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Runtime Complexity: TRS Innermost pair #487111636
details
property
value
status
complete
benchmark
clevermmult.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.559 seconds
cpu usage
415.915
user time
411.244
system time
4.67063
max virtual memory
1.9587772E7
max residence set size
5641532.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).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), 336 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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 137 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 425 ms] (16) CdtProblem (17) CdtKnowledgeProof [FINISHED, 0 ms] (18) BOUNDS(1, 1) (19) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRelTRS (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) typed CpxTrs (23) OrderProof [LOWER BOUND(ID), 0 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 18.5 s] (26) BEST (27) proven lower bound (28) LowerBoundPropagationProof [FINISHED, 0 ms] (29) BOUNDS(n^1, INF) (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 17.4 s] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 17.5 s] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 1644 ms] (36) typed CpxTrs ---------------------------------------- (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: *(@x, @y) -> #mult(@x, @y) +(@x, @y) -> #add(@x, @y) computeLine(@line, @m, @acc) -> computeLine#1(@line, @acc, @m) computeLine#1(::(@x, @xs), @acc, @m) -> computeLine#2(@m, @acc, @x, @xs) computeLine#1(nil, @acc, @m) -> @acc computeLine#2(::(@l, @ls), @acc, @x, @xs) -> computeLine(@xs, @ls, lineMult(@x, @l, @acc)) computeLine#2(nil, @acc, @x, @xs) -> nil lineMult(@n, @l1, @l2) -> lineMult#1(@l1, @l2, @n) lineMult#1(::(@x, @xs), @l2, @n) -> lineMult#2(@l2, @n, @x, @xs) lineMult#1(nil, @l2, @n) -> nil lineMult#2(::(@y, @ys), @n, @x, @xs) -> ::(+(*(@x, @n), @y), lineMult(@n, @xs, @ys)) lineMult#2(nil, @n, @x, @xs) -> ::(*(@x, @n), lineMult(@n, @xs, nil)) matrixMult(@m1, @m2) -> matrixMult#1(@m1, @m2) matrixMult#1(::(@l, @ls), @m2) -> ::(computeLine(@l, @m2, nil), matrixMult(@ls, @m2)) matrixMult#1(nil, @m2) -> nil The (relative) TRS S consists of the following rules: #add(#0, @y) -> @y #add(#neg(#s(#0)), @y) -> #pred(@y) #add(#neg(#s(#s(@x))), @y) -> #pred(#add(#pos(#s(@x)), @y)) #add(#pos(#s(#0)), @y) -> #succ(@y) #add(#pos(#s(#s(@x))), @y) -> #succ(#add(#pos(#s(@x)), @y)) #mult(#0, #0) -> #0 #mult(#0, #neg(@y)) -> #0 #mult(#0, #pos(@y)) -> #0 #mult(#neg(@x), #0) -> #0 #mult(#neg(@x), #neg(@y)) -> #pos(#natmult(@x, @y)) #mult(#neg(@x), #pos(@y)) -> #neg(#natmult(@x, @y)) #mult(#pos(@x), #0) -> #0 #mult(#pos(@x), #neg(@y)) -> #neg(#natmult(@x, @y)) #mult(#pos(@x), #pos(@y)) -> #pos(#natmult(@x, @y)) #natmult(#0, @y) -> #0 #natmult(#s(@x), @y) -> #add(#pos(@y), #natmult(@x, @y)) #pred(#0) -> #neg(#s(#0)) #pred(#neg(#s(@x))) -> #neg(#s(#s(@x))) #pred(#pos(#s(#0))) -> #0 #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x)) #succ(#0) -> #pos(#s(#0)) #succ(#neg(#s(#0))) -> #0 #succ(#neg(#s(#s(@x)))) -> #neg(#s(@x)) #succ(#pos(#s(@x))) -> #pos(#s(#s(@x))) Rewrite Strategy: INNERMOST ----------------------------------------
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return to Runtime Complexity: TRS Innermost