/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_complex_bb2_in/5,eval_complex_bb3_in/5]
1. recursive  : [eval_complex_bb1_in/3,eval_complex_bb2_in_loop_cont/6,eval_complex_bb4_in/5]
2. non_recursive  : [eval_complex_stop/1]
3. non_recursive  : [eval_complex_bb5_in/1]
4. non_recursive  : [eval_complex_bb1_in_loop_cont/2]
5. non_recursive  : [eval_complex_bb0_in/3]
6. non_recursive  : [eval_complex_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_complex_bb2_in/5
1. SCC is partially evaluated into eval_complex_bb1_in/3
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_complex_bb0_in/3
6. SCC is partially evaluated into eval_complex_start/3

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

### Specialization of cost equations eval_complex_bb2_in/5 
* CE 7 is refined into CE [8] 
* CE 5 is refined into CE [9] 
* CE 6 is refined into CE [10] 


### Cost equations --> "Loop" of eval_complex_bb2_in/5 
* CEs [9] --> Loop 8 
* CEs [10] --> Loop 9 
* CEs [8] --> Loop 10 

### Ranking functions of CR eval_complex_bb2_in(V__12,V__1,B,C,D) 
* RF of phase [8]: [-V__12+V__1,-V__12/2+3]
* RF of phase [9]: [-V__12/6+V__1/6]

#### Partial ranking functions of CR eval_complex_bb2_in(V__12,V__1,B,C,D) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -V__12+V__1
    -V__12/2+3
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    -V__12/6+V__1/6


### Specialization of cost equations eval_complex_bb1_in/3 
* CE 4 is refined into CE [11] 
* CE 3 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of eval_complex_bb1_in/3 
* CEs [15] --> Loop 11 
* CEs [14] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [11] --> Loop 15 

### Ranking functions of CR eval_complex_bb1_in(V__01,V__0,B) 
* RF of phase [11,12]: [-V__0/3+10]
* RF of phase [13]: [V__01/14-V__0/7+4/7]
* RF of phase [14]: [-V__0/2+15,V__01/12-V__0/12+1/12]

#### Partial ranking functions of CR eval_complex_bb1_in(V__01,V__0,B) 
* Partial RF of phase [11,12]:
  - RF of loop [11:1]:
    -V__0/4+15/2
  - RF of loop [12:1]:
    -V__0/3+10
    V__01/24-7/24*V__0+33/4
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    V__01/14-V__0/7+4/7
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    -V__0/2+15
    V__01/12-V__0/12+1/12


### Specialization of cost equations eval_complex_bb0_in/3 
* CE 2 is refined into CE [16,17,18,19,20,21] 


### Cost equations --> "Loop" of eval_complex_bb0_in/3 
* CEs [21] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [16] --> Loop 20 
* CEs [17] --> Loop 21 

### Ranking functions of CR eval_complex_bb0_in(V_a,V_b,B) 

#### Partial ranking functions of CR eval_complex_bb0_in(V_a,V_b,B) 


### Specialization of cost equations eval_complex_start/3 
* CE 1 is refined into CE [22,23,24,25,26,27] 


### Cost equations --> "Loop" of eval_complex_start/3 
* CEs [27] --> Loop 22 
* CEs [26] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [24] --> Loop 25 
* CEs [23] --> Loop 26 
* CEs [22] --> Loop 27 

### Ranking functions of CR eval_complex_start(V_a,V_b,B) 

#### Partial ranking functions of CR eval_complex_start(V_a,V_b,B) 


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

#### Cost of chains of eval_complex_bb2_in(V__12,V__1,B,C,D):
* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< -V__12/6+V__1/6

  with precondition: [B=2,V__12+7*D=7*V__1+C,V__12>=6,C>=V__12+7,V__12+6*C>=7*V__1,7*V__1+35>=6*C+V__12] 

* Chain [[8],[9],10]: 1*it(8)+1*it(9)+0
  Such that:it(8) =< -V__12/2+3
it(9) =< -V__12/5+2/5*V__1+C/30-7/30*D

  with precondition: [B=2,D+5>=C,C>=D,7*V__12+14*D>=14*V__1+2*C+30,2*C+14*V__1+35>=14*D+7*V__12,V__12+7*D>=7*V__1+C+5,C+2*V__1>=2*D+V__12+5] 

* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -V__12/2+3
it(8) =< -V__12/2+D/2

  with precondition: [B=2,V__12+C=2*V__1,V__12+D=2*V__1,V__12+7>=2*V__1,V__1>=V__12+1] 

* Chain [10]: 0
  with precondition: [B=2,V__12=C,V__1=D,V__12>=V__1] 


#### Cost of chains of eval_complex_bb1_in(V__01,V__0,B):
* Chain [[14],[13],[11,12],15]: 1*it(11)+1*it(12)+1*it(13)+1*it(14)+1*s(7)+1*s(8)+1*s(9)+1*s(12)+0
  Such that:s(9) =< 35
aux(4) =< 34/3
it(12) =< 35/4
s(7) =< 55/2
aux(1) =< 187/8
s(8) =< 440/29
aux(5) =< 641/36
aux(2) =< 4727/96
aux(7) =< -132*V__01-660*V__0+26158
aux(5) =< -48*V__01-240*V__0+38113/4
aux(7) =< -44*V__01-220*V__0+5786
aux(1) =< -42*V__01-210*V__0+10601/2
aux(2) =< -42*V__01-210*V__0+282391/32
aux(5) =< -16*V__01-80*V__0+8429/4
aux(2) =< -14*V__01-70*V__0+62123/32
aux(4) =< -12*V__01-60*V__0+1988
aux(8) =< -12*V__01-60*V__0+2053
s(7) =< -12*V__01-60*V__0+3131/2
it(12) =< -6*V__01-30*V__0+2053/2
aux(4) =< -4*V__01-20*V__0+448
aux(8) =< -4*V__01-20*V__0+461
s(7) =< -4*V__01-20*V__0+727/2
it(12) =< -2*V__01-10*V__0+461/2
it(11) =< -V__01-5*V__0+49
it(11) =< -V__01-5*V__0+119
aux(3) =< -V__01-5*V__0+1213/12
it(13) =< -V__01/7-5/7*V__0+39/7
it(13) =< -V__01/7-5/7*V__0+69/7
it(14) =< V__01/12-V__0/12+1/12
aux(9) =< -14*V__01-70*V__0+2473/2
aux(10) =< -V__01-5*V__0+545/12
aux(1) =< aux(9)
aux(6) =< aux(9)
aux(3) =< aux(10)
aux(6) =< aux(10)
s(8) =< aux(7)
s(12) =< aux(7)
s(9) =< aux(8)
s(12) =< aux(8)
it(11) =< aux(4)
it(12) =< aux(4)
it(11) =< aux(5)
it(12) =< aux(5)
s(7) =< it(12)*(3/8)+aux(2)
s(7) =< it(12)*(3/8)+aux(1)
s(7) =< it(11)*aux(3)
s(12) =< it(13)*aux(6)

  with precondition: [B=3,35>=5*V__0+V__01,V__01>=2*V__0+7,V__01>=V__0] 

* Chain [[14],[11,12],15]: 1*it(11)+1*it(12)+1*it(14)+1*s(7)+1*s(8)+1*s(9)+0
  Such that:aux(3) =< 25/2
aux(2) =< -97/96*V__01-485/96*V__0+16745/96
s(7) =< -47/24*V__01-235/24*V__0+737/2
aux(5) =< -29/24*V__01-145/24*V__0+461/2
s(7) =< -13/4*V__01-65/4*V__0+2311/4
aux(4) =< -13/6*V__01-65/6*V__0+2311/6
aux(5) =< -7/4*V__01-35/4*V__0+1273/4
aux(4) =< -7/6*V__01-35/6*V__0+1273/6
aux(2) =< -7/36*V__01-35/36*V__0+4055/96
aux(1) =< -7/48*V__01-35/48*V__0+145/8
it(12) =< -V__01/2-5/2*V__0+199/2
aux(3) =< -V__01/2-5/2*V__0+935/12
s(9) =< -V__01/6-5/6*V__0+29
s(7) =< -V__01/6-5/6*V__0+43/2
aux(3) =< -V__01/12-5/12*V__0+125/12
it(14) =< V__01/12-V__0/12+1/12
aux(11) =< -3*V__01-15*V__0+570
aux(12) =< -V__01-5*V__0+361/2
aux(13) =< -29/12*V__01-145/12*V__0+951/2
aux(14) =< -V__01/2-5/2*V__0+151/2
it(11) =< aux(11)
s(8) =< aux(11)
aux(3) =< aux(12)
it(11) =< aux(12)
it(12) =< aux(13)
s(8) =< aux(13)
aux(1) =< aux(14)
s(7) =< aux(14)
it(11) =< aux(4)
it(12) =< aux(4)
it(11) =< aux(5)
it(12) =< aux(5)
s(7) =< it(12)*(3/8)+aux(2)
s(7) =< it(12)*(3/8)+aux(1)
s(7) =< it(11)*aux(3)

  with precondition: [B=3,27>=V__0,173>=5*V__0+V__01,V__01>=V__0,V__01+5*V__0+36>=0] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< V__01/12-V__0/12+1/12
it(14) =< -V__0/2+15

  with precondition: [B=3,29>=V__0,V__01>=V__0,V__01+5*V__0>=168] 

* Chain [[13],[11,12],15]: 1*it(11)+1*it(12)+1*it(13)+1*s(7)+1*s(8)+1*s(9)+1*s(12)+0
  Such that:s(9) =< 35
aux(4) =< 34/3
it(12) =< 35/4
s(7) =< 55/2
aux(1) =< 187/8
s(8) =< 440/29
aux(5) =< 641/36
aux(2) =< 4727/96
aux(5) =< -4*V__01-48*V__0+7309/4
aux(4) =< -V__01-12*V__0+378
s(7) =< -V__01-12*V__0+587/2
aux(1) =< -7/2*V__01-42*V__0+1983/2
aux(2) =< -7/2*V__01-42*V__0+54283/32
aux(6) =< -3/14*V__01-4/7*V__0+5
aux(6) =< -V__01/2+7
it(11) =< -V__01/2-6*V__0+189
it(12) =< -V__01/2-6*V__0+391/2
aux(3) =< -V__01/2-6*V__0+1709/12
aux(3) =< V__01/2-V__0+125/12
it(11) =< V__01/4-V__0/2+7
it(13) =< V__01/14-V__0/7+4/7
aux(7) =< -11*V__01-132*V__0+5016
aux(8) =< -V__01-12*V__0+391
s(8) =< aux(7)
s(12) =< aux(7)
s(9) =< aux(8)
s(12) =< aux(8)
it(11) =< aux(4)
it(12) =< aux(4)
it(11) =< aux(5)
it(12) =< aux(5)
s(7) =< it(12)*(3/8)+aux(2)
s(7) =< it(12)*(3/8)+aux(1)
s(7) =< it(11)*aux(3)
s(12) =< it(13)*aux(6)

  with precondition: [B=3,V__01+7>=2*V__0,V__0>=V__01+1] 

* Chain [[11,12],15]: 1*it(11)+1*it(12)+1*s(7)+1*s(8)+1*s(9)+0
  Such that:aux(3) =< -V__01+V__0+1/2
s(8) =< -113/348*V__01-21/116*V__0+5171/348
aux(2) =< -97/96*V__01-5/32*V__0+3115/96
s(7) =< -13/12*V__01-V__0/4+451/12
aux(5) =< -7/36*V__01-V__0/4+493/36
it(12) =< -5/48*V__01-11/48*V__0+169/16
s(8) =< -3/29*V__01-8/29*V__0+360/29
aux(3) =< -V__01/2+65/12
aux(1) =< -V__01/2-3/8*V__0+111/8
s(7) =< -V__01/2-V__0/2+35/2
s(9) =< -V__01/6-5/6*V__0+29
it(12) =< V__01/24-7/24*V__0+33/4
s(9) =< 23/144*V__01-161/144*V__0+5083/144
aux(4) =< -V__0/3+10
it(11) =< -V__0/4+15/2
it(11) =< aux(4)
it(12) =< aux(4)
it(11) =< aux(5)
it(12) =< aux(5)
s(7) =< it(12)*(3/8)+aux(2)
s(7) =< it(12)*(3/8)+aux(1)
s(7) =< it(11)*aux(3)

  with precondition: [B=3,29>=V__0,V__0>=V__01+1,2*V__0>=V__01+8] 

* Chain [15]: 0
  with precondition: [B=3,V__0>=30] 


#### Cost of chains of eval_complex_bb0_in(V_a,V_b,B):
* Chain [21]: 1*s(13)+0
  Such that:s(13) =< -V_a/2+15
s(13) =< -V_a/12+V_b/12+1/12

  with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 

* Chain [20]: 1*s(15)+1*s(17)+1*s(19)+1*s(21)+1*s(23)+0
  Such that:s(14) =< V_a-V_b+1/2
s(21) =< -161/144*V_a+23/144*V_b+5083/144
s(15) =< -21/116*V_a-113/348*V_b+5171/348
s(19) =< -11/48*V_a-5/48*V_b+169/16
s(15) =< -8/29*V_a-3/29*V_b+360/29
s(19) =< -7/24*V_a+V_b/24+33/4
s(21) =< -5/6*V_a-V_b/6+29
s(16) =< -5/32*V_a-97/96*V_b+3115/96
s(20) =< -3/8*V_a-V_b/2+111/8
s(17) =< -V_a/2-V_b/2+35/2
s(22) =< -V_a/3+10
s(23) =< -V_a/4+15/2
s(17) =< -V_a/4-13/12*V_b+451/12
s(18) =< -V_a/4-7/36*V_b+493/36
s(17) =< -V_b+17
s(16) =< -209/192*V_b+3055/96
s(21) =< -115/288*V_b+4439/144
s(20) =< -11/16*V_b+99/8
s(19) =< -5/48*V_b+85/12
s(14) =< -V_b/2+65/12
s(23) =< s(22)
s(19) =< s(22)
s(23) =< s(18)
s(19) =< s(18)
s(17) =< s(19)*(3/8)+s(16)
s(17) =< s(19)*(3/8)+s(20)
s(17) =< s(23)*s(14)

  with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 

* Chain [19]: 1*s(26)+1*s(30)+1*s(31)+1*s(32)+1*s(37)+1*s(38)+0
  Such that:s(24) =< 25/2
s(26) =< 55/2
s(24) =< 161/12
s(36) =< 187/2
s(29) =< 187/8
s(24) =< 1151/12
s(25) =< 20237/96
s(33) =< -15*V_a-3*V_b+570
s(34) =< -5*V_a-V_b+361/2
s(25) =< -485/96*V_a-97/96*V_b+16745/96
s(26) =< -235/24*V_a-47/24*V_b+737/2
s(35) =< -145/12*V_a-29/12*V_b+951/2
s(27) =< -145/24*V_a-29/24*V_b+461/2
s(26) =< -65/4*V_a-13/4*V_b+2311/4
s(27) =< -35/4*V_a-7/4*V_b+1273/4
s(28) =< -35/6*V_a-7/6*V_b+1273/6
s(25) =< -35/36*V_a-7/36*V_b+4055/96
s(29) =< -35/48*V_a-7/48*V_b+145/8
s(36) =< -5/2*V_a-V_b/2+151/2
s(30) =< -5/2*V_a-V_b/2+199/2
s(24) =< -5/2*V_a-V_b/2+935/12
s(31) =< -5/6*V_a-V_b/6+29
s(26) =< -5/6*V_a-V_b/6+43/2
s(24) =< -5/12*V_a-V_b/12+125/12
s(32) =< -V_a/12+V_b/12+1/12
s(37) =< s(33)
s(38) =< s(33)
s(24) =< s(34)
s(37) =< s(34)
s(30) =< s(35)
s(38) =< s(35)
s(29) =< s(36)
s(26) =< s(36)
s(37) =< s(28)
s(30) =< s(28)
s(37) =< s(27)
s(30) =< s(27)
s(26) =< s(30)*(3/8)+s(25)
s(26) =< s(30)*(3/8)+s(29)
s(26) =< s(37)*s(24)

  with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 

* Chain [18]: 0
  with precondition: [V_a>=30] 

* Chain [17]: 1*s(39)+1*s(41)+1*s(42)+1*s(44)+1*s(49)+1*s(51)+1*s(52)+1*s(56)+0
  Such that:s(39) =< 35
s(40) =< 34/3
s(41) =< 35/4
s(42) =< 55/2
s(43) =< 187/8
s(44) =< 440/29
s(45) =< 641/36
s(46) =< 4727/96
s(47) =< -220*V_a-44*V_b+5786
s(43) =< -210*V_a-42*V_b+10601/2
s(45) =< -80*V_a-16*V_b+8429/4
s(53) =< -70*V_a-14*V_b+2473/2
s(46) =< -70*V_a-14*V_b+62123/32
s(40) =< -20*V_a-4*V_b+448
s(48) =< -20*V_a-4*V_b+461
s(42) =< -20*V_a-4*V_b+727/2
s(41) =< -10*V_a-2*V_b+461/2
s(49) =< -5*V_a-V_b+49
s(54) =< -5*V_a-V_b+545/12
s(50) =< -5*V_a-V_b+1213/12
s(51) =< -5/7*V_a-V_b/7+39/7
s(52) =< -V_a/12+V_b/12+1/12
s(43) =< s(53)
s(55) =< s(53)
s(50) =< s(54)
s(55) =< s(54)
s(44) =< s(47)
s(56) =< s(47)
s(39) =< s(48)
s(56) =< s(48)
s(49) =< s(40)
s(41) =< s(40)
s(49) =< s(45)
s(41) =< s(45)
s(42) =< s(41)*(3/8)+s(46)
s(42) =< s(41)*(3/8)+s(43)
s(42) =< s(49)*s(50)
s(56) =< s(51)*s(55)

  with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 

* Chain [16]: 1*s(57)+1*s(59)+1*s(60)+1*s(62)+1*s(66)+1*s(68)+1*s(71)+0
  Such that:s(57) =< 35
s(58) =< 34/3
s(59) =< 35/4
s(60) =< 55/2
s(61) =< 187/8
s(62) =< 440/29
s(63) =< 641/36
s(64) =< 4727/96
s(69) =< -132*V_a-11*V_b+5016
s(63) =< -48*V_a-4*V_b+7309/4
s(61) =< -42*V_a-7/2*V_b+1983/2
s(64) =< -42*V_a-7/2*V_b+54283/32
s(58) =< -12*V_a-V_b+378
s(70) =< -12*V_a-V_b+391
s(60) =< -12*V_a-V_b+587/2
s(59) =< -6*V_a-V_b/2+391/2
s(67) =< -V_a+V_b/2+125/12
s(65) =< -4/7*V_a-3/14*V_b+5
s(66) =< -V_a/2+V_b/4+7
s(68) =< -V_a/7+V_b/14+4/7
s(65) =< -V_b/2+7
s(62) =< s(69)
s(71) =< s(69)
s(57) =< s(70)
s(71) =< s(70)
s(66) =< s(58)
s(59) =< s(58)
s(66) =< s(63)
s(59) =< s(63)
s(60) =< s(59)*(3/8)+s(64)
s(60) =< s(59)*(3/8)+s(61)
s(60) =< s(66)*s(67)
s(71) =< s(68)*s(65)

  with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 


#### Cost of chains of eval_complex_start(V_a,V_b,B):
* Chain [27]: 1*s(72)+0
  Such that:s(72) =< -V_a/2+15
s(72) =< -V_a/12+V_b/12+1/12

  with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 

* Chain [26]: 1*s(74)+1*s(75)+1*s(76)+1*s(79)+1*s(81)+0
  Such that:s(73) =< V_a-V_b+1/2
s(74) =< -161/144*V_a+23/144*V_b+5083/144
s(75) =< -21/116*V_a-113/348*V_b+5171/348
s(76) =< -11/48*V_a-5/48*V_b+169/16
s(75) =< -8/29*V_a-3/29*V_b+360/29
s(76) =< -7/24*V_a+V_b/24+33/4
s(74) =< -5/6*V_a-V_b/6+29
s(77) =< -5/32*V_a-97/96*V_b+3115/96
s(78) =< -3/8*V_a-V_b/2+111/8
s(79) =< -V_a/2-V_b/2+35/2
s(80) =< -V_a/3+10
s(81) =< -V_a/4+15/2
s(79) =< -V_a/4-13/12*V_b+451/12
s(82) =< -V_a/4-7/36*V_b+493/36
s(79) =< -V_b+17
s(77) =< -209/192*V_b+3055/96
s(74) =< -115/288*V_b+4439/144
s(78) =< -11/16*V_b+99/8
s(76) =< -5/48*V_b+85/12
s(73) =< -V_b/2+65/12
s(81) =< s(80)
s(76) =< s(80)
s(81) =< s(82)
s(76) =< s(82)
s(79) =< s(76)*(3/8)+s(77)
s(79) =< s(76)*(3/8)+s(78)
s(79) =< s(81)*s(73)

  with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 

* Chain [25]: 1*s(84)+1*s(93)+1*s(94)+1*s(95)+1*s(96)+1*s(97)+0
  Such that:s(83) =< 25/2
s(84) =< 55/2
s(83) =< 161/12
s(85) =< 187/2
s(86) =< 187/8
s(83) =< 1151/12
s(87) =< 20237/96
s(88) =< -15*V_a-3*V_b+570
s(89) =< -5*V_a-V_b+361/2
s(87) =< -485/96*V_a-97/96*V_b+16745/96
s(84) =< -235/24*V_a-47/24*V_b+737/2
s(90) =< -145/12*V_a-29/12*V_b+951/2
s(91) =< -145/24*V_a-29/24*V_b+461/2
s(84) =< -65/4*V_a-13/4*V_b+2311/4
s(91) =< -35/4*V_a-7/4*V_b+1273/4
s(92) =< -35/6*V_a-7/6*V_b+1273/6
s(87) =< -35/36*V_a-7/36*V_b+4055/96
s(86) =< -35/48*V_a-7/48*V_b+145/8
s(85) =< -5/2*V_a-V_b/2+151/2
s(93) =< -5/2*V_a-V_b/2+199/2
s(83) =< -5/2*V_a-V_b/2+935/12
s(94) =< -5/6*V_a-V_b/6+29
s(84) =< -5/6*V_a-V_b/6+43/2
s(83) =< -5/12*V_a-V_b/12+125/12
s(95) =< -V_a/12+V_b/12+1/12
s(96) =< s(88)
s(97) =< s(88)
s(83) =< s(89)
s(96) =< s(89)
s(93) =< s(90)
s(97) =< s(90)
s(86) =< s(85)
s(84) =< s(85)
s(96) =< s(92)
s(93) =< s(92)
s(96) =< s(91)
s(93) =< s(91)
s(84) =< s(93)*(3/8)+s(87)
s(84) =< s(93)*(3/8)+s(86)
s(84) =< s(96)*s(83)

  with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 

* Chain [24]: 0
  with precondition: [V_a>=30] 

* Chain [23]: 1*s(98)+1*s(100)+1*s(101)+1*s(103)+1*s(109)+1*s(112)+1*s(113)+1*s(115)+0
  Such that:s(98) =< 35
s(99) =< 34/3
s(100) =< 35/4
s(101) =< 55/2
s(102) =< 187/8
s(103) =< 440/29
s(104) =< 641/36
s(105) =< 4727/96
s(106) =< -220*V_a-44*V_b+5786
s(102) =< -210*V_a-42*V_b+10601/2
s(104) =< -80*V_a-16*V_b+8429/4
s(107) =< -70*V_a-14*V_b+2473/2
s(105) =< -70*V_a-14*V_b+62123/32
s(99) =< -20*V_a-4*V_b+448
s(108) =< -20*V_a-4*V_b+461
s(101) =< -20*V_a-4*V_b+727/2
s(100) =< -10*V_a-2*V_b+461/2
s(109) =< -5*V_a-V_b+49
s(110) =< -5*V_a-V_b+545/12
s(111) =< -5*V_a-V_b+1213/12
s(112) =< -5/7*V_a-V_b/7+39/7
s(113) =< -V_a/12+V_b/12+1/12
s(102) =< s(107)
s(114) =< s(107)
s(111) =< s(110)
s(114) =< s(110)
s(103) =< s(106)
s(115) =< s(106)
s(98) =< s(108)
s(115) =< s(108)
s(109) =< s(99)
s(100) =< s(99)
s(109) =< s(104)
s(100) =< s(104)
s(101) =< s(100)*(3/8)+s(105)
s(101) =< s(100)*(3/8)+s(102)
s(101) =< s(109)*s(111)
s(115) =< s(112)*s(114)

  with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 

* Chain [22]: 1*s(116)+1*s(118)+1*s(119)+1*s(121)+1*s(128)+1*s(129)+1*s(130)+0
  Such that:s(116) =< 35
s(117) =< 34/3
s(118) =< 35/4
s(119) =< 55/2
s(120) =< 187/8
s(121) =< 440/29
s(122) =< 641/36
s(123) =< 4727/96
s(124) =< -132*V_a-11*V_b+5016
s(122) =< -48*V_a-4*V_b+7309/4
s(120) =< -42*V_a-7/2*V_b+1983/2
s(123) =< -42*V_a-7/2*V_b+54283/32
s(117) =< -12*V_a-V_b+378
s(125) =< -12*V_a-V_b+391
s(119) =< -12*V_a-V_b+587/2
s(118) =< -6*V_a-V_b/2+391/2
s(126) =< -V_a+V_b/2+125/12
s(127) =< -4/7*V_a-3/14*V_b+5
s(128) =< -V_a/2+V_b/4+7
s(129) =< -V_a/7+V_b/14+4/7
s(127) =< -V_b/2+7
s(121) =< s(124)
s(130) =< s(124)
s(116) =< s(125)
s(130) =< s(125)
s(128) =< s(117)
s(118) =< s(117)
s(128) =< s(122)
s(118) =< s(122)
s(119) =< s(118)*(3/8)+s(123)
s(119) =< s(118)*(3/8)+s(120)
s(119) =< s(128)*s(126)
s(130) =< s(129)*s(127)

  with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 


Closed-form bounds of eval_complex_start(V_a,V_b,B): 
-------------------------------------
* Chain [27] with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 
    - Upper bound: -V_a/2+15 
    - Complexity: n 
* Chain [26] with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 
    - Upper bound: -V_a/4+15/2+(-11/48*V_a-5/48*V_b+169/16+(-21/116*V_a-113/348*V_b+5171/348+nat(-161/144*V_a+23/144*V_b+5083/144))+nat(-V_a/2-V_b/2+35/2)) 
    - Complexity: n 
* Chain [25] with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 
    - Upper bound: -401/12*V_a-79/12*V_b+15553/12 
    - Complexity: n 
* Chain [24] with precondition: [V_a>=30] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 
    - Upper bound: -18547/84*V_a-3701/84*V_b+3586651/609 
    - Complexity: n 
* Chain [22] with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 
    - Upper bound: -925/7*V_a-153/14*V_b+12458501/2436 
    - Complexity: n 

### Maximum cost of eval_complex_start(V_a,V_b,B): max([max([nat(-V_a/2+15),nat(-21/116*V_a-113/348*V_b+5171/348)+nat(-161/144*V_a+23/144*V_b+5083/144)+nat(-11/48*V_a-5/48*V_b+169/16)+nat(-V_a/2-V_b/2+35/2)+nat(-V_a/4+15/2),34019/348+nat(-V_a/7+V_b/14+4/7)+nat(-132*V_a-11*V_b+5016)]),55/2+nat(-V_a/12+V_b/12+1/12)+max([nat(-15*V_a-3*V_b+570)*2+nat(-5/2*V_a-V_b/2+199/2)+nat(-5/6*V_a-V_b/6+29),24449/348+nat(-220*V_a-44*V_b+5786)+nat(-5/7*V_a-V_b/7+39/7)])]) 
Asymptotic class: n 
* Total analysis performed in 622 ms.