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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313857
details
property
value
status
complete
benchmark
inssort_better.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.547 seconds
cpu usage
349.735
user time
346.595
system time
3.14022
max virtual memory
1.934524E7
max residence set size
5610632.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
349.56/291.49 WORST_CASE(Omega(n^1), O(n^2)) 349.56/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 349.56/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 349.56/291.51 349.56/291.51 349.56/291.51 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 349.56/291.51 349.56/291.51 (0) CpxRelTRS 349.56/291.51 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 172 ms] 349.56/291.51 (2) CpxRelTRS 349.56/291.51 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (4) CpxWeightedTrs 349.56/291.51 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (6) CpxWeightedTrs 349.56/291.51 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] 349.56/291.51 (8) CpxTypedWeightedTrs 349.56/291.51 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (10) CpxTypedWeightedCompleteTrs 349.56/291.51 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (12) CpxTypedWeightedCompleteTrs 349.56/291.51 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (14) CpxRNTS 349.56/291.51 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (16) CpxRNTS 349.56/291.51 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (18) CpxRNTS 349.56/291.51 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (20) CpxRNTS 349.56/291.51 (21) IntTrsBoundProof [UPPER BOUND(ID), 486 ms] 349.56/291.51 (22) CpxRNTS 349.56/291.51 (23) IntTrsBoundProof [UPPER BOUND(ID), 89 ms] 349.56/291.51 (24) CpxRNTS 349.56/291.51 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (26) CpxRNTS 349.56/291.51 (27) IntTrsBoundProof [UPPER BOUND(ID), 1409 ms] 349.56/291.51 (28) CpxRNTS 349.56/291.51 (29) IntTrsBoundProof [UPPER BOUND(ID), 364 ms] 349.56/291.51 (30) CpxRNTS 349.56/291.51 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (32) CpxRNTS 349.56/291.51 (33) IntTrsBoundProof [UPPER BOUND(ID), 511 ms] 349.56/291.51 (34) CpxRNTS 349.56/291.51 (35) IntTrsBoundProof [UPPER BOUND(ID), 286 ms] 349.56/291.51 (36) CpxRNTS 349.56/291.51 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (38) CpxRNTS 349.56/291.51 (39) IntTrsBoundProof [UPPER BOUND(ID), 178 ms] 349.56/291.51 (40) CpxRNTS 349.56/291.51 (41) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 349.56/291.51 (42) CpxRNTS 349.56/291.51 (43) FinalProof [FINISHED, 0 ms] 349.56/291.51 (44) BOUNDS(1, n^2) 349.56/291.51 (45) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (46) CpxRelTRS 349.56/291.51 (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 349.56/291.51 (48) typed CpxTrs 349.56/291.51 (49) OrderProof [LOWER BOUND(ID), 0 ms] 349.56/291.51 (50) typed CpxTrs 349.56/291.51 (51) RewriteLemmaProof [LOWER BOUND(ID), 302 ms] 349.56/291.51 (52) typed CpxTrs 349.56/291.51 (53) RewriteLemmaProof [LOWER BOUND(ID), 9662 ms] 349.56/291.51 (54) BEST 349.56/291.51 (55) proven lower bound 349.56/291.51 (56) LowerBoundPropagationProof [FINISHED, 0 ms] 349.56/291.51 (57) BOUNDS(n^1, INF) 349.56/291.51 (58) typed CpxTrs 349.56/291.51 349.56/291.51 349.56/291.51 ---------------------------------------- 349.56/291.51 349.56/291.51 (0) 349.56/291.51 Obligation: 349.56/291.51 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 349.56/291.51 349.56/291.51 349.56/291.51 The TRS R consists of the following rules: 349.56/291.51 349.56/291.51 isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) 349.56/291.51 insert(x', Cons(x, xs)) -> insert[Ite][False][Ite](<(x', x), x', Cons(x, xs)) 349.56/291.51 isort(Nil, r) -> r 349.56/291.51 insert(x, Nil) -> Cons(x, Nil) 349.56/291.51 inssort(xs) -> isort(xs, Nil) 349.56/291.51 349.56/291.51 The (relative) TRS S consists of the following rules: 349.56/291.51 349.56/291.51 <(S(x), S(y)) -> <(x, y) 349.56/291.51 <(0, S(y)) -> True 349.56/291.51 <(x, 0) -> False 349.56/291.51 insert[Ite][False][Ite](False, x', Cons(x, xs)) -> Cons(x, insert(x', xs)) 349.56/291.51 insert[Ite][False][Ite](True, x, r) -> Cons(x, r) 349.56/291.51 349.56/291.51 Rewrite Strategy: INNERMOST 349.56/291.51 ---------------------------------------- 349.56/291.51 349.56/291.51 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 349.56/291.51 proved termination of relative rules 349.56/291.51 ---------------------------------------- 349.56/291.51 349.56/291.51 (2) 349.56/291.51 Obligation:
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