%% Instances of of the leak test benchmarks, as described in: 
%% A. Fehnker and F. Ivancic, Benchmarks for Hybrid System Verification, 2004. 
%%
%% For each instance we define:
%%   segments: the number of segments
%%   valves  : the number of valves
%%   seg2val : denotes for each segments the ID of the downstream valve
%%   val2seg : denotes for each valve the ID of the upstream segment
%%   xsource : the pressure at the source
%%   xsink   : the pressure in the environment
%%   xinit   : the initial pressure in each segment
%%   c_open  : for each valve the coefficent if open 
%%   c_closed: for each valve the coefficent if closed 
%%   leak    : which valve leaks 
%%   d       : coefficient for tap valves
%%   z_off   : the threshold of the tap valves
%%   t_init  : initial waiting time
%%   t_wait  : waiting time for each segment (upstream valves closed)
%%   t_test  : testing time for each segment (upstream valves open)
 




%% LEAK01
segments = 3
valves   = 4
seg2val  = [1 2 3]
val2seg  = [0 1 2 3]
xsource  = 3
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5]
c_closed \in [0,0.1] x [0,0.1] x [0,0.1] x [0.5,5]
leak     = 'valve 4' 
d        = 0.1000
z_off    = 1.1000
t_init   = 5
t_wait   = [7 6 5]
t_test   = [1.5 1 0.75]

%% LEAK02
segments = 3
valves   = 4
seg2val  = [1 2 3]
val2seg  = [0 1 2 3]
xsource  = 3
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5]
c_closed \in [0,0.1] x [0,0.1] x [0.5,5] x [0,0.1]
leak     = 'valve 3' 
d        = 0.1000
z_off    = 1.1000
t_init   = 5
t_wait   = [7 6 5]
t_test   = [1.5 1 0.75]

%% LEAK03
segments = 3
valves   = 4
seg2val  = [1 2 3]
val2seg  = [0 1 2 3]
xsource  = 3
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5]
c_closed \in [0,0.1] x [0.5,5] x [0,0.1] x [0,0.1]
leak     = 'valve 2' 
d        = 0.1000
z_off    = 1.1000
t_init   = 5
t_wait   = [7 6 5]
t_test   = [1.5 1 0.75]



%% LEAK04
segments = 3
valves   = 5
seg2val  = [1 2 4]
val2seg  = [0 1 2 1 3]
xsource  \in [2.5 3]
xsink    = 1
xinit    = [2 2 2]
c_open   = [5 5 5 5 5]
c_closed \in [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0.5,5] 
leak     = 'valve 5'
d        = 0.1000
z_off    = 1.02
t_init   = 5
t_wait   = [7 5 5]
t_test   = [0.5 0.25 0.25]

%% LEAK05
segments = 3
valves   = 5
seg2val  = [1 2 4]
val2seg  = [0 1 2 1 3]
xsource  \in [2.5 3]
xsink    = 1
xinit    = [2 2 2]
c_open   = [5 5 5 5 5]
c_closed \in [0,0.05] x [0.5,5] x [0,0.05] x [0,0.05] x [0,0.05] 
leak     = 'valve 2'
d        = 0.1000
z_off    = 1.02
t_init   = 5
t_wait   = [7 5 5]
t_test   = [0.5 0.25 0.25]

%% LEAK06
segments = 3
valves   = 5
seg2val  = [1 2 4]
val2seg  = [0 1 2 1 3]
xsource  \in [2.5 3]
xsink    = 1
xinit    = [2 2 2]
c_open   = [5 5 5 5 5]
c_closed \in [0.5,5] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] 
leak     = 'valve 1'
d        = 0.1000
z_off    = 1.02
t_init   = 5
t_wait   = [7 5 5]
t_test   = [0.5 0.25 0.25]

%% LEAK07
segments = 4
valves   = 6
seg2val  = [1 2 4 5]
val2seg  = [0 1 2 1 3 4]
xsource  \in [4,5]
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5 5 5]
c_closed \in [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0.5,5] x [0,0.05]
leak     = 'valve 5' 
d        = 0.10
z_off    = 1.03
t_init   = 5.00
t_wait   = [7 5 5 4]
t_test   = [0.75 0.4 0.75 0.5]

%% LEAK08
segments = 4
valves   = 6
seg2val  = [1 2 4 5]
val2seg  = [0 1 2 1 3 4]
xsource  \in [4,5]
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5 5 5]
c_closed \in [0,0.05] x [0,0.05] x [0,0.05] x [0.5,5] x [0,0.05] x [0,0.05]
leak     = 'valve 4' 
d        = 0.10
z_off    = 1.03
t_init   = 5.00
t_wait   = [7 5 5 4]
t_test   = [0.75 0.4 0.75 0.5]

%% LEAK09
segments = 4
valves   = 6
seg2val  = [1 2 4 5]
val2seg  = [0 1 2 1 3 4]
xsource  \in [4,5]
xsink    = 1
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]
c_open   = [5 5 5 5 5 5]
c_closed \in [0,0.05] x [0.5,5] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05]
leak     = 'valve 2' 
d        = 0.10
z_off    = 1.03
t_init   = 5.00
t_wait   = [7 5 5 4]
t_test   = [0.75 0.4 0.75 0.5]

%% LEAK10
segments = 5
valves   = 8
seg2val  = [1 2 3 6 7]
val2seg  = [0 1 2 3 2 1 4 5]
xsource  = 5.00
xsink    = 1.00
xinit    = [2 2 2 2 2]
c_open   \in [8,7] x 6 x 3 x 3 x 3 x [5,4] x 3 x 3
c_closed \in [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0.5,5]
leak     = 'valve 8'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 5 4 6 5]
t_test   = [1 1.5 1 2 1.5]

%% LEAK11
segments = 5
valves   = 8
seg2val  = [1 2 3 6 7]
val2seg  = [0 1 2 3 2 1 4 5]
xsource  = 5.00
xsink    = 1.00
xinit    = [2 2 2 2 2]
c_open   \in [8,7] x 6 x 3 x 3 x 3 x [5,4] x 3 x 3
c_closed \in [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0,0.05] x [0.5,5] x [0,0.05] x [0,0.05]
leak     = 'valve 8'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 5 4 6 5]
t_test   = [1 1.5 1 2 1.5]

%% LEAK12
segments = 5
valves   = 8
seg2val  = [1 2 3 6 7]
val2seg  = [0 1 2 3 2 1 4 5]
xsource  = 5.00
xsink    = 1.00
xinit    = [2 2 2 2 2]
c_open   \in [8,7] x 6 x 3 x 3 x 3 x [5,4] x 3 x 3
c_closed \in [0,0.005] x [0.5,5] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005]
leak     = 'valve 8'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 5 4 6 5]
t_test   = [1 1.5 1 2 1.5]

%% LEAK13

segments = 7
valves   = 10
seg2val  = [1 2 3 4 5 6 7]
val2seg  = [0 1 2 3 3 2 6 5 4 7]
xsource  = 5.00
xsink    = 1.00
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]x [1,2] x [1,2] x [1,2]
c_open   \in 7 x 6 x 4 x 3 x 3 x 5 x 3 x [3,4] x [3,4]x [3,4]
c_closed \in [0,0.005]  x [0,0.005] x [0,0.005] x [0,0.005] x [0.5,5] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005]
leak     = 'valve 5'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 3 5 4]
t_test   = [1.5 0.75 1 0.75 1.5 2 0.75]

%% LEAK14
segments = 7
valves   = 10
seg2val  = [1 2 3 4 5 6 7]
val2seg  = [0 1 2 3 3 2 6 5 4 7]
xsource  = 5.00
xsink    = 1.00
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]x [1,2] x [1,2] x [1,2]
c_open   \in 7 x 6 x 4 x 3 x 3 x 5 x 3 x [3,4] x [3,4]x [3,4]
c_closed \in [0,0.005]  x [0,0.005] x [0.5,5] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005]
leak     = 'valve 3'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 3 5 4]
t_test   = [1.5 0.75 1 0.75 1.5 2 0.75]

%% LEAK15
segments = 7
valves   = 10
seg2val  = [1 2 3 4 5 6 7]
val2seg  = [0 1 2 3 3 2 6 5 4 7]
xsource  = 5.00
xsink    = 1.00
xinit    \in [1,2] x [1,2] x [1,2] x [1,2]x [1,2] x [1,2] x [1,2]
c_open   \in 7 x 6 x 4 x 3 x 3 x 5 x 3 x [3,4] x [3,4]x [3,4]
c_closed \in [0,0.005] x [0.5,5] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005] x [0,0.005]
leak     = 'valve 2'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 3 5 4]
t_test   = [1.5 0.75 1 0.75 1.5 2 0.75]

%% LEAK16

segments = 9
valves   = 12
seg2val  = [1 2 3 4 5 6 7 8 9]
val2seg  = [0 1 2 3 1 5 6 3 8 4 7 9]
xsource  \in [5 6]
xsink    = 1.00
xinit    = [2 2 2 2 2 2 2 2 2]
c_open   = [7 6 4 3 4 4 3 4 3 3 3 3]
c_closed \in [0 0.005]^7 x [0.5 6] x [0 0.005]^4
leak     = 'valve 8'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 4 4 3 4 3]
t_test   = [1.75 1.75 1 0.75 3 1.75 0.75 1 0.75]

%% LEAK17

segments = 9
valves   = 12
seg2val  = [1 2 3 4 5 6 7 8 9]
val2seg  = [0 1 2 3 1 5 6 3 8 4 7 9]
xsource  \in [5 6]
xsink    = 1.00
xinit    = [2 2 2 2 2 2 2 2 2]
c_open   = [7 6 4 3 4 4 3 4 3 3 3 3]
c_closed \in [0 0.005]^4 x [0.5 6] x [0 0.005]^7
leak     = 'valve 5'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 4 4 3 4 3]
t_test   = [1.75 1.75 1 0.75 3 1.75 0.75 1 0.75]

%% LEAK18

segments = 9
valves   = 12
seg2val  = [1 2 3 4 5 6 7 8 9]
val2seg  = [0 1 2 3 1 5 6 3 8 4 7 9]
xsource  \in [5 6]
xsink    = 1.00
xinit    = [2 2 2 2 2 2 2 2 2]
c_open   = [7 6 4 3 4 4 3 4 3 3 3 3]
c_closed \in [0 0.005] x [0.5 6] x [0 0.005]^10
leak     = 'valve 2'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 4 3 4 4 3 4 3]
t_test   = [1.75 1.75 1 0.75 3 1.75 0.75 1 0.75]

%% LEAK19
segments = 11
valves   = 14
seg2val  = [1 2 3 4 5 6 7 8 9 10 11]
val2seg  = [0 1 2 3 4 5 2 7 8 2 10 6 9 11]
xsource  = 5.00
xsink    = 1.00
xinit    = [1,3]^11
c_open   = [7 6 4 3 3 3 4 3 3 4 3 3 3 3]
c_closed = [0 0.005]^9 x [0.5 5] x [0 0.005]^4
leak     = 'valve 10'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 3 4 3 3 3 4 3 3 4 3]
t_test   = [2 1.5 2.75 1.75 1 0.5 2 1.5 0.75 2.75 0.75]

%% LEAK20
segments = 11
valves   = 14
seg2val  = [1 2 3 4 5 6 7 8 9 10 11]
val2seg  = [0 1 2 3 4 5 2 7 8 2 10 6 9 11]
xsource  = 5.00
xsink    = 1.00
xinit    = [1,3]^11
c_open   = [7 6 4 3 3 3 4 3 3 4 3 3 3 3]
c_closed = [0 0.005]^6 x [0.5 5] x [0 0.005]^7
leak     = 'valve 7'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 3 4 3 3 3 4 3 3 4 3]
t_test   = [2 1.5 2.75 1.75 1 0.5 2 1.5 0.75 2.75 0.75]

%% LEAK21
segments = 11
valves   = 14
seg2val  = [1 2 3 4 5 6 7 8 9 10 11]
val2seg  = [0 1 2 3 4 5 2 7 8 2 10 6 9 11]
xsource  = 5.00
xsink    = 1.00
xinit    = [1,3]^11
c_open   = [7 6 4 3 3 3 4 3 3 4 3 3 3 3]
c_closed = [0 0.005]^2 x [0.5 5] x [0 0.005]^11
leak     = 'valve 3'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 3 4 3 3 3 4 3 3 4 3]
t_test   = [2 1.5 2.75 1.75 1 0.5 2 1.5 0.75 2.75 0.75]

%% LEAK22
segments = 14
valves   = 18
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 6 9 11 14]
xsource  = 5.00
xsink    = 1
xinit    \in [1,3]^14
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 3 3 3 3]
c_closed \in [0 0.005]^4 x [0.5 5] x [0 0.005]^9
leak     = 'valve 5'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3]
t_test   = [2 1.75 1.25 1 1 0.5 2 1.5 0.75 1 0.5 1.75 1 0.5]

%% LEAK23
segments = 14
valves   = 18
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 6 9 11 14]
xsource  = 5.00
xsink    = 1
xinit    \in [1,3]^14
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 3 3 3 3]
c_closed \in [0 0.005]^3 x [0.5 5] x [0 0.005]^10
leak     = 'valve 4'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3]
t_test   = [2 1.75 1.25 1 1 0.5 2 1.5 0.75 1 0.5 1.75 1 0.5]

%% LEAK24
segments = 14
valves   = 18
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 6 9 11 14]
xsource  = 5.00
xsink    = 1
xinit    \in [1,3]^14
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 3 3 3 3]
c_closed \in [0 0.005]^2 x [0.5 5] x [0 0.005]^11
leak     = 'valve 3'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3]
t_test   = [2 1.75 1.25 1 1 0.5 2 1.5 0.75 1 0.5 1.75 1 0.5]

%% LEAK25
segments = 17
valves   = 22
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 4 15 16 6 9 11 14 17]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^17
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 4 4 3 1 2 1 2 1]
c_closed \in [0 0.005]^4 x [0.5 5] x [0 0.005]^17
leak     = 'valve 5'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3.5 4 3 4 4 3 4 4 3]
t_test   = [2 1.75 1.25 1.25 2.75 1.75 2.75 2 1.5 2.75 1.75 2.25 1.5 1 3.5 2.75 1.75]

%% LEAK26
segments = 17
valves   = 22
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 4 15 16 6 9 11 14 17]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^17
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 4 4 3 1 2 1 2 1]
c_closed \in [0 0.005]^3 x [0.5 5] x [0 0.005]^18
leak     = 'valve 4'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3.5 4 3 4 4 3 4 4 3]
t_test   = [2 1.75 1.25 1.25 2.75 1.75 2.75 2 1.5 2.75 1.75 2.25 1.5 1 3.5 2.75 1.75]

%% LEAK27
segments = 17
valves   = 22
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17]
val2seg  = [0 1 2 3 4 5 2 7 8 4 10 3 12 13 4 15 16 6 9 11 14 17]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^17
c_open   = [7 6 5 4 3 3 4 4 3 4 3 4 4 3 4 4 3 1 2 1 2 1]
c_closed \in [0 0.005] x [0.5 5] x [0 0.005]^20
leak     = 'valve 2'
d        = 0.10
z_off    = 1.04
t_init   = 5.00
t_wait   = [7 6 5 4 3 3 4 4 3.5 4 3 4 4 3 4 4 3]
t_test   = [2 1.75 1.25 1.25 2.75 1.75 2.75 2 1.5 2.75 1.75 2.25 1.5 1 3.5 2.75 1.75]

%% LEAK28
segments = 20
valves   = 26
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]
val2seg  = [0 1 2 3 4 1 6 7 6 9 10 11 1 13 14 14 16 17 4 19 5 8 12 15 18 20]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^20
c_open   = [9 7 5 4 3 7 4 3 4 4 3 3 5 4 3 4 4 3 4 3 2 1 2 1 2 1]
c_closed = \in [0 0.005]^3 x [0.5 5] x [0 0.005]^22
leak     = 'valve 4'
d        = 0.10
z_off    = 1.04
t_init   = 8.00
t_wait   = [7 6 5 4 3 5 4 3 6 5 4 3 5 4 3 5 4 3 4 3]
t_test   = [2.25 3.75 2.75 1.75 1 3.5 5.75 3.25 4.25 3.25 2 1 4 2.75 2.75 3.5 2.25 2.25 4.25 2.5]

%% LEAK29
segments = 20
valves   = 26
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]
val2seg  = [0 1 2 3 4 1 6 7 6 9 10 11 1 13 14 14 16 17 4 19 5 8 12 15 18 20]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^20
c_open   = [9 7 5 4 3 7 4 3 4 4 3 3 5 4 3 4 4 3 4 3 2 1 2 1 2 1]
c_closed = \in [0 0.005]^13 x [0.5 5] x [0 0.005]^12
leak     = 'valve 14'
d        = 0.10
z_off    = 1.04
t_init   = 8.00
t_wait   = [7 6 5 4 3 5 4 3 6 5 4 3 5 4 3 5 4 3 4 3]
t_test   = [2.25 3.75 2.75 1.75 1 3.5 5.75 3.25 4.25 3.25 2 1 4 2.75 2.75 3.5 2.25 2.25 4.25 2.5]

%% LEAK30
segments = 20
valves   = 26
seg2val  = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]
val2seg  = [0 1 2 3 4 1 6 7 6 9 10 11 1 13 14 14 16 17 4 19 5 8 12 15 18 20]
xsource  = 5.00
xsink    = 1.00
xinit    \in [2 3]^20
c_open   = [9 7 5 4 3 7 4 3 4 4 3 3 5 4 3 4 4 3 4 3 2 1 2 1 2 1]
c_closed = \in [0 0.005]^5 x [0.5 5] x [0 0.005]^20
leak     = 'valve 6'
d        = 0.10
z_off    = 1.04
t_init   = 8.00
t_wait   = [7 6 5 4 3 5 4 3 6 5 4 3 5 4 3 5 4 3 4 3]
t_test   = [2.25 3.75 2.75 1.75 1 3.5 5.75 3.25 4.25 3.25 2 1 4 2.75 2.75 3.5 2.25 2.25 4.25 2.5]