details

property	value
status	complete
benchmark	flatten.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.755 seconds
cpu usage	369.097
user time	363.185
system time	5.91118
max virtual memory	1.9526816E7
max residence set size	7226160.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 188 ms] (2) CpxRelTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 114 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 72 ms] (20) CdtProblem (21) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 522 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 515 ms] (26) CdtProblem (27) CdtKnowledgeProof [FINISHED, 0 ms] (28) BOUNDS(1, 1) (29) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (30) TRS for Loop Detection (31) DecreasingLoopProof [LOWER BOUND(ID), 39 ms] (32) BEST (33) proven lower bound (34) LowerBoundPropagationProof [FINISHED, 0 ms] (35) BOUNDS(n^1, INF) (36) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: #less(@x, @y) -> #cklt(#compare(@x, @y)) append(@l1, @l2) -> append#1(@l1, @l2) append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) append#1(nil, @l2) -> @l2 flatten(@t) -> flatten#1(@t) flatten#1(leaf) -> nil flatten#1(node(@l, @t1, @t2)) -> append(@l, append(flatten(@t1), flatten(@t2))) flattensort(@t) -> insertionsort(flatten(@t)) insert(@x, @l) -> insert#1(@l, @x) insert#1(::(@y, @ys), @x) -> insert#2(#less(@y, @x), @x, @y, @ys) insert#1(nil, @x) -> ::(@x, nil) insert#2(#false, @x, @y, @ys) -> ::(@x, ::(@y, @ys)) insert#2(#true, @x, @y, @ys) -> ::(@y, insert(@x, @ys)) insertionsort(@l) -> insertionsort#1(@l) insertionsort#1(::(@x, @xs)) -> insert(@x, insertionsort(@xs)) insertionsort#1(nil) -> nil The (relative) TRS S consists of the following rules: #cklt(#EQ) -> #false #cklt(#GT) -> #false #cklt(#LT) -> #true #compare(#0, #0) -> #EQ #compare(#0, #neg(@y)) -> #GT #compare(#0, #pos(@y)) -> #LT #compare(#0, #s(@y)) -> #LT #compare(#neg(@x), #0) -> #LT #compare(#neg(@x), #neg(@y)) -> #compare(@y, @x) #compare(#neg(@x), #pos(@y)) -> #LT #compare(#pos(@x), #0) -> #GT #compare(#pos(@x), #neg(@y)) -> #GT #compare(#pos(@x), #pos(@y)) -> #compare(@x, @y) #compare(#s(@x), #0) -> #GT #compare(#s(@x), #s(@y)) -> #compare(@x, @y) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). popout

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all output return to Runtime Complexity: TRS Innermost