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	n148.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.69 seconds
cpu usage	1120.07
user time	1104.75
system time	15.3147
max virtual memory	3.8856956E7
max residence set size	1.5167676E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 338 ms] (2) CpxRelTRS (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (4) TRS for Loop Detection (5) DecreasingLoopProof [LOWER BOUND(ID), 365 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 #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)) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost