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Runti Compl Inner Rewri 22807 pair #381904705
details
property
value
status
complete
benchmark
matrix.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.181214094 seconds
cpu usage
1146.18803668
max memory
1.559939072E10
stage attributes
key
value
output-size
24353
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).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), 343 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 306 ms] (6) BEST (7) proven lower bound (8) LowerBoundPropagationProof [FINISHED, 0 ms] (9) BOUNDS(n^1, INF) (10) TRS for Loop Detection ---------------------------------------- (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: #abs(#0) -> #0 #abs(#neg(@x)) -> #pos(@x) #abs(#pos(@x)) -> #pos(@x) #abs(#s(@x)) -> #pos(#s(@x)) *(@x, @y) -> #mult(@x, @y) +(@x, @y) -> #add(@x, @y) attach(@line, @m) -> attach#1(@line, @m) attach#1(::(@x, @xs), @m) -> attach#2(@m, @x, @xs) attach#1(nil, @m) -> nil attach#2(::(@l, @ls), @x, @xs) -> ::(::(@x, @l), attach(@xs, @ls)) attach#2(nil, @x, @xs) -> nil lineMult(@l, @m2) -> lineMult#1(@m2, @l) lineMult#1(::(@x, @xs), @l) -> ::(mult(@l, @x), lineMult(@l, @xs)) lineMult#1(nil, @l) -> nil m1(@x) -> ::(::(#abs(#pos(#s(#0))), ::(#abs(#pos(#s(#s(#0)))), ::(#abs(#pos(#s(#s(#s(#0))))), nil))), ::(::(#abs(#pos(#s(#s(#0)))), ::(#abs(#pos(#s(#s(#s(#0))))), ::(#abs(#pos(#s(#s(#s(#s(#0)))))), nil))), nil)) m2(@x) -> ::(::(#abs(#pos(#s(#0))), ::(#abs(#pos(#s(#s(#0)))), nil)), ::(::(#abs(#pos(#s(#s(#0)))), ::(#abs(#pos(#s(#s(#s(#0))))), nil)), ::(::(#abs(#pos(#s(#s(#s(#s(#0)))))), ::(#abs(#pos(#s(#s(#s(#s(#s(#0))))))), nil)), nil))) m3(@x) -> ::(::(#abs(#pos(#s(#0))), ::(#abs(#pos(#s(#s(#0)))), ::(#abs(#pos(#s(#s(#s(#0))))), ::(#abs(#pos(#s(#s(#s(#s(#s(#0))))))), nil)))), ::(::(#abs(#pos(#s(#s(#0)))), ::(#abs(#pos(#s(#s(#s(#0))))), ::(#abs(#pos(#s(#s(#s(#s(#0)))))), ::(#abs(#pos(#s(#s(#s(#s(#s(#0))))))), nil)))), nil)) m4(@x) -> ::(::(#abs(#pos(#s(#0))), nil), ::(::(#abs(#pos(#s(#s(#0)))), nil), ::(::(#abs(#pos(#s(#s(#s(#0))))), nil), ::(::(#abs(#pos(#s(#s(#s(#s(#0)))))), nil), nil)))) makeBase(@m) -> makeBase#1(@m) makeBase#1(::(@l, @m')) -> mkBase(@l) makeBase#1(nil) -> nil matrixMult(@m1, @m2) -> matrixMult'(@m1, transAcc(@m2, makeBase(@m2))) matrixMult'(@m1, @m2) -> matrixMult'#1(@m1, @m2) matrixMult'#1(::(@l, @ls), @m2) -> ::(lineMult(@l, @m2), matrixMult'(@ls, @m2)) matrixMult'#1(nil, @m2) -> nil matrixMult3(@m1, @m2, @m3) -> matrixMult(matrixMult(@m1, @m2), @m3) matrixMultList(@acc, @mm) -> matrixMultList#1(@mm, @acc) matrixMultList#1(::(@m, @ms), @acc) -> matrixMultList(matrixMult(@acc, @m), @ms) matrixMultList#1(nil, @acc) -> @acc matrixMultOld(@m1, @m2) -> matrixMult'(@m1, transpose(@m2)) mkBase(@m) -> mkBase#1(@m) mkBase#1(::(@l, @m')) -> ::(nil, mkBase(@m')) mkBase#1(nil) -> nil mult(@l1, @l2) -> mult#1(@l1, @l2) mult#1(::(@x, @xs), @l2) -> mult#2(@l2, @x, @xs) mult#1(nil, @l2) -> #abs(#0) mult#2(::(@y, @ys), @x, @xs) -> +(*(@x, @y), mult(@xs, @ys)) mult#2(nil, @x, @xs) -> #abs(#0) split(@m) -> split#1(@m) split#1(::(@l, @ls)) -> split#2(@l, @ls) split#1(nil) -> tuple#2(nil, nil) split#2(::(@x, @xs), @ls) -> split#3(split(@ls), @x, @xs) split#2(nil, @ls) -> tuple#2(nil, nil) split#3(tuple#2(@ys, @m'), @x, @xs) -> tuple#2(::(@x, @ys), ::(@xs, @m')) transAcc(@m, @base) -> transAcc#1(@m, @base) transAcc#1(::(@l, @m'), @base) -> attach(@l, transAcc(@m', @base)) transAcc#1(nil, @base) -> @base transpose(@m) -> transpose#1(@m, @m) transpose#1(::(@xs, @xss), @m) -> transpose#2(split(@m)) transpose#1(nil, @m) -> nil transpose#2(tuple#2(@l, @m')) -> transpose#3(@m', @l) transpose#3(::(@y, @ys), @l) -> ::(@l, transpose(::(@y, @ys))) transpose#3(nil, @l) -> nil transpose'(@m) -> transAcc(@m, makeBase(@m)) 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
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