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


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_set_color_ht_extracted_bb4_in/3]
1. recursive  : [eval_set_color_ht_extracted_bb2_in/3,eval_set_color_ht_extracted_bb3_in/3,eval_set_color_ht_extracted_bb4_in_loop_cont/4]
2. recursive  : [eval_set_color_ht_extracted_bb1_in/3,eval_set_color_ht_extracted_bb2_in_loop_cont/6,eval_set_color_ht_extracted_bb5_in/5]
3. non_recursive  : [eval_set_color_ht_extracted_stop/1]
4. non_recursive  : [eval_set_color_ht_extracted_bb6_in/1]
5. non_recursive  : [eval_set_color_ht_extracted_bb1_in_loop_cont/2]
6. non_recursive  : [eval_set_color_ht_extracted_bb0_in/3]
7. non_recursive  : [eval_set_color_ht_extracted_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_set_color_ht_extracted_bb4_in/3
1. SCC is partially evaluated into eval_set_color_ht_extracted_bb2_in/3
2. SCC is partially evaluated into eval_set_color_ht_extracted_bb1_in/3
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_set_color_ht_extracted_bb0_in/3
7. SCC is partially evaluated into eval_set_color_ht_extracted_start/3

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

### Specialization of cost equations eval_set_color_ht_extracted_bb4_in/3 
* CE 9 is refined into CE [10] 
* CE 8 is refined into CE [11] 


### Cost equations --> "Loop" of eval_set_color_ht_extracted_bb4_in/3 
* CEs [11] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR eval_set_color_ht_extracted_bb4_in(V_x_0,V_i_0,B) 
* RF of phase [10]: [V_i_0]

#### Partial ranking functions of CR eval_set_color_ht_extracted_bb4_in(V_x_0,V_i_0,B) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V_i_0


### Specialization of cost equations eval_set_color_ht_extracted_bb2_in/3 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 5 is refined into CE [14] 


### Cost equations --> "Loop" of eval_set_color_ht_extracted_bb2_in/3 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR eval_set_color_ht_extracted_bb2_in(V_x_0,B,C) 
* RF of phase [12]: [V_x_0-7]

#### Partial ranking functions of CR eval_set_color_ht_extracted_bb2_in(V_x_0,B,C) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V_x_0-7


### Specialization of cost equations eval_set_color_ht_extracted_bb1_in/3 
* CE 4 is refined into CE [15,16,17,18] 
* CE 3 is refined into CE [19,20,21,22] 


### Cost equations --> "Loop" of eval_set_color_ht_extracted_bb1_in/3 
* CEs [21] --> Loop 15 
* CEs [20] --> Loop 16 
* CEs [22] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [16] --> Loop 20 
* CEs [18] --> Loop 21 
* CEs [15] --> Loop 22 

### Ranking functions of CR eval_set_color_ht_extracted_bb1_in(V_w,V_y_0,B) 
* RF of phase [15,16]: [V_y_0-1]
* RF of phase [17]: [V_y_0-1]
* RF of phase [18]: [V_y_0-1]

#### Partial ranking functions of CR eval_set_color_ht_extracted_bb1_in(V_w,V_y_0,B) 
* Partial RF of phase [15,16]:
  - RF of loop [15:1,16:1]:
    V_y_0-1
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    V_y_0-1
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    V_y_0-1


### Specialization of cost equations eval_set_color_ht_extracted_bb0_in/3 
* CE 2 is refined into CE [23,24,25,26,27,28,29,30] 


### Cost equations --> "Loop" of eval_set_color_ht_extracted_bb0_in/3 
* CEs [30] --> Loop 23 
* CEs [29] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [24] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [25] --> Loop 29 
* CEs [23] --> Loop 30 

### Ranking functions of CR eval_set_color_ht_extracted_bb0_in(V_h,V_w,B) 

#### Partial ranking functions of CR eval_set_color_ht_extracted_bb0_in(V_h,V_w,B) 


### Specialization of cost equations eval_set_color_ht_extracted_start/3 
* CE 1 is refined into CE [31,32,33,34,35,36,37,38] 


### Cost equations --> "Loop" of eval_set_color_ht_extracted_start/3 
* CEs [38] --> Loop 31 
* CEs [37] --> Loop 32 
* CEs [36] --> Loop 33 
* CEs [35] --> Loop 34 
* CEs [34] --> Loop 35 
* CEs [33] --> Loop 36 
* CEs [32] --> Loop 37 
* CEs [31] --> Loop 38 

### Ranking functions of CR eval_set_color_ht_extracted_start(V_h,V_w,B) 

#### Partial ranking functions of CR eval_set_color_ht_extracted_start(V_h,V_w,B) 


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

#### Cost of chains of eval_set_color_ht_extracted_bb4_in(V_x_0,V_i_0,B):
* Chain [[10],11]: 1*it(10)+0
  Such that:it(10) =< V_i_0

  with precondition: [B=2,8>=V_i_0,V_i_0>=1,V_x_0>=V_i_0] 


#### Cost of chains of eval_set_color_ht_extracted_bb2_in(V_x_0,B,C):
* Chain [[12],14]: 1*it(12)+1*s(3)+0
  Such that:aux(4) =< V_x_0
it(12) =< aux(4)
s(3) =< aux(4)*8

  with precondition: [B=3,C=0,V_x_0>=8] 

* Chain [[12],13,14]: 1*it(12)+1*s(3)+1*s(4)+1
  Such that:s(4) =< 7
aux(5) =< V_x_0
s(4) =< aux(5)
it(12) =< aux(5)
s(3) =< aux(5)*8

  with precondition: [B=3,C=0,V_x_0>=9] 

* Chain [14]: 0
  with precondition: [B=3,V_x_0=C,0>=V_x_0] 

* Chain [13,14]: 1*s(4)+1
  Such that:s(4) =< V_x_0

  with precondition: [B=3,C=0,7>=V_x_0,V_x_0>=1] 


#### Cost of chains of eval_set_color_ht_extracted_bb1_in(V_w,V_y_0,B):
* Chain [[18],22]: 2*it(18)+1*s(5)+1*s(8)+1
  Such that:s(5) =< V_w
it(18) =< V_y_0
s(8) =< 7*V_y_0

  with precondition: [B=4,7>=V_w,V_w>=1,V_y_0>=2] 

* Chain [[17],21]: 1*it(17)+0
  Such that:it(17) =< V_y_0

  with precondition: [B=4,0>=V_w,V_y_0>=2] 

* Chain [[15,16],20]: 3*it(15)+1*s(10)+1*s(11)+1*s(26)+1*s(27)+1*s(28)+1*s(30)+1*s(31)+0
  Such that:aux(11) =< V_w
aux(12) =< V_y_0
s(10) =< aux(11)
s(11) =< aux(11)*8
it(15) =< aux(12)
aux(8) =< aux(11)
s(29) =< it(15)*aux(11)
s(26) =< aux(12)*7
s(32) =< it(15)*aux(8)
s(30) =< s(32)
s(31) =< s(32)*8
s(26) =< s(29)
s(27) =< s(29)
s(28) =< s(29)*8

  with precondition: [B=4,V_w>=8,V_y_0>=2] 

* Chain [[15,16],19]: 3*it(15)+1*s(26)+1*s(27)+1*s(28)+1*s(30)+1*s(31)+1*s(33)+1*s(35)+1*s(36)+1
  Such that:s(33) =< 7
aux(13) =< V_w
aux(14) =< V_y_0
s(33) =< aux(13)
s(35) =< aux(13)
s(36) =< aux(13)*8
it(15) =< aux(14)
aux(8) =< aux(13)
s(29) =< it(15)*aux(13)
s(26) =< aux(14)*7
s(32) =< it(15)*aux(8)
s(30) =< s(32)
s(31) =< s(32)*8
s(26) =< s(29)
s(27) =< s(29)
s(28) =< s(29)*8

  with precondition: [B=4,V_w>=9,V_y_0>=2] 

* Chain [22]: 1*s(5)+1
  Such that:s(5) =< V_w

  with precondition: [B=4,7>=V_w,1>=V_y_0,V_w>=1] 

* Chain [21]: 0
  with precondition: [B=4,0>=V_w,1>=V_y_0] 

* Chain [20]: 1*s(10)+1*s(11)+0
  Such that:s(9) =< V_w
s(10) =< s(9)
s(11) =< s(9)*8

  with precondition: [B=4,1>=V_y_0,V_w>=8] 

* Chain [19]: 1*s(33)+1*s(35)+1*s(36)+1
  Such that:s(33) =< 7
s(34) =< V_w
s(33) =< s(34)
s(35) =< s(34)
s(36) =< s(34)*8

  with precondition: [B=4,1>=V_y_0,V_w>=9] 


#### Cost of chains of eval_set_color_ht_extracted_bb0_in(V_h,V_w,B):
* Chain [30]: 1*s(37)+1
  Such that:s(37) =< V_w

  with precondition: [1>=V_h,7>=V_w,V_w>=1] 

* Chain [29]: 0
  with precondition: [1>=V_h,0>=V_w] 

* Chain [28]: 1*s(39)+1*s(40)+0
  Such that:s(38) =< V_w
s(39) =< s(38)
s(40) =< s(38)*8

  with precondition: [1>=V_h,V_w>=8] 

* Chain [27]: 1*s(41)+1*s(43)+1*s(44)+1
  Such that:s(41) =< 7
s(42) =< V_w
s(41) =< s(42)
s(43) =< s(42)
s(44) =< s(42)*8

  with precondition: [1>=V_h,V_w>=9] 

* Chain [26]: 1*s(45)+2*s(46)+1*s(47)+1
  Such that:s(46) =< V_h
s(47) =< 7*V_h
s(45) =< V_w

  with precondition: [7>=V_w,V_h>=2,V_w>=1] 

* Chain [25]: 1*s(48)+0
  Such that:s(48) =< V_h

  with precondition: [0>=V_w,V_h>=2] 

* Chain [24]: 1*s(51)+1*s(52)+3*s(53)+1*s(56)+1*s(58)+1*s(59)+1*s(60)+1*s(61)+0
  Such that:s(50) =< V_h
s(49) =< V_w
s(51) =< s(49)
s(52) =< s(49)*8
s(53) =< s(50)
s(54) =< s(49)
s(55) =< s(53)*s(49)
s(56) =< s(50)*7
s(57) =< s(53)*s(54)
s(58) =< s(57)
s(59) =< s(57)*8
s(56) =< s(55)
s(60) =< s(55)
s(61) =< s(55)*8

  with precondition: [V_h>=2,V_w>=8] 

* Chain [23]: 1*s(62)+1*s(65)+1*s(66)+3*s(67)+1*s(70)+1*s(72)+1*s(73)+1*s(74)+1*s(75)+1
  Such that:s(62) =< 7
s(64) =< V_h
s(63) =< V_w
s(62) =< s(63)
s(65) =< s(63)
s(66) =< s(63)*8
s(67) =< s(64)
s(68) =< s(63)
s(69) =< s(67)*s(63)
s(70) =< s(64)*7
s(71) =< s(67)*s(68)
s(72) =< s(71)
s(73) =< s(71)*8
s(70) =< s(69)
s(74) =< s(69)
s(75) =< s(69)*8

  with precondition: [V_h>=2,V_w>=9] 


#### Cost of chains of eval_set_color_ht_extracted_start(V_h,V_w,B):
* Chain [38]: 1*s(76)+1
  Such that:s(76) =< V_w

  with precondition: [1>=V_h,7>=V_w,V_w>=1] 

* Chain [37]: 0
  with precondition: [1>=V_h,0>=V_w] 

* Chain [36]: 1*s(78)+1*s(79)+0
  Such that:s(77) =< V_w
s(78) =< s(77)
s(79) =< s(77)*8

  with precondition: [1>=V_h,V_w>=8] 

* Chain [35]: 1*s(80)+1*s(82)+1*s(83)+1
  Such that:s(80) =< 7
s(81) =< V_w
s(80) =< s(81)
s(82) =< s(81)
s(83) =< s(81)*8

  with precondition: [1>=V_h,V_w>=9] 

* Chain [34]: 2*s(84)+1*s(85)+1*s(86)+1
  Such that:s(84) =< V_h
s(85) =< 7*V_h
s(86) =< V_w

  with precondition: [7>=V_w,V_h>=2,V_w>=1] 

* Chain [33]: 1*s(87)+0
  Such that:s(87) =< V_h

  with precondition: [0>=V_w,V_h>=2] 

* Chain [32]: 1*s(90)+1*s(91)+3*s(92)+1*s(95)+1*s(97)+1*s(98)+1*s(99)+1*s(100)+0
  Such that:s(88) =< V_h
s(89) =< V_w
s(90) =< s(89)
s(91) =< s(89)*8
s(92) =< s(88)
s(93) =< s(89)
s(94) =< s(92)*s(89)
s(95) =< s(88)*7
s(96) =< s(92)*s(93)
s(97) =< s(96)
s(98) =< s(96)*8
s(95) =< s(94)
s(99) =< s(94)
s(100) =< s(94)*8

  with precondition: [V_h>=2,V_w>=8] 

* Chain [31]: 1*s(101)+1*s(104)+1*s(105)+3*s(106)+1*s(109)+1*s(111)+1*s(112)+1*s(113)+1*s(114)+1
  Such that:s(101) =< 7
s(102) =< V_h
s(103) =< V_w
s(101) =< s(103)
s(104) =< s(103)
s(105) =< s(103)*8
s(106) =< s(102)
s(107) =< s(103)
s(108) =< s(106)*s(103)
s(109) =< s(102)*7
s(110) =< s(106)*s(107)
s(111) =< s(110)
s(112) =< s(110)*8
s(109) =< s(108)
s(113) =< s(108)
s(114) =< s(108)*8

  with precondition: [V_h>=2,V_w>=9] 


Closed-form bounds of eval_set_color_ht_extracted_start(V_h,V_w,B): 
-------------------------------------
* Chain [38] with precondition: [1>=V_h,7>=V_w,V_w>=1] 
    - Upper bound: V_w+1 
    - Complexity: n 
* Chain [37] with precondition: [1>=V_h,0>=V_w] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [36] with precondition: [1>=V_h,V_w>=8] 
    - Upper bound: 9*V_w 
    - Complexity: n 
* Chain [35] with precondition: [1>=V_h,V_w>=9] 
    - Upper bound: 9*V_w+8 
    - Complexity: n 
* Chain [34] with precondition: [7>=V_w,V_h>=2,V_w>=1] 
    - Upper bound: 9*V_h+V_w+1 
    - Complexity: n 
* Chain [33] with precondition: [0>=V_w,V_h>=2] 
    - Upper bound: V_h 
    - Complexity: n 
* Chain [32] with precondition: [V_h>=2,V_w>=8] 
    - Upper bound: 18*V_h*V_w+10*V_h+9*V_w 
    - Complexity: n^2 
* Chain [31] with precondition: [V_h>=2,V_w>=9] 
    - Upper bound: 10*V_h+8+18*V_h*V_w+9*V_w 
    - Complexity: n^2 

### Maximum cost of eval_set_color_ht_extracted_start(V_h,V_w,B): max([nat(V_h),nat(V_w)+1+max([nat(V_h)*2+nat(7*V_h),nat(V_h)*18*nat(V_w)+nat(V_h)*10+(nat(V_w)*8+7)])]) 
Asymptotic class: n^2 
* Total analysis performed in 272 ms.