Runti Compl Inner Rewri 22807 pair #381904419

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	n048.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.982991934 seconds
cpu usage	432.172129894
max memory	5.75987712E9

stage attributes

key	value
output-size	83211
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1), O(n^2))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, n^2).

(0) CpxRelTRS
(1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 364 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)), 174 ms]
    (12) CdtProblem
    (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CdtProblem
    (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 471 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), 20.0 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), 18.9 s]
            (34) typed CpxTrs
            (35) RewriteLemmaProof [LOWER BOUND(ID), 1895 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))

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