(* DLMP6(5) extendend *)
(*--- case with reducing the step to t*h=0.8*h after rejection ---*)
c={0,1/9,1/6,1/4,5/9,1/2,48/49,1,1,4/139,17/38,4/5};
a={{0,0,0,0,0,0,0,0,0,0,0,0},
{1/9,0,0,0,0,0,0,0,0,0,0,0},
{1/24,1/8,0,0,0,0,0,0,0,0,0,0},
{1/16,0,3/16,0,0,0,0,0,0,0,0,0},
{280/729,0,-325/243,1100/729,0,0,0,0,0,0,0,0},
{6127/14680,0,-1077/734,6494/4037,-9477/161480,0,0,0,0,0,0,0},
{-13426273320/14809773769,0,4192558704/2115681967,14334750144/14809773769,117092732328/14809773769,-361966176/40353607,0,0,0,0,0,0},
{-2340689/1901060,0,31647/13579,253549596/149518369,10559024082/977620105,-152952/12173,-5764801/186010396,0,0,0,0,0},
{203/2880,0,0,30208/70785,177147/164560,-536/705,1977326743/3619661760,-259/720,0,0,0,0},
{793671517057908299246521398682524951865747626196277/28749892053204987590003848913521596470193895225395200,0,-1183715466877966119464008811407214115/6337465403852137250437278846667270528,6139417892981044827067310757892746262584844546299208667/15686929381767970150554506349523785339016452150123994080,2196773948286668739010211721658793143696020151703297409/2011144792534355147506987993528690428079032326938973600,-283868874309072722200910465977367715701262678769979/232208612276397108398950457923337516697116595539520,-9072572612685762349951180019447884404330890719121/16311228299888749944917771817626538445452615690240,41/115,31416554901218890381967996925268762915453/248454644705367927449605308529503868494080,0,0,0},
{3227711527576422893162294263994144002431787/167630336487962800296955450653939318000000000,0,-13565669161390868843471411/24870458595823317576000000,5297292611238655415365642467431692349355607/10678147140688025838125269526119580850000000,-17710145534487994283291750136488594870343598293/15001880360509164683365803231980322422000000000,3887478921030611987021960429243098686249931/2991767585820589487588714446276028700000000,27/46,-32/87,-29/204,73840657140482677271688211/262188308160824982553125000,0,0},
{-12312177215137786779137736763517425352817037477023607553/14997104937581608807384600217284761591200707200000000000,0,44859174373527624072275557/29549140257579018944000000,-1974527859185223920263993769716824762831542830425441253219/3022525902310783427545796943166706654066585029530000000000,26371405743224906691149150282911201303076147129365059/6101057375962823992352997075941580436991600000000000,-580673479879597851077038420366326860630503447980113/108142464477369408330736831721221462489020000000000,-84848375471902448895905143934594177177948889969229/76654013615322505064545344015160425018240000000000,84997896003578063956854031707585181/123542289279900104933355120000000000,35557633596698667673094871927961191552739/129733711771249860092175713091120000000000,2417827928742659001344548539811/4296610899985519401589335937500,529702/382375,0}};
b={203/2880,0,0,30208/70785,177147/164560,-536/705,1977326743/3619661760,-259/720,0,0,0,0};  (* 6th order *)
bb={36567/458800, 0, 0, 9925984/27063465, 85382667/117968950, -310378/808635, 262119736669/345979336560, -1/2, -101/2294, 0, 0, 0};  (* 5th order *)
bstar={-581795734946708629/9576189077550000000,0,0,2180622542964431994368/8684960093134202109375,160801684535650498177329/270440158219393971875000,-17851147090093833108/30708643828372578125,-43561859307009122332861979/3897131486087504580630000000,1/512,98576454027353109959/21718796827883400000000,203810762373037972509469703533/1111233065640090497287762500000,268/805,5/59};  (* 7th order at t=0.8 *)
bbstar={-(8448913271401781941265878389631368959/139066409592478291874400282043200000000),0,0,1180736366528559029605206582935030477448787/3255572910005069346698205781048004568281250,7713378637572498992161242536932016284792322073/6487998698882231063936738126232147568400000000,-(132916455920064230146492317009211919945791/110507427510795966308809964872191478500000),-(1194057171089689016410093969122184780952630749087/3339078277002866460104468303548394431730880000000),4837474317/20778673664,619185212186935255343654412095670485548903/8141330050170058521630047111584546800000000,8122168682498855738349433728735210592277/49763501017567548327627080611822987500000,2320648289/7370619445,39975/483623}; (* 5th order at t=0.8 *)
t=8/10;


(* observe that 6th order is satisfied for b, e.g *)
{b.c-1/2,b.a.c^4-1/30,b.a.a.a.a.c-1/720}   (* etc *)

(* observe that 5th order is satisfied at most for bb, e.g *)
{bb.c-1/2,b.a.c^3-1/20,bb.a.a.a.c-1/120}  (* etc *)

(* observe that 7th order is satisfied for bstar at t=8/10, e.g *)
{bstar.c-t^2/2,bstar.a.c^5-t^7/42,bstar.a.a.a.a.a.c-t^7/7!}  (* etc *)

(* observe that 5th order is satisfied at most for bbstar at t=8/10, e.g *)
{bbstar.c-t^2/2,bstar.a.c^3-t^5/20,bstar.a.a.a.c-t^5/5!}     (* etc *)