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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307770
details
property
value
status
complete
benchmark
thiemann27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n126.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.532 seconds
cpu usage
903.312
user time
898.664
system time
4.64867
max virtual memory
3.8305604E7
max residence set size
5583396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
903.00/291.48 WORST_CASE(Omega(n^1), O(n^2)) 903.00/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 903.00/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 903.00/291.49 903.00/291.49 903.00/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 903.00/291.49 903.00/291.49 (0) CpxTRS 903.00/291.49 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 903.00/291.49 (2) CpxTRS 903.00/291.49 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 903.00/291.49 (4) CpxWeightedTrs 903.00/291.49 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 903.00/291.49 (6) CpxTypedWeightedTrs 903.00/291.49 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 903.00/291.49 (8) CpxTypedWeightedCompleteTrs 903.00/291.49 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 903.00/291.49 (10) CpxRNTS 903.00/291.49 (11) CompleteCoflocoProof [FINISHED, 219 ms] 903.00/291.49 (12) BOUNDS(1, n^2) 903.00/291.49 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 903.00/291.49 (14) CpxTRS 903.00/291.49 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 903.00/291.49 (16) CpxTRS 903.00/291.49 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 903.00/291.49 (18) typed CpxTrs 903.00/291.49 (19) OrderProof [LOWER BOUND(ID), 0 ms] 903.00/291.49 (20) typed CpxTrs 903.00/291.49 (21) RewriteLemmaProof [LOWER BOUND(ID), 305 ms] 903.00/291.49 (22) BEST 903.00/291.49 (23) proven lower bound 903.00/291.49 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 903.00/291.49 (25) BOUNDS(n^1, INF) 903.00/291.49 (26) typed CpxTrs 903.00/291.49 903.00/291.49 903.00/291.49 ---------------------------------------- 903.00/291.49 903.00/291.49 (0) 903.00/291.49 Obligation: 903.00/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 903.00/291.49 903.00/291.49 903.00/291.49 The TRS R consists of the following rules: 903.00/291.49 903.00/291.49 le(0, y) -> true 903.00/291.49 le(s(x), 0) -> false 903.00/291.49 le(s(x), s(y)) -> le(x, y) 903.00/291.49 int(x, y) -> if(le(x, y), x, y) 903.00/291.49 if(true, x, y) -> cons(x, int(s(x), y)) 903.00/291.49 if(false, x, y) -> nil 903.00/291.49 903.00/291.49 S is empty. 903.00/291.49 Rewrite Strategy: FULL 903.00/291.49 ---------------------------------------- 903.00/291.49 903.00/291.49 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 903.00/291.49 Converted rc-obligation to irc-obligation. 903.00/291.49 903.00/291.49 The duplicating contexts are: 903.00/291.49 int([], y) 903.00/291.49 int(x, []) 903.00/291.49 if(true, [], y) 903.00/291.49 903.00/291.49 903.00/291.49 The defined contexts are: 903.00/291.49 if([], x1, x2) 903.00/291.49 903.00/291.49 903.00/291.49 [] just represents basic- or constructor-terms in the following defined contexts: 903.00/291.49 if([], x1, x2) 903.00/291.49 903.00/291.49 903.00/291.49 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 903.00/291.49 ---------------------------------------- 903.00/291.49 903.00/291.49 (2) 903.00/291.49 Obligation: 903.00/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 903.00/291.49 903.00/291.49 903.00/291.49 The TRS R consists of the following rules: 903.00/291.49 903.00/291.49 le(0, y) -> true 903.00/291.49 le(s(x), 0) -> false 903.00/291.49 le(s(x), s(y)) -> le(x, y) 903.00/291.49 int(x, y) -> if(le(x, y), x, y) 903.00/291.49 if(true, x, y) -> cons(x, int(s(x), y)) 903.00/291.49 if(false, x, y) -> nil 903.00/291.49 903.00/291.49 S is empty. 903.00/291.49 Rewrite Strategy: INNERMOST 903.00/291.49 ---------------------------------------- 903.00/291.49 903.00/291.49 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 903.00/291.49 Transformed relative TRS to weighted TRS 903.00/291.49 ---------------------------------------- 903.00/291.49 903.00/291.49 (4) 903.00/291.49 Obligation:
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