ---------------------------------------- 404.78/291.71 404.78/291.71 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 404.78/291.71 proved termination of relative rules 404.78/291.71 ---------------------------------------- 404.78/291.71 404.78/291.71 (2) 404.78/291.71 Obligation: 404.78/291.71 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 404.78/291.71 404.78/291.71
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
