/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_terminatorbubble_5/9,eval_terminatorbubble_6/10,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/3,eval_terminatorbubble_bb2_in_loop_cont/6,eval_terminatorbubble_bb6_in/5]
2. non_recursive  : [eval_terminatorbubble_stop/1]
3. non_recursive  : [eval_terminatorbubble_bb7_in/1]
4. non_recursive  : [eval_terminatorbubble_bb1_in_loop_cont/2]
5. non_recursive  : [eval_terminatorbubble_bb0_in/2]
6. non_recursive  : [eval_terminatorbubble_start/2]

#### 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/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_terminatorbubble_bb0_in/2
6. SCC is partially evaluated into eval_terminatorbubble_start/2

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

### Specialization of cost equations eval_terminatorbubble_bb2_in/9 
* CE 13 is discarded (unfeasible) 
* CE 14 is discarded (unfeasible) 
* CE 10 is refined into CE [16] 
* CE 15 is refined into CE [17] 
* CE 12 is refined into CE [18] 
* CE 11 is refined into CE [19] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb2_in/9 
* CEs [18] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR eval_terminatorbubble_bb2_in(V_size,V_b_0,V_j_0,V_t_0,B,C,D,E,F) 
* RF of phase [14,15]: [V_b_0-V_j_0,V_size-V_j_0]

#### Partial ranking functions of CR eval_terminatorbubble_bb2_in(V_size,V_b_0,V_j_0,V_t_0,B,C,D,E,F) 
* Partial RF of phase [14,15]:
  - RF of loop [14:1,15:1]:
    V_b_0-V_j_0
    V_size-V_j_0
  - RF of loop [15:1]:
    V_b_0-V_t_0-1
    V_size-V_t_0-1


### Specialization of cost equations eval_terminatorbubble_bb1_in/3 
* CE 5 is discarded (unfeasible) 
* CE 6 is refined into CE [20,21] 
* CE 7 is refined into CE [22,23] 
* CE 8 is discarded (unfeasible) 
* CE 9 is refined into CE [24] 
* CE 4 is refined into CE [25] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb1_in/3 
* CEs [25] --> Loop 18 
* CEs [21] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [24] --> Loop 21 
* CEs [20] --> Loop 22 
* CEs [22] --> Loop 23 

### Ranking functions of CR eval_terminatorbubble_bb1_in(V_size,V_b_0,B) 
* RF of phase [18]: [V_b_0-1]

#### Partial ranking functions of CR eval_terminatorbubble_bb1_in(V_size,V_b_0,B) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    V_b_0-1


### Specialization of cost equations eval_terminatorbubble_bb0_in/2 
* CE 3 is refined into CE [26,27,28] 
* CE 2 is refined into CE [29] 


### Cost equations --> "Loop" of eval_terminatorbubble_bb0_in/2 
* CEs [28] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [29] --> Loop 26 
* CEs [26] --> Loop 27 

### Ranking functions of CR eval_terminatorbubble_bb0_in(V_size,B) 

#### Partial ranking functions of CR eval_terminatorbubble_bb0_in(V_size,B) 


### Specialization of cost equations eval_terminatorbubble_start/2 
* CE 1 is refined into CE [30,31,32,33] 


### Cost equations --> "Loop" of eval_terminatorbubble_start/2 
* CEs [33] --> Loop 28 
* CEs [32] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [30] --> Loop 31 

### Ranking functions of CR eval_terminatorbubble_start(V_size,B) 

#### Partial ranking functions of CR eval_terminatorbubble_start(V_size,B) 


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

#### Cost of chains of eval_terminatorbubble_bb2_in(V_size,V_b_0,V_j_0,V_t_0,B,C,D,E,F):
* Chain [[14,15],17]: 1*it(14)+1*it(15)+0
  Such that:aux(1) =< -V_j_0+C
it(15) =< -V_t_0+F
aux(5) =< -V_j_0+E
it(14) =< aux(1)
it(15) =< aux(1)
it(14) =< aux(5)
it(15) =< aux(5)

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

* Chain [[14,15],16]: 1*it(14)+1*it(15)+0
  Such that:it(15) =< V_size-V_t_0
aux(3) =< V_b_0-V_j_0
aux(6) =< V_size-V_j_0
it(14) =< aux(6)
it(15) =< aux(6)
it(14) =< aux(3)
it(15) =< aux(3)

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

* Chain [17]: 0
  with precondition: [B=2,V_j_0=V_b_0,V_size=C,V_j_0=D,V_j_0=E,V_t_0=F,V_t_0>=0,V_size>=V_j_0,V_j_0>=V_t_0+1] 

* Chain [16]: 0
  with precondition: [B=3,V_j_0=V_size,V_t_0>=0,V_b_0>=V_j_0+1,V_j_0>=V_t_0+1] 


#### Cost of chains of eval_terminatorbubble_bb1_in(V_size,V_b_0,B):
* Chain [[18],22]: 1*it(18)+1*s(9)+1*s(10)+0
  Such that:aux(10) =< V_size
aux(12) =< V_b_0
it(18) =< aux(12)
aux(7) =< aux(10)
aux(7) =< aux(12)
aux(9) =< aux(7)-1
aux(9) =< aux(10)-1
s(12) =< it(18)*aux(10)
s(11) =< it(18)*aux(7)
s(9) =< it(18)*aux(9)
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 [[18],19]: 1*it(18)+1*s(9)+1*s(10)+1*s(16)+0
  Such that:aux(13) =< V_size
aux(14) =< V_b_0
it(18) =< aux(14)
s(16) =< aux(13)
s(16) =< aux(14)
aux(7) =< aux(13)
aux(7) =< aux(14)
aux(9) =< aux(7)-1
aux(9) =< aux(13)-1
s(12) =< it(18)*aux(13)
s(11) =< it(18)*aux(7)
s(9) =< it(18)*aux(9)
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 [22]: 0
  with precondition: [V_b_0=1,B=3,V_size>=1] 

* Chain [19]: 1*s(16)+0
  Such that:s(13) =< V_size
s(15) =< V_b_0
s(16) =< s(13)
s(16) =< s(15)

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


#### Cost of chains of eval_terminatorbubble_bb0_in(V_size,B):
* Chain [27]: 0
  with precondition: [V_size=1] 

* Chain [26]: 0
  with precondition: [0>=V_size] 

* Chain [25]: 2*s(31)+1*s(37)+1*s(38)+0
  Such that:aux(17) =< V_size
s(31) =< aux(17)
s(34) =< aux(17)-1
s(35) =< s(31)*aux(17)
s(37) =< s(31)*s(34)
s(38) =< s(35)
s(37) =< s(35)

  with precondition: [V_size>=2] 

* Chain [24]: 2*s(41)+1*s(47)+1*s(48)+0
  Such that:aux(18) =< V_size
s(41) =< aux(18)
s(44) =< aux(18)-1
s(45) =< s(41)*aux(18)
s(47) =< s(41)*s(44)
s(48) =< s(45)
s(47) =< s(45)

  with precondition: [V_size>=3] 


#### Cost of chains of eval_terminatorbubble_start(V_size,B):
* Chain [31]: 0
  with precondition: [V_size=1] 

* Chain [30]: 0
  with precondition: [0>=V_size] 

* Chain [29]: 2*s(50)+1*s(53)+1*s(54)+0
  Such that:s(49) =< V_size
s(50) =< s(49)
s(51) =< s(49)-1
s(52) =< s(50)*s(49)
s(53) =< s(50)*s(51)
s(54) =< s(52)
s(53) =< s(52)

  with precondition: [V_size>=2] 

* Chain [28]: 2*s(56)+1*s(59)+1*s(60)+0
  Such that:s(55) =< V_size
s(56) =< s(55)
s(57) =< s(55)-1
s(58) =< s(56)*s(55)
s(59) =< s(56)*s(57)
s(60) =< s(58)
s(59) =< s(58)

  with precondition: [V_size>=3] 


Closed-form bounds of eval_terminatorbubble_start(V_size,B): 
-------------------------------------
* Chain [31] with precondition: [V_size=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [0>=V_size] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [V_size>=2] 
    - Upper bound: 2*V_size+V_size*V_size+(V_size-1)*V_size 
    - Complexity: n^2 
* Chain [28] with precondition: [V_size>=3] 
    - Upper bound: 2*V_size+V_size*V_size+(V_size-1)*V_size 
    - Complexity: n^2 

### Maximum cost of eval_terminatorbubble_start(V_size,B): nat(V_size)*nat(V_size)+nat(V_size)*2+nat(nat(V_size)+ -1)*nat(V_size) 
Asymptotic class: n^2 
* Total analysis performed in 341 ms.