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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313859
details
property
value
status
complete
benchmark
inssort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n031.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.58 seconds
cpu usage
335.194
user time
331.822
system time
3.37207
max virtual memory
1.9212092E7
max residence set size
5548332.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
335.04/291.51 WORST_CASE(Omega(n^1), O(n^2)) 335.08/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 335.08/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 335.08/291.52 335.08/291.52 335.08/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 335.08/291.52 335.08/291.52 (0) CpxRelTRS 335.08/291.52 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 175 ms] 335.08/291.52 (2) CpxRelTRS 335.08/291.52 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 335.08/291.52 (4) CpxWeightedTrs 335.08/291.52 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 335.08/291.52 (6) CpxWeightedTrs 335.08/291.52 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] 335.08/291.52 (8) CpxTypedWeightedTrs 335.08/291.52 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (10) CpxTypedWeightedCompleteTrs 335.08/291.52 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 335.08/291.52 (12) CpxTypedWeightedCompleteTrs 335.08/291.52 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (14) CpxRNTS 335.08/291.52 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 4 ms] 335.08/291.52 (16) CpxRNTS 335.08/291.52 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 335.08/291.52 (18) CpxRNTS 335.08/291.52 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (20) CpxRNTS 335.08/291.52 (21) IntTrsBoundProof [UPPER BOUND(ID), 538 ms] 335.08/291.52 (22) CpxRNTS 335.08/291.52 (23) IntTrsBoundProof [UPPER BOUND(ID), 98 ms] 335.08/291.52 (24) CpxRNTS 335.08/291.52 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (26) CpxRNTS 335.08/291.52 (27) IntTrsBoundProof [UPPER BOUND(ID), 1683 ms] 335.08/291.52 (28) CpxRNTS 335.08/291.52 (29) IntTrsBoundProof [UPPER BOUND(ID), 451 ms] 335.08/291.52 (30) CpxRNTS 335.08/291.52 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (32) CpxRNTS 335.08/291.52 (33) IntTrsBoundProof [UPPER BOUND(ID), 381 ms] 335.08/291.52 (34) CpxRNTS 335.08/291.52 (35) IntTrsBoundProof [UPPER BOUND(ID), 206 ms] 335.08/291.52 (36) CpxRNTS 335.08/291.52 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (38) CpxRNTS 335.08/291.52 (39) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] 335.08/291.52 (40) CpxRNTS 335.08/291.52 (41) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 335.08/291.52 (42) CpxRNTS 335.08/291.52 (43) FinalProof [FINISHED, 0 ms] 335.08/291.52 (44) BOUNDS(1, n^2) 335.08/291.52 (45) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 335.08/291.52 (46) TRS for Loop Detection 335.08/291.52 (47) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 335.08/291.52 (48) BEST 335.08/291.52 (49) proven lower bound 335.08/291.52 (50) LowerBoundPropagationProof [FINISHED, 0 ms] 335.08/291.52 (51) BOUNDS(n^1, INF) 335.08/291.52 (52) TRS for Loop Detection 335.08/291.52 335.08/291.52 335.08/291.52 ---------------------------------------- 335.08/291.52 335.08/291.52 (0) 335.08/291.52 Obligation: 335.08/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 335.08/291.52 335.08/291.52 335.08/291.52 The TRS R consists of the following rules: 335.08/291.52 335.08/291.52 isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) 335.08/291.52 isort(Nil, r) -> Nil 335.08/291.52 insert(S(x), r) -> insert[Ite](<(S(x), x), S(x), r) 335.08/291.52 inssort(xs) -> isort(xs, Nil) 335.08/291.52 335.08/291.52 The (relative) TRS S consists of the following rules: 335.08/291.52 335.08/291.52 <(S(x), S(y)) -> <(x, y) 335.08/291.52 <(0, S(y)) -> True 335.08/291.52 <(x, 0) -> False 335.08/291.52 insert[Ite](False, x', Cons(x, xs)) -> Cons(x, insert(x', xs)) 335.08/291.52 insert[Ite](True, x, r) -> Cons(x, r) 335.08/291.52 335.08/291.52 Rewrite Strategy: INNERMOST 335.08/291.52 ---------------------------------------- 335.08/291.52 335.08/291.52 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 335.08/291.52 proved termination of relative rules 335.08/291.52 ---------------------------------------- 335.08/291.52 335.08/291.52 (2) 335.08/291.52 Obligation: 335.08/291.52 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 335.08/291.52 335.08/291.52 335.08/291.52 The TRS R consists of the following rules: 335.08/291.52 335.08/291.52 isort(Cons(x, xs), r) -> isort(xs, insert(x, r)) 335.08/291.52 isort(Nil, r) -> Nil
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