/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_terminatorbubble_10/9,eval_terminatorbubble_9/9,eval_terminatorbubble_bb2_in/9,eval_terminatorbubble_bb3_in/9,eval_terminatorbubble_bb4_in/9,eval_terminatorbubble_bb5_in/9]
1. recursive  : [eval_terminatorbubble_bb1_in/11,eval_terminatorbubble_bb2_in_loop_cont/12,eval_terminatorbubble_bb6_in/11]
2. non_recursive  : [eval_terminatorbubble_stop/6]
3. non_recursive  : [eval_terminatorbubble_bb7_in/6]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_terminatorbubble_bb1_in_loop_cont/7]
6. non_recursive  : [eval_terminatorbubble_3/6]
7. non_recursive  : [eval_terminatorbubble_2/6]
8. non_recursive  : [eval_terminatorbubble_1/6]
9. non_recursive  : [eval_terminatorbubble_0/6]
10. non_recursive  : [eval_terminatorbubble_bb0_in/6]
11. non_recursive  : [eval_terminatorbubble_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_terminatorbubble_bb2_in/9
1. SCC is partially evaluated into eval_terminatorbubble_bb1_in/11
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_terminatorbubble_bb1_in_loop_cont/7
6. SCC is partially evaluated into eval_terminatorbubble_3/6
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is completely evaluated into other SCCs
11. SCC is partially evaluated into eval_terminatorbubble_start/6

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

### Specialization of cost equations eval_terminatorbubble_bb2_in/9 
* CE 17 is discarded (unfeasible) 
* CE 18 is discarded (unfeasible) 
* CE 14 is discarded (unfeasible) 
* CE 20 is refined into CE [21] 
* CE 19 is refined into CE [22] 
* CE 16 is refined into CE [23] 
* CE 15 is refined into CE [24] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb2_in/9 
* CEs [23] --> Loop 21 
* CEs [24] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [22] --> Loop 24 

### Ranking functions of CR eval_terminatorbubble_bb2_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E) 
* RF of phase [21,22]: [V_b_0-V_j_0,-V_j_0+V_size]

#### Partial ranking functions of CR eval_terminatorbubble_bb2_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E) 
* Partial RF of phase [21,22]:
  - RF of loop [21:1,22:1]:
    V_b_0-V_j_0
    -V_j_0+V_size
  - RF of loop [22:1]:
    V_b_0-V_t_0-1
    V_size-V_t_0-1


### Specialization of cost equations eval_terminatorbubble_bb1_in/11 
* CE 5 is discarded (unfeasible) 
* CE 7 is discarded (unfeasible) 
* CE 6 is refined into CE [25,26] 
* CE 10 is discarded (unfeasible) 
* CE 9 is discarded (unfeasible) 
* CE 8 is refined into CE [27,28] 
* CE 11 is refined into CE [29] 
* CE 4 is refined into CE [30] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb1_in/11 
* CEs [30] --> Loop 25 
* CEs [26] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27,29] --> Loop 28 
* CEs [25] --> Loop 29 

### Ranking functions of CR eval_terminatorbubble_bb1_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E,F,G) 
* RF of phase [25]: [V_b_0-1]

#### Partial ranking functions of CR eval_terminatorbubble_bb1_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E,F,G) 
* Partial RF of phase [25]:
  - RF of loop [25:1]:
    V_b_0-1


### Specialization of cost equations eval_terminatorbubble_bb1_in_loop_cont/7 
* CE 12 is refined into CE [31] 
* CE 13 is refined into CE [32] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb1_in_loop_cont/7 
* CEs [31] --> Loop 30 
* CEs [32] --> Loop 31 

### Ranking functions of CR eval_terminatorbubble_bb1_in_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR eval_terminatorbubble_bb1_in_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations eval_terminatorbubble_3/6 
* CE 3 is refined into CE [33,34,35,36,37,38,39] 
* CE 2 is refined into CE [40] 


### Cost equations --> "Loop" of eval_terminatorbubble_3/6 
* CEs [36,39] --> Loop 32 
* CEs [35,37,38] --> Loop 33 
* CEs [34] --> Loop 34 
* CEs [40] --> Loop 35 
* CEs [33] --> Loop 36 

### Ranking functions of CR eval_terminatorbubble_3(V_11,V_b_0,V_j_0,V_size,V_t_0,B) 

#### Partial ranking functions of CR eval_terminatorbubble_3(V_11,V_b_0,V_j_0,V_size,V_t_0,B) 


### Specialization of cost equations eval_terminatorbubble_start/6 
* CE 1 is refined into CE [41,42,43,44,45] 


### Cost equations --> "Loop" of eval_terminatorbubble_start/6 
* CEs [45] --> Loop 37 
* CEs [44] --> Loop 38 
* CEs [43] --> Loop 39 
* CEs [42] --> Loop 40 
* CEs [41] --> Loop 41 

### Ranking functions of CR eval_terminatorbubble_start(V_11,V_b_0,V_j_0,V_size,V_t_0,B) 

#### Partial ranking functions of CR eval_terminatorbubble_start(V_11,V_b_0,V_j_0,V_size,V_t_0,B) 


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

#### Cost of chains of eval_terminatorbubble_bb2_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E):
* Chain [[21,22],24]: 1*it(21)+1*it(22)+0
  Such that:aux(3) =< -V_j_0+V_size
it(22) =< -V_t_0+E
aux(5) =< -V_j_0+D
it(21) =< aux(5)
it(22) =< aux(5)
it(21) =< aux(3)
it(22) =< aux(3)

  with precondition: [B=2,V_b_0=D,V_t_0>=0,V_size>=V_b_0,V_b_0>=V_j_0+1,V_j_0>=V_t_0+1,E>=V_t_0,V_b_0>=E+1] 

* Chain [[21,22],23]: 1*it(21)+1*it(22)+0
  Such that:it(22) =< V_b_0-V_t_0
aux(3) =< -V_j_0+V_size
aux(6) =< V_b_0-V_j_0
it(21) =< aux(6)
it(22) =< aux(6)
it(21) =< aux(3)
it(22) =< aux(3)

  with precondition: [B=3,V_t_0>=0,V_size>=V_b_0,V_b_0>=V_j_0+1,V_j_0>=V_t_0+1] 

* Chain [24]: 0
  with precondition: [B=2,C=V_11,V_j_0=V_b_0,V_j_0=D,V_t_0=E,V_t_0>=0,V_size>=V_j_0,V_j_0>=V_t_0+1] 

* Chain [23]: 0
  with precondition: [B=3,V_t_0>=0,V_size>=V_b_0,V_b_0>=V_j_0,V_j_0>=V_t_0+1] 


#### Cost of chains of eval_terminatorbubble_bb1_in(V_11,V_b_0,V_j_0,V_size,V_t_0,B,C,D,E,F,G):
* Chain [[25],29]: 1*it(25)+1*s(9)+1*s(10)+0
  Such that:aux(7) =< F
aux(11) =< V_b_0
it(25) =< aux(11)
aux(7) =< aux(11)
aux(9) =< aux(7)-1
aux(8) =< aux(7)
s(12) =< it(25)*aux(7)
s(9) =< it(25)*aux(9)
s(11) =< it(25)*aux(8)
s(10) =< s(12)
s(9) =< s(12)
s(10) =< s(11)
s(9) =< s(11)

  with precondition: [B=4,D=1,E=1,G=0,V_size=F,V_b_0>=2,V_size>=V_b_0] 

* Chain [[25],28]: 1*it(25)+1*s(9)+1*s(10)+0
  Such that:aux(7) =< V_size
aux(12) =< V_b_0
it(25) =< aux(12)
aux(7) =< aux(12)
aux(9) =< aux(7)-1
aux(8) =< aux(7)
s(12) =< it(25)*aux(7)
s(9) =< it(25)*aux(9)
s(11) =< it(25)*aux(8)
s(10) =< s(12)
s(9) =< s(12)
s(10) =< s(11)
s(9) =< s(11)

  with precondition: [B=3,V_b_0>=2,V_size>=V_b_0] 

* Chain [[25],27]: 1*it(25)+1*s(9)+1*s(10)+2*s(13)+0
  Such that:aux(14) =< V_b_0
aux(15) =< V_size
it(25) =< aux(14)
aux(7) =< aux(15)
s(13) =< aux(14)
s(13) =< aux(15)
aux(7) =< aux(14)
aux(9) =< aux(7)-1
aux(8) =< aux(7)
s(12) =< it(25)*aux(7)
s(9) =< it(25)*aux(9)
s(11) =< it(25)*aux(8)
s(10) =< s(12)
s(9) =< s(12)
s(10) =< s(11)
s(9) =< s(11)

  with precondition: [B=3,V_b_0>=3,V_size>=V_b_0] 

* Chain [[25],26]: 1*it(25)+1*s(9)+1*s(10)+1*s(20)+0
  Such that:aux(10) =< V_b_0
it(25) =< V_b_0-D
s(19) =< D
aux(16) =< F
aux(7) =< aux(16)
s(20) =< s(19)
s(20) =< aux(16)
aux(7) =< aux(10)
it(25) =< aux(10)
aux(9) =< aux(7)-1
aux(8) =< aux(7)
s(12) =< it(25)*aux(7)
s(9) =< it(25)*aux(9)
s(11) =< it(25)*aux(8)
s(10) =< s(12)
s(9) =< s(12)
s(10) =< s(11)
s(9) =< s(11)

  with precondition: [B=4,G=0,D=E,V_size=F,D>=2,V_size>=V_b_0,V_b_0>=D+1] 

* Chain [29]: 0
  with precondition: [V_b_0=1,B=4,D=1,E=1,G=0,C=V_11,V_size=F,V_size>=1] 

* Chain [28]: 0
  with precondition: [B=3,V_b_0>=1,V_size>=V_b_0] 

* Chain [27]: 2*s(13)+0
  Such that:s(14) =< V_size
aux(13) =< V_b_0
s(13) =< aux(13)
s(13) =< s(14)

  with precondition: [B=3,V_b_0>=2,V_size>=V_b_0] 

* Chain [26]: 1*s(20)+0
  Such that:s(19) =< V_b_0
s(17) =< V_size
s(20) =< s(19)
s(20) =< s(17)

  with precondition: [B=4,G=0,V_b_0=D,V_b_0=E,V_size=F,V_b_0>=2,V_size>=V_b_0] 


#### Cost of chains of eval_terminatorbubble_bb1_in_loop_cont(A,B,C,D,E,F,G):
* Chain [31]: 0
  with precondition: [A=3] 

* Chain [30]: 0
  with precondition: [A=4] 


#### Cost of chains of eval_terminatorbubble_3(V_11,V_b_0,V_j_0,V_size,V_t_0,B):
* Chain [36]: 0
  with precondition: [V_size=1] 

* Chain [35]: 0
  with precondition: [0>=V_size] 

* Chain [34]: 0
  with precondition: [V_size>=1] 

* Chain [33]: 5*s(36)+2*s(41)+2*s(43)+0
  Such that:aux(22) =< V_size
s(36) =< aux(22)
s(38) =< aux(22)-1
s(39) =< aux(22)
s(40) =< s(36)*aux(22)
s(41) =< s(36)*s(38)
s(42) =< s(36)*s(39)
s(43) =< s(40)
s(41) =< s(40)
s(43) =< s(42)
s(41) =< s(42)

  with precondition: [V_size>=2] 

* Chain [32]: 5*s(58)+2*s(64)+2*s(66)+0
  Such that:aux(25) =< V_size
s(58) =< aux(25)
s(61) =< aux(25)-1
s(62) =< aux(25)
s(63) =< s(58)*aux(25)
s(64) =< s(58)*s(61)
s(65) =< s(58)*s(62)
s(66) =< s(63)
s(64) =< s(63)
s(66) =< s(65)
s(64) =< s(65)

  with precondition: [V_size>=3] 


#### Cost of chains of eval_terminatorbubble_start(V_11,V_b_0,V_j_0,V_size,V_t_0,B):
* Chain [41]: 0
  with precondition: [V_size=1] 

* Chain [40]: 0
  with precondition: [0>=V_size] 

* Chain [39]: 0
  with precondition: [V_size>=1] 

* Chain [38]: 5*s(80)+2*s(84)+2*s(86)+0
  Such that:s(79) =< V_size
s(80) =< s(79)
s(81) =< s(79)-1
s(82) =< s(79)
s(83) =< s(80)*s(79)
s(84) =< s(80)*s(81)
s(85) =< s(80)*s(82)
s(86) =< s(83)
s(84) =< s(83)
s(86) =< s(85)
s(84) =< s(85)

  with precondition: [V_size>=2] 

* Chain [37]: 5*s(88)+2*s(92)+2*s(94)+0
  Such that:s(87) =< V_size
s(88) =< s(87)
s(89) =< s(87)-1
s(90) =< s(87)
s(91) =< s(88)*s(87)
s(92) =< s(88)*s(89)
s(93) =< s(88)*s(90)
s(94) =< s(91)
s(92) =< s(91)
s(94) =< s(93)
s(92) =< s(93)

  with precondition: [V_size>=3] 


Closed-form bounds of eval_terminatorbubble_start(V_11,V_b_0,V_j_0,V_size,V_t_0,B): 
-------------------------------------
* Chain [41] with precondition: [V_size=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [0>=V_size] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [V_size>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [38] with precondition: [V_size>=2] 
    - Upper bound: 2*V_size*V_size+5*V_size+(V_size-1)*(2*V_size) 
    - Complexity: n^2 
* Chain [37] with precondition: [V_size>=3] 
    - Upper bound: 2*V_size*V_size+5*V_size+(V_size-1)*(2*V_size) 
    - Complexity: n^2 

### Maximum cost of eval_terminatorbubble_start(V_11,V_b_0,V_j_0,V_size,V_t_0,B): nat(V_size)*2*nat(V_size)+nat(V_size)*5+nat(V_size)*2*nat(nat(V_size)+ -1) 
Asymptotic class: n^2 
* Total analysis performed in 572 ms.