
Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [f1/7,f2/7,f3/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f1_loop_cont/2]
3. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f0/8

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations f1/7 
* CE 14 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 8 is refined into CE [17] 
* CE 6 is refined into CE [18] 
* CE 7 is refined into CE [19] 
* CE 5 is refined into CE [20] 
* CE 4 is refined into CE [21] 
* CE 2 is refined into CE [22] 
* CE 3 is refined into CE [23] 
* CE 12 is refined into CE [24] 
* CE 10 is refined into CE [25] 
* CE 13 is refined into CE [26] 
* CE 11 is refined into CE [27] 


### Cost equations --> "Loop" of f1/7 
* CEs [16] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 
* CEs [22] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [24] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [27] --> Loop 26 
* CEs [15] --> Loop 27 

### Ranking functions of CR f1(A,B,D,E,F,G,H) 
* RF of phase [16,17]: [B/2-D+1,-D+3]
* RF of phase [18]: [-A-D+5,-A/2+E-1/2,-A/3-D/3+2/3*E-1/3,B/2-D+1,-D+3,-D/3+2/3*E-1/3,E]
* RF of phase [19,22]: [-B/2+D-3/2,D-1]
* RF of phase [21]: [A+D-1,A/3+D/3-2/3*E,-B/2+D-3/2,D-1,D/3-2/3*E+1]
* RF of phase [23]: [A/2+B/4-E+1/2,A/2+D/2-E,A/2-E+3/2,B/4-E+2,D/2-E+3/2,-E+4]
* RF of phase [24]: [-A/2-B/4+E-3/2,-A/2-D/2+E-1/2,-A/2+E-1,-B/4+E-3/2,-D/2+E-1/2,E]
* RF of phase [25]: [A/2+B/4-E+1/4,A/2+D/2-E,A/2-E+3/2,B/4-E+7/4,D/2-E+3/2,-E+4]
* RF of phase [26]: [-A/2-B/4+E-5/4,-A/2-D/2+E-1/2,-A/2+E-1,-B/4+E-5/4,-D/2+E-1/2,E]

#### Partial ranking functions of CR f1(A,B,D,E,F,G,H) 
* Partial RF of phase [16,17]:
  - RF of loop [16:1]:
    -A-D+2*E+1 depends on loops [17:1] 
    -D+2*E+1 depends on loops [17:1] 
  - RF of loop [16:1,17:1]:
    B/2-D+1
    -D+3
  - RF of loop [17:1]:
    A+D-2*E depends on loops [16:1] 
    A/2+B/4-E
    A/2-E+1
    B/4-E+3/2
    D-2*E+3 depends on loops [16:1] 
    -E+3
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    -A-D+5
    -A/2+E-1/2
    -A/3-D/3+2/3*E-1/3
    B/2-D+1
    -D+3
    -D/3+2/3*E-1/3
    E
* Partial RF of phase [19,22]:
  - RF of loop [19:1]:
    A+D-2*E+2 depends on loops [22:1] 
    D-2*E+5 depends on loops [22:1] 
  - RF of loop [19:1,22:1]:
    -B/2+D-3/2
    D-1
  - RF of loop [22:1]:
    -A-D+2*E-1 depends on loops [19:1] 
    -A/2-B/4+E-7/4
    -A/2+E-3/2
    -B/4+E-7/4
    -D+2*E-1 depends on loops [19:1] 
    E-1
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    A+D-1
    A/3+D/3-2/3*E
    -B/2+D-3/2
    D-1
    D/3-2/3*E+1
* Partial RF of phase [23]:
  - RF of loop [23:1]:
    A/2+B/4-E+1/2
    A/2+D/2-E
    A/2-E+3/2
    B/4-E+2
    D/2-E+3/2
    -E+4
* Partial RF of phase [24]:
  - RF of loop [24:1]:
    -A/2-B/4+E-3/2
    -A/2-D/2+E-1/2
    -A/2+E-1
    -B/4+E-3/2
    -D/2+E-1/2
    E
* Partial RF of phase [25]:
  - RF of loop [25:1]:
    A/2+B/4-E+1/4
    A/2+D/2-E
    A/2-E+3/2
    B/4-E+7/4
    D/2-E+3/2
    -E+4
* Partial RF of phase [26]:
  - RF of loop [26:1]:
    -A/2-B/4+E-5/4
    -A/2-D/2+E-1/2
    -A/2+E-1
    -B/4+E-5/4
    -D/2+E-1/2
    E


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] 


### Cost equations --> "Loop" of f0/8 
* CEs [59] --> Loop 28 
* CEs [58] --> Loop 29 
* CEs [63] --> Loop 30 
* CEs [62] --> Loop 31 
* CEs [61] --> Loop 32 
* CEs [60] --> Loop 33 
* CEs [51] --> Loop 34 
* CEs [49] --> Loop 35 
* CEs [48] --> Loop 36 
* CEs [47] --> Loop 37 
* CEs [57] --> Loop 38 
* CEs [56] --> Loop 39 
* CEs [55] --> Loop 40 
* CEs [54] --> Loop 41 
* CEs [53] --> Loop 42 
* CEs [52] --> Loop 43 
* CEs [46] --> Loop 44 
* CEs [50] --> Loop 45 
* CEs [44] --> Loop 46 
* CEs [45] --> Loop 47 
* CEs [43] --> Loop 48 
* CEs [42] --> Loop 49 
* CEs [41] --> Loop 50 
* CEs [40] --> Loop 51 
* CEs [39] --> Loop 52 
* CEs [38] --> Loop 53 
* CEs [37] --> Loop 54 
* CEs [36] --> Loop 55 
* CEs [35] --> Loop 56 
* CEs [34] --> Loop 57 
* CEs [33] --> Loop 58 
* CEs [32] --> Loop 59 
* CEs [30] --> Loop 60 
* CEs [31] --> Loop 61 
* CEs [29] --> Loop 62 
* CEs [28] --> Loop 63 

### Ranking functions of CR f0(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H) 


Computing Bounds
=====================================

#### Cost of chains of f1(A,B,D,E,F,G,H):
* Chain [[26],27]: 1*it(26)+0
  Such that:it(26) =< -A/2-D/2+E

  with precondition: [H=2,2*D=B+2,5>=2*D,3>=A,A>=0,D>=1,2*E>=A+D+2] 

* Chain [[25],27]: 1*it(25)+0
  Such that:it(25) =< A/2+D/2-E

  with precondition: [H=2,B+2=2*D,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A>=4*E] 

* Chain [[24],27]: 1*it(24)+0
  Such that:it(24) =< -A/2-D/2+E

  with precondition: [H=2,2*D=B+3,3>=A,3>=D,A>=0,2*D>=3,2*E>=A+D+2] 

* Chain [[23],27]: 1*it(23)+0
  Such that:it(23) =< A/2+D/2-E

  with precondition: [H=2,2*D=B+3,3>=A,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 

* Chain [[21],[26],27]: 1*it(21)+1*it(26)+0
  Such that:it(26) =< 1
it(21) =< A/3+D/3-2/3*E

  with precondition: [H=2,2*A+3*B+10=4*D+4*E,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A+2>=4*E,B+2*A+4*E>=2] 

* Chain [[21],[25],27]: 1*it(21)+1*it(25)+0
  Such that:it(25) =< A/2+3/4*B-D-E+3/2
it(21) =< -B/2+D

  with precondition: [H=2,3>=A,3>=B,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 

* Chain [[21],[24],27]: 1*it(21)+1*it(24)+0
  Such that:it(24) =< 1
it(21) =< -B/2+D

  with precondition: [H=2,2*A+3*B+13=4*D+4*E,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A+3>=4*E,3*B+4*E+6*A>=3] 

* Chain [[21],[23],27]: 1*it(21)+1*it(23)+0
  Such that:it(23) =< A/2+3/4*B-D-E+9/4
it(21) =< -B/2+D

  with precondition: [H=2,3>=A,3>=B,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 

* Chain [[21],[19,22],[26],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(1)+0
  Such that:aux(32) =< -A/2-B/2+D+E
aux(32) =< -A/2+D+E
it(21) =< A/3+D/3-2/3*E
aux(35) =< -3/4*B+D+E
aux(35) =< -B/4+D+E
aux(40) =< -A/2-3/4*B+D+E
aux(41) =< -A/2-B/4+D+E
aux(42) =< -B/2+D+E
aux(43) =< D+E
aux(31) =< aux(40)
aux(33) =< aux(40)
aux(31) =< aux(41)
aux(37) =< aux(41)
aux(33) =< aux(42)
it(22) =< aux(42)
aux(37) =< aux(43)
it(22) =< aux(43)
it(22) =< aux(31)
s(1) =< aux(31)
it(22) =< aux(32)
s(1) =< aux(32)
it(19) =< aux(33)
it(22) =< aux(33)
it(22) =< aux(35)
it(19) =< aux(37)
it(22) =< aux(37)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 

* Chain [[21],[19,22],[24],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(2)+0
  Such that:aux(56) =< -A/2-3/4*B+D+E
aux(56) =< -A/2-B/4+D+E
it(21) =< A/3+D/3-2/3*E
aux(64) =< -A/2-B/2+D+E
aux(65) =< -A/2+D+E
aux(66) =< -3/4*B+D+E
aux(67) =< -B/4+D+E
aux(57) =< aux(64)
aux(58) =< aux(64)
aux(57) =< aux(65)
aux(61) =< aux(65)
aux(58) =< aux(66)
it(22) =< aux(66)
aux(61) =< aux(67)
it(22) =< aux(67)
it(22) =< aux(56)
s(2) =< aux(56)
it(22) =< aux(57)
s(2) =< aux(57)
it(19) =< aux(58)
it(22) =< aux(58)
it(19) =< aux(61)
it(22) =< aux(61)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 

* Chain [[21],[19,22],27]: 1*it(19)+1*it(21)+1*it(22)+0
  Such that:aux(68) =< -A/3-B/2+2/3*D+2/3*E
aux(11) =< -A/3+2/3*D+2/3*E
it(21) =< A/3+D/3-2/3*E
aux(69) =< -A/2-3/4*B+D+E
aux(70) =< -A/2-B/4+D+E
aux(68) =< aux(69)
it(22) =< aux(69)
aux(11) =< aux(70)
it(22) =< aux(70)
it(22) =< aux(68)
it(19) =< aux(68)
it(19) =< aux(11)
it(22) =< aux(11)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 

* Chain [[21],27]: 1*it(21)+0
  Such that:it(21) =< A/3+D/3-2/3*E
it(21) =< -B/2+D

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 

* Chain [[21],20,[19,22],[26],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(1)+1
  Such that:aux(33) =< -A/3-B/2+2/3*D+2/3*E
aux(37) =< -A/3+2/3*D+2/3*E
aux(31) =< -A/6-B/4+D/3+E/3
aux(32) =< -A/6+D/3+E/3
aux(35) =< A/3-B/4+D/3+E/3
it(21) =< A/3+D/3-2/3*E
it(22) =< A/3+D/3+E/3
it(22) =< aux(31)
s(1) =< aux(31)
it(22) =< aux(32)
s(1) =< aux(32)
it(19) =< aux(33)
it(22) =< aux(33)
it(22) =< aux(35)
it(19) =< aux(37)
it(22) =< aux(37)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 

* Chain [[21],20,[19,22],[24],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(2)+1
  Such that:aux(58) =< -A/3-B/2+2/3*D+2/3*E
aux(61) =< -A/3+2/3*D+2/3*E
aux(56) =< -A/6-B/4+D/3+E/3
aux(57) =< -A/6+D/3+E/3
it(22) =< A/3-B/4+D/3+E/3
it(21) =< A/3+D/3-2/3*E
it(22) =< aux(56)
s(2) =< aux(56)
it(22) =< aux(57)
s(2) =< aux(57)
it(19) =< aux(58)
it(22) =< aux(58)
it(19) =< aux(61)
it(22) =< aux(61)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 

* Chain [[21],20,[19,22],27]: 1*it(19)+1*it(21)+1*it(22)+1
  Such that:aux(68) =< -A/3-B/2+2/3*D+2/3*E
aux(11) =< -A/3+2/3*D+2/3*E
it(22) =< -A/6-B/4+D/3+E/3
it(21) =< A/3+D/3-2/3*E
it(22) =< aux(68)
it(19) =< aux(68)
it(19) =< aux(11)
it(22) =< aux(11)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 

* Chain [[21],20,27]: 1*it(21)+1
  Such that:it(21) =< A/3+D/3-2/3*E

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 

* Chain [[19,22],[26],27]: 1*it(19)+1*it(22)+1*s(1)+0
  Such that:it(22) =< E
aux(31) =< -A/2-B/4+E
aux(32) =< -A/2+E
aux(33) =< -B/2+D
aux(35) =< -B/4+E
aux(37) =< D
it(22) =< aux(31)
s(1) =< aux(31)
it(22) =< aux(32)
s(1) =< aux(32)
it(19) =< aux(33)
it(22) =< aux(33)
it(22) =< aux(35)
it(19) =< aux(37)
it(22) =< aux(37)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 

* Chain [[19,22],[24],27]: 1*it(19)+1*it(22)+1*s(2)+0
  Such that:it(22) =< -B/4+E
it(22) =< E
aux(56) =< -A/2-B/4+E
aux(57) =< -A/2+E
aux(58) =< -B/2+D
aux(61) =< D
it(22) =< aux(56)
s(2) =< aux(56)
it(22) =< aux(57)
s(2) =< aux(57)
it(19) =< aux(58)
it(22) =< aux(58)
it(19) =< aux(61)
it(22) =< aux(61)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 

* Chain [[19,22],27]: 1*it(19)+1*it(22)+0
  Such that:it(22) =< -A-B/2+2*E
it(22) =< -A/2-B/4+E
aux(11) =< D
aux(68) =< -B/2+D
it(22) =< aux(68)
it(19) =< aux(68)
it(19) =< aux(11)
it(22) =< aux(11)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 

* Chain [[18],[26],27]: 1*it(18)+1*it(26)+0
  Such that:it(26) =< -A/2-3/4*B+D+E
it(18) =< B/2-D+1

  with precondition: [H=2,B=2*D,3>=E,A>=0,B>=0,4*E>=2*A+B+10] 

* Chain [[18],[25],27]: 1*it(18)+1*it(25)+0
  Such that:it(25) =< 1/2
it(18) =< B/2-D+2/3

  with precondition: [H=2,4*D+4*E=3*B+2*A+4,3>=B,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 

* Chain [[18],[24],27]: 1*it(18)+1*it(24)+0
  Such that:it(24) =< -A/2-3/4*B+D+E
it(18) =< B/2-D+1

  with precondition: [H=2,B+1=2*D,3>=E,A>=0,B>=0,4*E>=2*A+B+11] 

* Chain [[18],[23],27]: 1*it(18)+1*it(23)+0
  Such that:it(23) =< 1/2
it(18) =< -A/3-D/3+2/3*E

  with precondition: [H=2,4*D+4*E=3*B+2*A+7,3>=B,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 

* Chain [[18],[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(18)+1*it(25)+0
  Such that:it(18) =< -A/3-D/3+2/3*E
it(25) =< A/2+1/2
aux(83) =< B/2-D
aux(81) =< -D+2
aux(84) =< A/2+B/4-D-E+3
aux(85) =< A/2+3/4*B-D-E+1
aux(81) =< aux(84)
it(17) =< aux(84)
aux(83) =< aux(85)
it(17) =< aux(85)
it(17) =< aux(83)
it(16) =< aux(83)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 

* Chain [[18],[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(18)+1*it(23)+0
  Such that:it(18) =< -A/3-D/3+2/3*E
it(23) =< A/2+1/2
aux(81) =< A/2+B/4-D-E+13/4
it(17) =< A/6+B/3+5/4
it(17) =< 2/3*A+B/3
aux(79) =< B/2-D
aux(86) =< B/2-D+1/2
it(17) =< B/4-E+5/2
it(17) =< 3/4*B-D-E+2
aux(81) =< -D+2
aux(87) =< A/2+3/4*B-D-E+5/4
aux(88) =< A/2+3/4*B-D-E+7/4
aux(79) =< aux(87)
it(17) =< aux(87)
aux(86) =< aux(88)
it(17) =< aux(88)
it(17) =< aux(86)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(86)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 

* Chain [[18],[16,17],27]: 1*it(16)+1*it(17)+1*it(18)+0
  Such that:it(17) =< -A/2+B/4-E+4
it(18) =< -A/3-D/3+2/3*E
it(17) =< A/2+3/4*B-D-E+1/2
aux(81) =< A/2-D-E+4
aux(89) =< B+1
aux(79) =< B/2-D
aux(90) =< B/2-D+1/2
it(17) =< B/4-E+5/2
it(17) =< 3/4*B-D-E+2
aux(81) =< -D+2
aux(91) =< A/2+B/2-D-E+2
aux(92) =< A/2+B/2-D-E+5/2
aux(79) =< aux(91)
it(17) =< aux(91)
aux(90) =< aux(92)
it(17) =< aux(92)
aux(80) =< aux(89)
it(17) =< aux(89)
aux(80) =< aux(90)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(80)
it(17) =< aux(80)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 

* Chain [[18],27]: 1*it(18)+0
  Such that:it(18) =< -A/3-D/3+2/3*E
it(18) =< B/2-D+1

  with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 

* Chain [[18],15,[16,17],[23],27]: 1*it(16)+1*it(18)+1*it(23)+1
  Such that:aux(79) =< 1/2
it(23) =< A/2+1/2
aux(93) =< 1
it(18) =< aux(93)
it(16) =< aux(79)
it(16) =< aux(93)

  with precondition: [B=3,D=0,H=2,2*E=A+4,3>=E,E>=2] 

* Chain [[18],15,[16,17],27]: 1*it(16)+1*it(18)+1
  Such that:aux(89) =< 4
aux(79) =< 1/2
aux(94) =< 1
it(18) =< aux(94)
aux(80) =< aux(89)
aux(80) =< aux(94)
it(16) =< aux(79)
it(16) =< aux(80)
it(16) =< aux(94)

  with precondition: [B=3,D=0,H=2,2*E=A+4,3>=E,E>=2] 

* Chain [[18],15,27]: 1*it(18)+1
  Such that:it(18) =< -A/3-D/3+2/3*E

  with precondition: [H=2,2*E=A+D+4,3>=B,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 

* Chain [[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(25)+0
  Such that:it(25) =< A/2+1/2
it(17) =< A/2+B/4-E
aux(81) =< -D+3
aux(83) =< B/2-D+1
it(17) =< aux(83)
it(16) =< aux(83)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 

* Chain [[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(23)+0
  Such that:it(23) =< A/2+1/2
it(17) =< A/2+B/4-E
it(17) =< A/2+B/4-E+1/4
it(23) =< A/2+B/4+3*E
it(17) =< A/2-E+1
aux(79) =< B/2-D+1
it(17) =< B/4-E+3/2
aux(81) =< -D+3
aux(86) =< B/2-D+3/2
it(17) =< aux(86)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(86)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 

* Chain [[16,17],27]: 1*it(16)+1*it(17)+0
  Such that:it(17) =< 2*A+B
it(17) =< A/2+B/4-E
it(17) =< A/2-E+1
aux(79) =< B/2-D+1
it(17) =< B/4-E+3/2
aux(81) =< -D+3
aux(89) =< B+1
aux(90) =< B/2-D+3/2
aux(80) =< aux(89)
it(17) =< aux(89)
aux(80) =< aux(90)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(80)
it(17) =< aux(80)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 

* Chain [27]: 0
  with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,D>=0,E>=0] 

* Chain [20,[19,22],[26],27]: 1*it(19)+1*it(22)+1*s(1)+1
  Such that:aux(33) =< -A-B/2+2*E
aux(37) =< -A+2*E
aux(31) =< -A/2-B/4+E
aux(32) =< -A/2+E
aux(35) =< -B/4+E
it(22) =< E
it(22) =< aux(31)
s(1) =< aux(31)
it(22) =< aux(32)
s(1) =< aux(32)
it(19) =< aux(33)
it(22) =< aux(33)
it(22) =< aux(35)
it(19) =< aux(37)
it(22) =< aux(37)

  with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+6,2*E>=D] 

* Chain [20,[19,22],[24],27]: 1*it(19)+1*it(22)+1*s(2)+1
  Such that:aux(58) =< -A-B/2+2*E
aux(61) =< -A+2*E
aux(56) =< -A/2-B/4+E
aux(57) =< -A/2+E
it(22) =< -B/4+E
it(22) =< aux(56)
s(2) =< aux(56)
it(22) =< aux(57)
s(2) =< aux(57)
it(19) =< aux(58)
it(22) =< aux(58)
it(19) =< aux(61)
it(22) =< aux(61)

  with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+7,2*E>=D] 

* Chain [20,[19,22],27]: 1*it(19)+1*it(22)+1
  Such that:aux(68) =< -A-B/2+2*E
aux(11) =< -A+2*E
it(22) =< -A/2-B/4+E
it(22) =< aux(68)
it(19) =< aux(68)
it(19) =< aux(11)
it(22) =< aux(11)

  with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+6,2*E>=D] 

* Chain [20,27]: 1
  with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 

* Chain [15,[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(25)+1
  Such that:it(25) =< A/2+1/2
aux(83) =< B/2-D
it(17) =< B/4-D/2
aux(81) =< -D+2
it(17) =< aux(83)
it(16) =< aux(83)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 

* Chain [15,[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(23)+1
  Such that:it(17) =< -A/2+B/4-D/2+1
it(23) =< A/2+1/2
aux(79) =< B/2-D
aux(86) =< B/2-D+1/2
it(17) =< B/4-D/2
it(17) =< B/4-E+3/2
aux(81) =< -D+2
it(17) =< -D/2+1/4
it(17) =< aux(86)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(86)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 

* Chain [15,[16,17],27]: 1*it(16)+1*it(17)+1
  Such that:it(17) =< -A/2+B/4-D/2+1
aux(89) =< B+1
aux(79) =< B/2-D
aux(90) =< B/2-D+1/2
it(17) =< B/4-D/2
it(17) =< B/4-E+3/2
aux(81) =< -D+2
it(17) =< -D/2+1/2
it(17) =< -D/2+1/4
aux(80) =< aux(89)
it(17) =< aux(89)
aux(80) =< aux(90)
it(16) =< aux(79)
it(17) =< aux(79)
it(16) =< aux(80)
it(17) =< aux(80)
it(16) =< aux(81)
it(17) =< aux(81)

  with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 

* Chain [15,27]: 1
  with precondition: [H=2,A+D+1=2*E,3>=B,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H):
* Chain [63]: 1*s(86)+2*s(89)+1*s(91)+1*s(92)+1
  Such that:s(87) =< 1
s(85) =< 4
s(88) =< 1/2
s(86) =< E
s(89) =< s(87)
s(90) =< s(85)
s(90) =< s(87)
s(91) =< s(88)
s(91) =< s(90)
s(91) =< s(87)
s(92) =< s(88)
s(92) =< s(87)

  with precondition: [B=3,D=0,2*E=A+4,3>=C,3>=E,E>=2] 

* Chain [62]: 1*s(93)+0
  Such that:s(93) =< A/2+D/2-E

  with precondition: [B+2=2*D,3>=A,3>=B,3>=C,A>=0,B>=0,E>=0,B+2*A>=4*E] 

* Chain [61]: 1*s(94)+1*s(95)+0
  Such that:s(95) =< 1
s(94) =< -A/2-B/4+E

  with precondition: [2*D=B,3>=C,3>=E,A>=0,D>=0,2*E>=A+D+5] 

* Chain [60]: 1*s(96)+1*s(97)+0
  Such that:s(97) =< 1/2
s(96) =< -A/2-B/4+E+1/2

  with precondition: [2*D=B+1,3>=C,3>=E,A>=0,2*D>=1,2*E>=A+D+5] 

* Chain [59]: 1*s(98)+0
  Such that:s(98) =< -A/2-D/2+E

  with precondition: [2*D=B+2,5>=2*D,3>=C,3>=E,A>=0,D>=1,2*E>=A+D+2] 

* Chain [58]: 1*s(99)+0
  Such that:s(99) =< A/2+D/2-E

  with precondition: [2*D=B+3,3>=A,3>=C,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 

* Chain [57]: 1*s(100)+0
  Such that:s(100) =< -A/2-D/2+E

  with precondition: [2*D=B+3,3>=C,3>=D,3>=E,A>=0,2*D>=3,2*E>=A+D+2] 

* Chain [56]: 1
  with precondition: [2*E=A+D+1,3>=B,3>=C,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 

* Chain [55]: 1*s(101)+1*s(103)+1*s(111)+1*s(113)+1*s(114)+1
  Such that:s(110) =< A/2-E+3/4
s(102) =< B+1
s(105) =< B/2-D
s(106) =< B/2-D+1/2
s(107) =< B/4-D/2
s(109) =< -D+2
s(103) =< -D/2+1/2
s(110) =< -D/2+1/4
s(101) =< -D/2+E
aux(117) =< -A/2+B/4-D/2+1
aux(118) =< B/4-E+3/2
s(104) =< aux(117)
s(104) =< aux(118)
s(103) =< s(104)
s(111) =< s(104)
s(103) =< s(107)
s(111) =< s(107)
s(103) =< s(110)
s(111) =< s(110)
s(112) =< s(102)
s(103) =< s(102)
s(112) =< s(106)
s(113) =< s(105)
s(103) =< s(105)
s(113) =< s(112)
s(103) =< s(112)
s(113) =< s(109)
s(103) =< s(109)
s(111) =< s(106)
s(114) =< s(105)
s(111) =< s(105)
s(114) =< s(106)
s(114) =< s(109)
s(111) =< s(109)

  with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 

* Chain [54]: 1*s(115)+1*s(117)+1*s(119)+1
  Such that:s(115) =< A/2+1/2
s(116) =< B/2-D
s(117) =< B/4-D/2
s(118) =< -D+2
s(117) =< s(116)
s(119) =< s(116)
s(119) =< s(118)
s(117) =< s(118)

  with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 

* Chain [53]: 1
  with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 

* Chain [52]: 1*s(122)+1*s(126)+2*s(127)+1*s(128)+1
  Such that:s(123) =< -A-B/2+2*E
s(124) =< -A+2*E
s(125) =< -A/2-B/4+E
s(120) =< -A/2+E
s(121) =< -B/4+E
s(122) =< E
s(126) =< s(125)
s(126) =< s(123)
s(127) =< s(123)
s(127) =< s(124)
s(126) =< s(124)
s(122) =< s(125)
s(128) =< s(125)
s(122) =< s(120)
s(128) =< s(120)
s(122) =< s(123)
s(122) =< s(121)
s(122) =< s(124)

  with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+6,2*E>=D] 

* Chain [51]: 1*s(133)+1*s(134)+1*s(135)+1
  Such that:s(129) =< -A-B/2+2*E
s(130) =< -A+2*E
s(131) =< -A/2-B/4+E
s(132) =< -A/2+E
s(133) =< -B/4+E
s(133) =< s(131)
s(134) =< s(131)
s(133) =< s(132)
s(134) =< s(132)
s(135) =< s(129)
s(133) =< s(129)
s(135) =< s(130)
s(133) =< s(130)

  with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+7,2*E>=D] 

* Chain [50]: 1*s(136)+1
  Such that:s(136) =< 4/3

  with precondition: [A+D+4=2*E,3>=B,3>=C,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 

* Chain [49]: 1*s(137)+1*s(138)+0
  Such that:s(137) =< 1
s(138) =< -B/2+D

  with precondition: [4*D+4*E=3*B+2*A+13,3>=B,3>=C,B>=0,E>=0,2*D>=B+5,3*B+19>=4*D+4*E,4*D+4*E>=3*B+13,6*D+8*E>=3*B+21] 

* Chain [48]: 1*s(139)+1*s(140)+0
  Such that:s(139) =< 1
s(140) =< -B/2+D

  with precondition: [4*D+4*E=3*B+2*A+10,3>=B,3>=C,B>=0,E>=0,2*D>=B+4,3*B+16>=4*D+4*E,4*D+4*E>=3*B+10,2*D+4*E>=B+6] 

* Chain [47]: 1*s(141)+1*s(142)+0
  Such that:s(141) =< 1/2
s(142) =< B/2-D+7/6

  with precondition: [4*D+4*E=3*B+2*A+7,3>=B,3>=C,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 

* Chain [46]: 1*s(143)+1*s(144)+0
  Such that:s(143) =< 1/2
s(144) =< B/2-D+2/3

  with precondition: [4*D+4*E=3*B+2*A+4,3>=B,3>=C,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 

* Chain [45]: 0
  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,E>=0] 

* Chain [44]: 1*s(145)+0
  Such that:s(145) =< -A/3-D/3+2/3*E
s(145) =< B/2-D+1

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 

* Chain [43]: 1*s(146)+0
  Such that:s(146) =< A/3+D/3-2/3*E
s(146) =< -B/2+D

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 

* Chain [42]: 2*s(156)+1*s(160)+1*s(161)+1*s(162)+1*s(163)+1*s(164)+0
  Such that:s(153) =< -A/2-3/4*B+D+E
s(147) =< -A/2-B/2+D+E
s(154) =< -A/2-B/4+D+E
s(148) =< -A/3-B/2+2/3*D+2/3*E
s(149) =< -A/3+2/3*D+2/3*E
s(155) =< A/3+D/3-2/3*E
s(150) =< -3/4*B+D+E
s(151) =< -B/2+D+E
s(152) =< D+E
s(156) =< s(155)
s(157) =< s(153)
s(158) =< s(153)
s(157) =< s(154)
s(159) =< s(154)
s(158) =< s(151)
s(160) =< s(151)
s(159) =< s(152)
s(160) =< s(152)
s(160) =< s(157)
s(161) =< s(157)
s(160) =< s(147)
s(161) =< s(147)
s(162) =< s(158)
s(160) =< s(158)
s(160) =< s(150)
s(162) =< s(159)
s(160) =< s(159)
s(148) =< s(153)
s(163) =< s(153)
s(149) =< s(154)
s(163) =< s(154)
s(163) =< s(148)
s(164) =< s(148)
s(164) =< s(149)
s(163) =< s(149)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 

* Chain [41]: 1*s(166)+1*s(174)+1*s(175)+1*s(176)+0
  Such that:s(165) =< -A/2-3/4*B+D+E
s(167) =< -A/2-B/2+D+E
s(168) =< -A/2+D+E
s(166) =< A/3+D/3-2/3*E
s(169) =< -3/4*B+D+E
s(170) =< -B/4+D+E
s(171) =< s(167)
s(172) =< s(167)
s(171) =< s(168)
s(173) =< s(168)
s(172) =< s(169)
s(174) =< s(169)
s(173) =< s(170)
s(174) =< s(170)
s(174) =< s(165)
s(175) =< s(165)
s(174) =< s(171)
s(175) =< s(171)
s(176) =< s(172)
s(174) =< s(172)
s(176) =< s(173)
s(174) =< s(173)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 

* Chain [40]: 1*s(181)+1*s(182)+1*s(183)+1*s(184)+1
  Such that:s(177) =< -A/3-B/2+2/3*D+2/3*E
s(178) =< -A/3+2/3*D+2/3*E
s(179) =< -A/6-B/4+D/3+E/3
s(180) =< -A/6+D/3+E/3
s(181) =< A/3-B/4+D/3+E/3
s(182) =< A/3+D/3-2/3*E
s(181) =< s(179)
s(183) =< s(179)
s(181) =< s(180)
s(183) =< s(180)
s(184) =< s(177)
s(181) =< s(177)
s(184) =< s(178)
s(181) =< s(178)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 

* Chain [39]: 1*s(187)+1*s(192)+2*s(193)+2*s(194)+1*s(195)+1
  Such that:s(188) =< -A/3-B/2+2/3*D+2/3*E
s(189) =< -A/3+2/3*D+2/3*E
s(190) =< -A/6-B/4+D/3+E/3
s(185) =< -A/6+D/3+E/3
s(186) =< A/3-B/4+D/3+E/3
s(191) =< A/3+D/3-2/3*E
s(187) =< A/3+D/3+E/3
s(192) =< s(190)
s(193) =< s(191)
s(192) =< s(188)
s(194) =< s(188)
s(194) =< s(189)
s(192) =< s(189)
s(187) =< s(190)
s(195) =< s(190)
s(187) =< s(185)
s(195) =< s(185)
s(187) =< s(188)
s(187) =< s(186)
s(187) =< s(189)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 

* Chain [38]: 1*s(196)+1
  Such that:s(196) =< A/3+D/3-2/3*E

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 

* Chain [37]: 1*s(197)+1*s(198)+1*s(200)+1*s(205)+0
  Such that:s(197) =< -A/3-D/3+2/3*E
s(198) =< A/2+1/2
s(199) =< A/2+B/4-D-E+13/4
s(203) =< A/2+3/4*B-D-E+5/4
s(204) =< A/2+3/4*B-D-E+7/4
s(200) =< A/6+B/3+5/4
s(200) =< 2/3*A+B/3
s(201) =< B/2-D
s(202) =< B/2-D+1/2
s(200) =< B/4-E+5/2
s(200) =< 3/4*B-D-E+2
s(199) =< -D+2
s(200) =< -D-E+17/4
s(200) =< -E+13/4
s(201) =< s(203)
s(200) =< s(203)
s(202) =< s(204)
s(200) =< s(204)
s(200) =< s(202)
s(205) =< s(201)
s(200) =< s(201)
s(205) =< s(202)
s(205) =< s(199)
s(200) =< s(199)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 

* Chain [36]: 1*s(206)+1*s(207)+1*s(215)+0
  Such that:s(206) =< -A/2+B/4-E+4
s(207) =< -A/3-D/3+2/3*E
s(212) =< A/2+B/2-D-E+2
s(213) =< A/2+B/2-D-E+5/2
s(206) =< A/2+3/4*B-D-E+1/2
s(208) =< A/2-D-E+4
s(209) =< B+1
s(210) =< B/2-D
s(211) =< B/2-D+1/2
s(206) =< B/4-E+4
s(206) =< B/4-E+5/2
s(206) =< 3/4*B-D-E+2
s(206) =< 3/4*B-3/2*D
s(208) =< -D+2
s(206) =< -D-E+17/4
s(206) =< -E+13/4
s(210) =< s(212)
s(206) =< s(212)
s(211) =< s(213)
s(206) =< s(213)
s(214) =< s(209)
s(206) =< s(209)
s(214) =< s(211)
s(215) =< s(210)
s(206) =< s(210)
s(215) =< s(214)
s(206) =< s(214)
s(215) =< s(208)
s(206) =< s(208)

  with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 

* Chain [35]: 1*s(216)+1*s(217)+1*s(222)+1*s(223)+0
  Such that:s(216) =< -A/3-D/3+2/3*E
s(217) =< A/2+1/2
s(220) =< A/2+B/4-D-E+3
s(221) =< A/2+3/4*B-D-E+1
s(218) =< B/2-D
s(219) =< -D+2
s(219) =< s(220)
s(222) =< s(220)
s(218) =< s(221)
s(222) =< s(221)
s(222) =< s(218)
s(223) =< s(218)
s(223) =< s(219)
s(222) =< s(219)

  with precondition: [3>=A,3>=B,3>=C,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 

* Chain [34]: 1*s(224)+1*s(230)+0
  Such that:s(224) =< 2*A+B
s(224) =< A/2+B/4-E
s(224) =< A/2-E+1
s(227) =< B+1
s(225) =< B/2-D+1
s(228) =< B/2-D+3/2
s(224) =< B/4-E+3/2
s(226) =< -D+3
s(224) =< -E+9/4
s(229) =< s(227)
s(224) =< s(227)
s(229) =< s(228)
s(230) =< s(225)
s(224) =< s(225)
s(230) =< s(229)
s(224) =< s(229)
s(230) =< s(226)
s(224) =< s(226)

  with precondition: [3>=A,3>=B,3>=C,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 

* Chain [33]: 1*s(231)+1*s(232)+1*s(236)+0
  Such that:s(231) =< A/2+1/2
s(232) =< A/2+B/4-E
s(232) =< A/2+B/4-E+1/4
s(231) =< A/2+B/4+3*E
s(233) =< B/2-D+1
s(235) =< B/2-D+3/2
s(232) =< B/4-E+3/2
s(234) =< -D+3
s(232) =< -E+9/4
s(232) =< s(235)
s(236) =< s(233)
s(232) =< s(233)
s(236) =< s(235)
s(236) =< s(234)
s(232) =< s(234)

  with precondition: [3>=A,3>=B,3>=C,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 

* Chain [32]: 1*s(237)+1*s(238)+1*s(241)+0
  Such that:s(237) =< A/2+1/2
s(238) =< A/2+B/4-E
s(240) =< B/2-D+1
s(239) =< -D+3
s(238) =< s(240)
s(241) =< s(240)
s(241) =< s(239)
s(238) =< s(239)

  with precondition: [3>=A,3>=B,3>=C,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 

* Chain [31]: 1*s(242)+1*s(243)+0
  Such that:s(242) =< A/2+3/4*B-D-E+9/4
s(243) =< -B/2+D

  with precondition: [3>=A,3>=B,3>=C,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 

* Chain [30]: 1*s(244)+1*s(245)+0
  Such that:s(244) =< A/2+3/4*B-D-E+3/2
s(245) =< -B/2+D

  with precondition: [3>=A,3>=B,3>=C,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 

* Chain [29]: 1*s(246)+1*s(249)+2*s(253)+1*s(254)+0
  Such that:s(246) =< -A-B/2+2*E
s(250) =< -A/2-B/4+E
s(247) =< -A/2+E
s(251) =< -B/2+D
s(248) =< -B/4+E
s(252) =< D
s(249) =< E
s(246) =< s(250)
s(246) =< s(251)
s(253) =< s(251)
s(253) =< s(252)
s(246) =< s(252)
s(249) =< s(250)
s(254) =< s(250)
s(249) =< s(247)
s(254) =< s(247)
s(249) =< s(251)
s(249) =< s(248)
s(249) =< s(252)

  with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 

* Chain [28]: 1*s(255)+1*s(260)+1*s(261)+0
  Such that:s(256) =< -A/2-B/4+E
s(257) =< -A/2+E
s(258) =< -B/2+D
s(255) =< -B/4+E
s(259) =< D
s(255) =< s(256)
s(260) =< s(256)
s(255) =< s(257)
s(260) =< s(257)
s(261) =< s(258)
s(255) =< s(258)
s(261) =< s(259)
s(255) =< s(259)

  with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H): 
-------------------------------------
* Chain [63] with precondition: [B=3,D=0,2*E=A+4,3>=C,3>=E,E>=2] 
    - Upper bound: E+4 
    - Complexity: n 
* Chain [62] with precondition: [B+2=2*D,3>=A,3>=B,3>=C,A>=0,B>=0,E>=0,B+2*A>=4*E] 
    - Upper bound: A/2+D/2-E 
    - Complexity: n 
* Chain [61] with precondition: [2*D=B,3>=C,3>=E,A>=0,D>=0,2*E>=A+D+5] 
    - Upper bound: -A/2-B/4+E+1 
    - Complexity: n 
* Chain [60] with precondition: [2*D=B+1,3>=C,3>=E,A>=0,2*D>=1,2*E>=A+D+5] 
    - Upper bound: -A/2-B/4+E+1 
    - Complexity: n 
* Chain [59] with precondition: [2*D=B+2,5>=2*D,3>=C,3>=E,A>=0,D>=1,2*E>=A+D+2] 
    - Upper bound: -A/2-D/2+E 
    - Complexity: n 
* Chain [58] with precondition: [2*D=B+3,3>=A,3>=C,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 
    - Upper bound: A/2+D/2-E 
    - Complexity: n 
* Chain [57] with precondition: [2*D=B+3,3>=C,3>=D,3>=E,A>=0,2*D>=3,2*E>=A+D+2] 
    - Upper bound: -A/2-D/2+E 
    - Complexity: n 
* Chain [56] with precondition: [2*E=A+D+1,3>=B,3>=C,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [55] with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 
    - Upper bound: B-2*D+(-D/2+1/2+(-D/2+E+(nat(-A/2+B/4-D/2+1)+1))) 
    - Complexity: n 
* Chain [54] with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 
    - Upper bound: A/2+3/4*B-3/2*D+3/2 
    - Complexity: n 
* Chain [53] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [52] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+6,2*E>=D] 
    - Upper bound: -3*A-3/2*B+7*E+1 
    - Complexity: n 
* Chain [51] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+7,2*E>=D] 
    - Upper bound: -3/2*A-B+4*E+1 
    - Complexity: n 
* Chain [50] with precondition: [A+D+4=2*E,3>=B,3>=C,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 
    - Upper bound: 7/3 
    - Complexity: constant 
* Chain [49] with precondition: [4*D+4*E=3*B+2*A+13,3>=B,3>=C,B>=0,E>=0,2*D>=B+5,3*B+19>=4*D+4*E,4*D+4*E>=3*B+13,6*D+8*E>=3*B+21] 
    - Upper bound: -B/2+D+1 
    - Complexity: n 
* Chain [48] with precondition: [4*D+4*E=3*B+2*A+10,3>=B,3>=C,B>=0,E>=0,2*D>=B+4,3*B+16>=4*D+4*E,4*D+4*E>=3*B+10,2*D+4*E>=B+6] 
    - Upper bound: -B/2+D+1 
    - Complexity: n 
* Chain [47] with precondition: [4*D+4*E=3*B+2*A+7,3>=B,3>=C,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 
    - Upper bound: B/2-D+5/3 
    - Complexity: n 
* Chain [46] with precondition: [4*D+4*E=3*B+2*A+4,3>=B,3>=C,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 
    - Upper bound: B/2-D+7/6 
    - Complexity: n 
* Chain [45] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,E>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [44] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 
    - Upper bound: -A/3-D/3+2/3*E 
    - Complexity: n 
* Chain [43] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 
    - Upper bound: A/3+D/3-2/3*E 
    - Complexity: n 
* Chain [42] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 
    - Upper bound: -7/6*A-13/4*B+16/3*D+10/3*E 
    - Complexity: n 
* Chain [41] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 
    - Upper bound: -2/3*A-2*B+10/3*D+7/3*E 
    - Complexity: n 
* Chain [40] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 
    - Upper bound: A/6-B+5/3*D+2/3*E+1 
    - Complexity: n 
* Chain [39] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 
    - Upper bound: -3/2*B+3*D+E+1 
    - Complexity: n 
* Chain [38] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 
    - Upper bound: A/3+D/3-2/3*E+1 
    - Complexity: n 
* Chain [37] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 
    - Upper bound: A/3+5/6*B-4/3*D+2/3*E+7/4 
    - Complexity: n 
* Chain [36] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 
    - Upper bound: B/2-D+(-A/3-D/3+2/3*E+nat(-A/2+B/4-E+4)) 
    - Complexity: n 
* Chain [35] with precondition: [3>=A,3>=B,3>=C,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 
    - Upper bound: 2/3*A+3/4*B-7/3*D-E/3+7/2 
    - Complexity: n 
* Chain [34] with precondition: [3>=A,3>=B,3>=C,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 
    - Upper bound: 2*A+3/2*B-D+1 
    - Complexity: n 
* Chain [33] with precondition: [3>=A,3>=B,3>=C,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 
    - Upper bound: A/2+B/2-D+3/2+nat(A/2+B/4-E) 
    - Complexity: n 
* Chain [32] with precondition: [3>=A,3>=B,3>=C,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 
    - Upper bound: A+3/4*B-D-E+3/2 
    - Complexity: n 
* Chain [31] with precondition: [3>=A,3>=B,3>=C,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 
    - Upper bound: A/2+B/4-E+9/4 
    - Complexity: n 
* Chain [30] with precondition: [3>=A,3>=B,3>=C,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 
    - Upper bound: A/2+B/4-E+3/2 
    - Complexity: n 
* Chain [29] with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 
    - Upper bound: -3/2*A-7/4*B+2*D+4*E 
    - Complexity: n 
* Chain [28] with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 
    - Upper bound: -A/2-B+D+2*E 
    - Complexity: n 

### Maximum cost of f0(A,B,C,D,E,F,G,H): max([max([max([max([max([max([E+4,nat(-A/2-D/2+E),nat(-A/3-D/3+2/3*E),nat(A/2+D/2-E),1/2+nat(-A/2-B/4+E+1/2),1/2+nat(B/2-D+2/3),1/2+nat(B/2-D+7/6)]),nat(B/2-D+1)+max([2*A+B,A/2+1/2+nat(A/2+B/4-E)])]),nat(-B/2+D)+max([1,nat(A/2+3/4*B-D-E+3/2),nat(A/2+3/4*B-D-E+9/4)])]),nat(B/2-D)+max([max([nat(-D/2+E)+nat(-A/2+B/4-D/2+1)+nat(-D/2+1/2)+nat(B/2-D),A/2+1/2+nat(B/4-D/2)])+1,nat(-A/3-D/3+2/3*E)+max([nat(-A/2+B/4-E+4),A/2+1/2+max([A/6+B/3+5/4,nat(A/2+B/4-D-E+3)])])])]),nat(-A/2-B/4+E)+max([max([1,nat(-B/4+E)+nat(-B/2+D)]),nat(-A-B/2+2*E)+max([max([nat(-B/2+D)*2,nat(-A-B/2+2*E)+1+nat(-A/2-B/4+E)])+E,nat(-B/4+E)+1])])]),nat(A/3+D/3-2/3*E)+max([max([1,nat(-A/2-3/4*B+D+E)+nat(-3/4*B+D+E)+nat(-A/2-B/2+D+E)]),nat(-A/3-B/2+2/3*D+2/3*E)+max([nat(-A/6-B/4+D/3+E/3)+1+max([nat(A/3-B/4+D/3+E/3),A/3+D/3+E/3+(nat(-A/6-B/4+D/3+E/3)+nat(-A/3-B/2+2/3*D+2/3*E))+nat(A/3+D/3-2/3*E)]),nat(-A/2-3/4*B+D+E)*3+nat(-B/2+D+E)+nat(A/3+D/3-2/3*E)])])]) 
Asymptotic class: n 
* Total analysis performed in 1732 ms.

