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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307845
details
property
value
status
complete
benchmark
while.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n019.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.616 seconds
cpu usage
883.817
user time
879.462
system time
4.35529
max virtual memory
3.8325536E7
max residence set size
5343736.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
883.58/291.55 WORST_CASE(Omega(n^1), O(n^2)) 883.58/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 883.58/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 883.58/291.57 883.58/291.57 883.58/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 883.58/291.57 883.58/291.57 (0) CpxTRS 883.58/291.57 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 883.58/291.57 (2) CpxTRS 883.58/291.57 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 883.58/291.57 (4) CpxWeightedTrs 883.58/291.57 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 883.58/291.57 (6) CpxTypedWeightedTrs 883.58/291.57 (7) CompletionProof [UPPER BOUND(ID), 1 ms] 883.58/291.57 (8) CpxTypedWeightedCompleteTrs 883.58/291.57 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 883.58/291.57 (10) CpxRNTS 883.58/291.57 (11) CompleteCoflocoProof [FINISHED, 238 ms] 883.58/291.57 (12) BOUNDS(1, n^2) 883.58/291.57 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 883.58/291.57 (14) CpxTRS 883.58/291.57 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 883.58/291.57 (16) typed CpxTrs 883.58/291.57 (17) OrderProof [LOWER BOUND(ID), 0 ms] 883.58/291.57 (18) typed CpxTrs 883.58/291.57 (19) RewriteLemmaProof [LOWER BOUND(ID), 273 ms] 883.58/291.57 (20) BEST 883.58/291.57 (21) proven lower bound 883.58/291.57 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 883.58/291.57 (23) BOUNDS(n^1, INF) 883.58/291.57 (24) typed CpxTrs 883.58/291.57 883.58/291.57 883.58/291.57 ---------------------------------------- 883.58/291.57 883.58/291.57 (0) 883.58/291.57 Obligation: 883.58/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 883.58/291.57 883.58/291.57 883.58/291.57 The TRS R consists of the following rules: 883.58/291.57 883.58/291.57 f(t, x, y) -> f(g(x, y), x, s(y)) 883.58/291.57 g(s(x), 0) -> t 883.58/291.57 g(s(x), s(y)) -> g(x, y) 883.58/291.57 883.58/291.57 S is empty. 883.58/291.57 Rewrite Strategy: FULL 883.58/291.57 ---------------------------------------- 883.58/291.57 883.58/291.57 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 883.58/291.57 Converted rc-obligation to irc-obligation. 883.58/291.57 883.58/291.57 The duplicating contexts are: 883.58/291.57 f(t, [], y) 883.58/291.57 f(t, x, []) 883.58/291.57 883.58/291.57 883.58/291.57 The defined contexts are: 883.58/291.57 f([], x1, s(x2)) 883.58/291.57 883.58/291.57 883.58/291.57 [] just represents basic- or constructor-terms in the following defined contexts: 883.58/291.57 f([], x1, s(x2)) 883.58/291.57 883.58/291.57 883.58/291.57 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 883.58/291.57 ---------------------------------------- 883.58/291.57 883.58/291.57 (2) 883.58/291.57 Obligation: 883.58/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 883.58/291.57 883.58/291.57 883.58/291.57 The TRS R consists of the following rules: 883.58/291.57 883.58/291.57 f(t, x, y) -> f(g(x, y), x, s(y)) 883.58/291.57 g(s(x), 0) -> t 883.58/291.57 g(s(x), s(y)) -> g(x, y) 883.58/291.57 883.58/291.57 S is empty. 883.58/291.57 Rewrite Strategy: INNERMOST 883.58/291.57 ---------------------------------------- 883.58/291.57 883.58/291.57 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 883.58/291.57 Transformed relative TRS to weighted TRS 883.58/291.57 ---------------------------------------- 883.58/291.57 883.58/291.57 (4) 883.58/291.57 Obligation: 883.58/291.57 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 883.58/291.57 883.58/291.57 883.58/291.57 The TRS R consists of the following rules: 883.58/291.57 883.58/291.57 f(t, x, y) -> f(g(x, y), x, s(y)) [1] 883.58/291.57 g(s(x), 0) -> t [1] 883.58/291.57 g(s(x), s(y)) -> g(x, y) [1] 883.58/291.57
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