/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /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_realbubble_2/6,eval_realbubble_3/7,eval_realbubble_4/8,eval_realbubble_5/8,eval_realbubble_6/8,eval_realbubble_bb2_in/6,eval_realbubble_bb3_in/6,eval_realbubble_bb4_in/8,eval_realbubble_bb5_in/9]
1. recursive  : [eval_realbubble_bb1_in/2,eval_realbubble_bb2_in_loop_cont/5,eval_realbubble_bb6_in/4,eval_realbubble_bb7_in/4]
2. non_recursive  : [eval_realbubble_stop/1]
3. non_recursive  : [eval_realbubble_bb8_in/1]
4. non_recursive  : [eval_realbubble_bb1_in_loop_cont/2]
5. non_recursive  : [eval_realbubble_bb0_in/2]
6. non_recursive  : [eval_realbubble_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_realbubble_bb2_in/6
1. SCC is partially evaluated into eval_realbubble_bb1_in/2
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_realbubble_bb0_in/2
6. SCC is partially evaluated into eval_realbubble_start/2

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

### Specialization of cost equations eval_realbubble_bb2_in/6 
* CE 9 is refined into CE [10] 
* CE 7 is refined into CE [11] 
* CE 8 is refined into CE [12] 


### Cost equations --> "Loop" of eval_realbubble_bb2_in/6 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR eval_realbubble_bb2_in(V_i_0,V_j_0,V_test_0,B,C,D) 
* RF of phase [9,10]: [V_i_0-V_j_0]

#### Partial ranking functions of CR eval_realbubble_bb2_in(V_i_0,V_j_0,V_test_0,B,C,D) 
* Partial RF of phase [9,10]:
  - RF of loop [9:1,10:1]:
    V_i_0-V_j_0


### Specialization of cost equations eval_realbubble_bb1_in/2 
* CE 3 is refined into CE [13] 
* CE 6 is refined into CE [14] 
* CE 4 is discarded (unfeasible) 
* CE 5 is refined into CE [15] 


### Cost equations --> "Loop" of eval_realbubble_bb1_in/2 
* CEs [15] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR eval_realbubble_bb1_in(V_i_0,B) 
* RF of phase [12]: [V_i_0]

#### Partial ranking functions of CR eval_realbubble_bb1_in(V_i_0,B) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V_i_0


### Specialization of cost equations eval_realbubble_bb0_in/2 
* CE 2 is refined into CE [16,17,18] 


### Cost equations --> "Loop" of eval_realbubble_bb0_in/2 
* CEs [18] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_realbubble_bb0_in(V_length,B) 

#### Partial ranking functions of CR eval_realbubble_bb0_in(V_length,B) 


### Specialization of cost equations eval_realbubble_start/2 
* CE 1 is refined into CE [19,20,21] 


### Cost equations --> "Loop" of eval_realbubble_start/2 
* CEs [21] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR eval_realbubble_start(V_length,B) 

#### Partial ranking functions of CR eval_realbubble_start(V_length,B) 


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

#### Cost of chains of eval_realbubble_bb2_in(V_i_0,V_j_0,V_test_0,B,C,D):
* Chain [[9,10],11]: 2*it(9)+0
  Such that:aux(3) =< -V_j_0+C
it(9) =< aux(3)

  with precondition: [B=2,V_i_0=C,V_test_0>=0,D>=0,V_i_0>=V_j_0+1,V_j_0>=V_test_0,V_i_0+V_test_0>=V_j_0+D] 


#### Cost of chains of eval_realbubble_bb1_in(V_i_0,B):
* Chain [[12],14]: 1*it(12)+2*s(5)+0
  Such that:aux(6) =< V_i_0
it(12) =< aux(6)
s(6) =< it(12)*aux(6)
s(5) =< s(6)

  with precondition: [B=3,V_i_0>=1] 

* Chain [[12],13]: 3*it(12)+2*s(5)+0
  Such that:aux(7) =< V_i_0
it(12) =< aux(7)
s(6) =< it(12)*aux(7)
s(5) =< s(6)

  with precondition: [B=3,V_i_0>=2] 

* Chain [14]: 0
  with precondition: [B=3,0>=V_i_0] 

* Chain [13]: 2*s(8)+0
  Such that:s(7) =< V_i_0
s(8) =< s(7)

  with precondition: [B=3,V_i_0>=1] 


#### Cost of chains of eval_realbubble_bb0_in(V_length,B):
* Chain [17]: 0
  with precondition: [1>=V_length] 

* Chain [16]: 3*s(16)+2*s(18)+0
  Such that:s(15) =< V_length
s(16) =< s(15)
s(17) =< s(16)*s(15)
s(18) =< s(17)

  with precondition: [V_length>=2] 

* Chain [15]: 3*s(20)+2*s(22)+0
  Such that:s(19) =< V_length
s(20) =< s(19)
s(21) =< s(20)*s(19)
s(22) =< s(21)

  with precondition: [V_length>=3] 


#### Cost of chains of eval_realbubble_start(V_length,B):
* Chain [20]: 0
  with precondition: [1>=V_length] 

* Chain [19]: 3*s(24)+2*s(26)+0
  Such that:s(23) =< V_length
s(24) =< s(23)
s(25) =< s(24)*s(23)
s(26) =< s(25)

  with precondition: [V_length>=2] 

* Chain [18]: 3*s(28)+2*s(30)+0
  Such that:s(27) =< V_length
s(28) =< s(27)
s(29) =< s(28)*s(27)
s(30) =< s(29)

  with precondition: [V_length>=3] 


Closed-form bounds of eval_realbubble_start(V_length,B): 
-------------------------------------
* Chain [20] with precondition: [1>=V_length] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [19] with precondition: [V_length>=2] 
    - Upper bound: 2*V_length*V_length+3*V_length 
    - Complexity: n^2 
* Chain [18] with precondition: [V_length>=3] 
    - Upper bound: 2*V_length*V_length+3*V_length 
    - Complexity: n^2 

### Maximum cost of eval_realbubble_start(V_length,B): nat(V_length)*2*nat(V_length)+nat(V_length)*3 
Asymptotic class: n^2 
* Total analysis performed in 175 ms.