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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308416
details
property
value
status
complete
benchmark
2.39.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.72647 seconds
cpu usage
20.8316
user time
19.2739
system time
1.55767
max virtual memory
1.901424E7
max residence set size
3782388.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
20.58/7.66 WORST_CASE(Omega(n^2), O(n^2)) 20.58/7.67 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 20.58/7.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.58/7.67 20.58/7.67 20.58/7.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 20.58/7.67 20.58/7.67 (0) CpxTRS 20.58/7.67 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 20.58/7.67 (2) CpxTRS 20.58/7.67 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 20.58/7.67 (4) CpxWeightedTrs 20.58/7.67 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 20.58/7.67 (6) CpxTypedWeightedTrs 20.58/7.67 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 20.58/7.67 (8) CpxTypedWeightedCompleteTrs 20.58/7.67 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 20.58/7.67 (10) CpxRNTS 20.58/7.67 (11) CompleteCoflocoProof [FINISHED, 232 ms] 20.58/7.67 (12) BOUNDS(1, n^2) 20.58/7.67 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 20.58/7.67 (14) CpxTRS 20.58/7.67 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 20.58/7.67 (16) typed CpxTrs 20.58/7.67 (17) OrderProof [LOWER BOUND(ID), 0 ms] 20.58/7.67 (18) typed CpxTrs 20.58/7.67 (19) RewriteLemmaProof [LOWER BOUND(ID), 311 ms] 20.58/7.67 (20) BEST 20.58/7.67 (21) proven lower bound 20.58/7.67 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 20.58/7.67 (23) BOUNDS(n^1, INF) 20.58/7.67 (24) typed CpxTrs 20.58/7.67 (25) RewriteLemmaProof [LOWER BOUND(ID), 30 ms] 20.58/7.67 (26) proven lower bound 20.58/7.67 (27) LowerBoundPropagationProof [FINISHED, 0 ms] 20.58/7.67 (28) BOUNDS(n^2, INF) 20.58/7.67 20.58/7.67 20.58/7.67 ---------------------------------------- 20.58/7.67 20.58/7.67 (0) 20.58/7.67 Obligation: 20.58/7.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 20.58/7.67 20.58/7.67 20.58/7.67 The TRS R consists of the following rules: 20.58/7.67 20.58/7.67 rev(nil) -> nil 20.58/7.67 rev(.(x, y)) -> ++(rev(y), .(x, nil)) 20.58/7.67 car(.(x, y)) -> x 20.58/7.67 cdr(.(x, y)) -> y 20.58/7.67 null(nil) -> true 20.58/7.67 null(.(x, y)) -> false 20.58/7.67 ++(nil, y) -> y 20.58/7.67 ++(.(x, y), z) -> .(x, ++(y, z)) 20.58/7.67 20.58/7.67 S is empty. 20.58/7.67 Rewrite Strategy: FULL 20.58/7.67 ---------------------------------------- 20.58/7.67 20.58/7.67 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 20.58/7.67 Converted rc-obligation to irc-obligation. 20.58/7.67 20.58/7.67 As the TRS is a non-duplicating overlay system, we have rc = irc. 20.58/7.67 ---------------------------------------- 20.58/7.67 20.58/7.67 (2) 20.58/7.67 Obligation: 20.58/7.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 20.58/7.67 20.58/7.67 20.58/7.67 The TRS R consists of the following rules: 20.58/7.67 20.58/7.67 rev(nil) -> nil 20.58/7.67 rev(.(x, y)) -> ++(rev(y), .(x, nil)) 20.58/7.67 car(.(x, y)) -> x 20.58/7.67 cdr(.(x, y)) -> y 20.58/7.67 null(nil) -> true 20.58/7.67 null(.(x, y)) -> false 20.58/7.67 ++(nil, y) -> y 20.58/7.67 ++(.(x, y), z) -> .(x, ++(y, z)) 20.58/7.67 20.58/7.67 S is empty. 20.58/7.67 Rewrite Strategy: INNERMOST 20.58/7.67 ---------------------------------------- 20.58/7.67 20.58/7.67 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 20.58/7.67 Transformed relative TRS to weighted TRS 20.58/7.67 ---------------------------------------- 20.58/7.67 20.58/7.67 (4) 20.58/7.67 Obligation: 20.58/7.67 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 20.58/7.67 20.58/7.67 20.58/7.67 The TRS R consists of the following rules: 20.58/7.67 20.58/7.67 rev(nil) -> nil [1] 20.58/7.67 rev(.(x, y)) -> ++(rev(y), .(x, nil)) [1] 20.58/7.67 car(.(x, y)) -> x [1]
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