Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313374
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
n080.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.287 seconds
cpu usage
1136.18
user time
1119.44
system time
16.7438
max virtual memory
3.9228948E7
max residence set size
1.5167592E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1121.56/291.65 WORST_CASE(Omega(n^1), ?) 1136.01/295.20 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1136.01/295.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1136.01/295.20 1136.01/295.20 1136.01/295.20 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1136.01/295.20 1136.01/295.20 (0) CpxRelTRS 1136.01/295.20 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 361 ms] 1136.01/295.20 (2) CpxRelTRS 1136.01/295.20 (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1136.01/295.20 (4) TRS for Loop Detection 1136.01/295.20 (5) DecreasingLoopProof [LOWER BOUND(ID), 244 ms] 1136.01/295.20 (6) BEST 1136.01/295.20 (7) proven lower bound 1136.01/295.20 (8) LowerBoundPropagationProof [FINISHED, 0 ms] 1136.01/295.20 (9) BOUNDS(n^1, INF) 1136.01/295.20 (10) TRS for Loop Detection 1136.01/295.20 1136.01/295.20 1136.01/295.20 ---------------------------------------- 1136.01/295.20 1136.01/295.20 (0) 1136.01/295.20 Obligation: 1136.01/295.20 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1136.01/295.20 1136.01/295.20 1136.01/295.20 The TRS R consists of the following rules: 1136.01/295.20 1136.01/295.20 #abs(#0) -> #0 1136.01/295.20 #abs(#neg(@x)) -> #pos(@x) 1136.01/295.20 #abs(#pos(@x)) -> #pos(@x) 1136.01/295.20 #abs(#s(@x)) -> #pos(#s(@x)) 1136.01/295.20 *(@x, @y) -> #mult(@x, @y) 1136.01/295.20 +(@x, @y) -> #add(@x, @y) 1136.01/295.20 attach(@line, @m) -> attach#1(@line, @m) 1136.01/295.20 attach#1(::(@x, @xs), @m) -> attach#2(@m, @x, @xs) 1136.01/295.20 attach#1(nil, @m) -> nil 1136.01/295.20 attach#2(::(@l, @ls), @x, @xs) -> ::(::(@x, @l), attach(@xs, @ls)) 1136.01/295.20 attach#2(nil, @x, @xs) -> nil 1136.01/295.20 lineMult(@l, @m2) -> lineMult#1(@m2, @l) 1136.01/295.20 lineMult#1(::(@x, @xs), @l) -> ::(mult(@l, @x), lineMult(@l, @xs)) 1136.01/295.20 lineMult#1(nil, @l) -> nil 1136.01/295.20 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)) 1136.01/295.20 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))) 1136.01/295.20 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)) 1136.01/295.20 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)))) 1136.01/295.20 makeBase(@m) -> makeBase#1(@m) 1136.01/295.20 makeBase#1(::(@l, @m')) -> mkBase(@l) 1136.01/295.20 makeBase#1(nil) -> nil 1136.01/295.20 matrixMult(@m1, @m2) -> matrixMult'(@m1, transAcc(@m2, makeBase(@m2))) 1136.01/295.20 matrixMult'(@m1, @m2) -> matrixMult'#1(@m1, @m2) 1136.01/295.20 matrixMult'#1(::(@l, @ls), @m2) -> ::(lineMult(@l, @m2), matrixMult'(@ls, @m2)) 1136.01/295.20 matrixMult'#1(nil, @m2) -> nil 1136.01/295.20 matrixMult3(@m1, @m2, @m3) -> matrixMult(matrixMult(@m1, @m2), @m3) 1136.01/295.20 matrixMultList(@acc, @mm) -> matrixMultList#1(@mm, @acc) 1136.01/295.20 matrixMultList#1(::(@m, @ms), @acc) -> matrixMultList(matrixMult(@acc, @m), @ms) 1136.01/295.20 matrixMultList#1(nil, @acc) -> @acc 1136.01/295.20 matrixMultOld(@m1, @m2) -> matrixMult'(@m1, transpose(@m2)) 1136.01/295.20 mkBase(@m) -> mkBase#1(@m) 1136.01/295.20 mkBase#1(::(@l, @m')) -> ::(nil, mkBase(@m')) 1136.01/295.20 mkBase#1(nil) -> nil 1136.01/295.20 mult(@l1, @l2) -> mult#1(@l1, @l2) 1136.01/295.20 mult#1(::(@x, @xs), @l2) -> mult#2(@l2, @x, @xs) 1136.01/295.20 mult#1(nil, @l2) -> #abs(#0) 1136.01/295.20 mult#2(::(@y, @ys), @x, @xs) -> +(*(@x, @y), mult(@xs, @ys)) 1136.01/295.20 mult#2(nil, @x, @xs) -> #abs(#0) 1136.01/295.20 split(@m) -> split#1(@m) 1136.01/295.20 split#1(::(@l, @ls)) -> split#2(@l, @ls) 1136.01/295.20 split#1(nil) -> tuple#2(nil, nil) 1136.01/295.20 split#2(::(@x, @xs), @ls) -> split#3(split(@ls), @x, @xs) 1136.01/295.20 split#2(nil, @ls) -> tuple#2(nil, nil) 1136.01/295.20 split#3(tuple#2(@ys, @m'), @x, @xs) -> tuple#2(::(@x, @ys), ::(@xs, @m')) 1136.01/295.20 transAcc(@m, @base) -> transAcc#1(@m, @base) 1136.01/295.20 transAcc#1(::(@l, @m'), @base) -> attach(@l, transAcc(@m', @base)) 1136.01/295.20 transAcc#1(nil, @base) -> @base 1136.01/295.20 transpose(@m) -> transpose#1(@m, @m) 1136.01/295.20 transpose#1(::(@xs, @xss), @m) -> transpose#2(split(@m)) 1136.01/295.20 transpose#1(nil, @m) -> nil 1136.01/295.20 transpose#2(tuple#2(@l, @m')) -> transpose#3(@m', @l) 1136.01/295.20 transpose#3(::(@y, @ys), @l) -> ::(@l, transpose(::(@y, @ys))) 1136.01/295.20 transpose#3(nil, @l) -> nil 1136.01/295.20 transpose'(@m) -> transAcc(@m, makeBase(@m)) 1136.01/295.20 1136.01/295.20 The (relative) TRS S consists of the following rules: 1136.01/295.20 1136.01/295.20 #add(#0, @y) -> @y 1136.01/295.20 #add(#neg(#s(#0)), @y) -> #pred(@y) 1136.01/295.20 #add(#neg(#s(#s(@x))), @y) -> #pred(#add(#pos(#s(@x)), @y)) 1136.01/295.20 #add(#pos(#s(#0)), @y) -> #succ(@y) 1136.01/295.20 #add(#pos(#s(#s(@x))), @y) -> #succ(#add(#pos(#s(@x)), @y)) 1136.01/295.20 #mult(#0, #0) -> #0 1136.01/295.20 #mult(#0, #neg(@y)) -> #0 1136.01/295.20 #mult(#0, #pos(@y)) -> #0 1136.01/295.20 #mult(#neg(@x), #0) -> #0 1136.01/295.20 #mult(#neg(@x), #neg(@y)) -> #pos(#natmult(@x, @y)) 1136.01/295.20 #mult(#neg(@x), #pos(@y)) -> #neg(#natmult(@x, @y)) 1136.01/295.20 #mult(#pos(@x), #0) -> #0 1136.01/295.20 #mult(#pos(@x), #neg(@y)) -> #neg(#natmult(@x, @y)) 1136.01/295.20 #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_Innermost_Rewriting 2019-04-01 06.40