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Runti Compl Inner Rewri 22807 pair #381903991
details
property
value
status
complete
benchmark
bft_mmult.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.557494879 seconds
cpu usage
1113.74546139
max memory
1.579511808E10
stage attributes
key
value
output-size
96408
starexec-result
WORST_CASE(Omega(n^1), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 356 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 17.3 s] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 16.3 s] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 16.5 s] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 2247 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 17 ms] (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: *(@x, @y) -> #mult(@x, @y) +(@x, @y) -> #add(@x, @y) appendreverse(@toreverse, @sofar) -> appendreverse#1(@toreverse, @sofar) appendreverse#1(::(@a, @as), @sofar) -> appendreverse(@as, ::(@a, @sofar)) appendreverse#1(nil, @sofar) -> @sofar bftMult(@t, @acc) -> bftMult'(tuple#2(::(@t, nil), nil), @acc) bftMult'(@queue, @acc) -> bftMult'#1(bftMult'#2(@queue), @acc) bftMult'#1(tuple#2(@elem, @queue), @acc) -> bftMult'#3(@elem, @acc, @queue) bftMult'#2(tuple#2(@dequeue@1, @dequeue@2)) -> dequeue(@dequeue@1, @dequeue@2) bftMult'#3(::(@t, @_@3), @acc, @queue) -> bftMult'#4(@t, @acc, @queue) bftMult'#3(nil, @acc, @queue) -> @acc bftMult'#4(leaf, @acc, @queue) -> bftMult'(@queue, @acc) bftMult'#4(node(@y, @t1, @t2), @acc, @queue) -> bftMult'#5(enqueue(@t2, enqueue(@t1, @queue)), @acc, @y) bftMult'#5(@queue', @acc, @y) -> bftMult'(@queue', matrixMult(@acc, @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 dequeue(@outq, @inq) -> dequeue#1(@outq, @inq) dequeue#1(::(@t, @ts), @inq) -> tuple#2(::(@t, nil), tuple#2(@ts, @inq)) dequeue#1(nil, @inq) -> dequeue#2(reverse(@inq)) dequeue#2(::(@t, @ts)) -> tuple#2(::(@t, nil), tuple#2(@ts, nil)) dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil)) enqueue(@t, @queue) -> enqueue#1(@queue, @t) enqueue#1(tuple#2(@outq, @inq), @t) -> tuple#2(@outq, ::(@t, @inq)) 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 reverse(@xs) -> appendreverse(@xs, 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
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