/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_sipma91_bb1_in/5,eval_sipma91_bb2_in/5]
1. recursive  : [eval_sipma91_bb3_in/3,eval_sipma91_bb4_in/3,eval_sipma91_bb5_in/5,eval_sipma91_bb6_in/5,eval_sipma91_bb7_in/7]
2. non_recursive  : [eval_sipma91_stop/1]
3. non_recursive  : [eval_sipma91_bb8_in/1]
4. non_recursive  : [eval_sipma91_bb3_in_loop_cont/2]
5. non_recursive  : [eval_sipma91_bb1_in_loop_cont/4]
6. non_recursive  : [eval_sipma91_bb0_in/2]
7. non_recursive  : [eval_sipma91_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_sipma91_bb1_in/5
1. SCC is partially evaluated into eval_sipma91_bb3_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_sipma91_bb1_in_loop_cont/4
6. SCC is partially evaluated into eval_sipma91_bb0_in/2
7. SCC is partially evaluated into eval_sipma91_start/2

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

### Specialization of cost equations eval_sipma91_bb1_in/5 
* CE 5 is refined into CE [11] 
* CE 4 is refined into CE [12] 


### Cost equations --> "Loop" of eval_sipma91_bb1_in/5 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 

### Ranking functions of CR eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D) 
* RF of phase [11]: [-V_y1_0/11+101/11]

#### Partial ranking functions of CR eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    -V_y1_0/11+101/11


### Specialization of cost equations eval_sipma91_bb3_in/3 
* CE 10 is refined into CE [13] 
* CE 8 is refined into CE [14] 
* CE 9 is refined into CE [15] 
* CE 7 is refined into CE [16] 


### Cost equations --> "Loop" of eval_sipma91_bb3_in/3 
* CEs [14] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [16] --> Loop 15 
* CEs [13] --> Loop 16 

### Ranking functions of CR eval_sipma91_bb3_in(V_y2_1,V_y1_1,B) 

#### Partial ranking functions of CR eval_sipma91_bb3_in(V_y2_1,V_y1_1,B) 
* Partial RF of phase [13,14]:
  - RF of loop [13:1]:
    V_y1_1/9-110/9 depends on loops [14:1] 
    V_y2_1-2
  - RF of loop [14:1]:
    -V_y1_1+111 depends on loops [13:1] 


### Specialization of cost equations eval_sipma91_bb1_in_loop_cont/4 
* CE 6 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of eval_sipma91_bb1_in_loop_cont/4 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D) 


### Specialization of cost equations eval_sipma91_bb0_in/2 
* CE 2 is refined into CE [20] 
* CE 3 is refined into CE [21,22] 


### Cost equations --> "Loop" of eval_sipma91_bb0_in/2 
* CEs [20] --> Loop 20 
* CEs [22] --> Loop 21 
* CEs [21] --> Loop 22 

### Ranking functions of CR eval_sipma91_bb0_in(V_x,B) 

#### Partial ranking functions of CR eval_sipma91_bb0_in(V_x,B) 


### Specialization of cost equations eval_sipma91_start/2 
* CE 1 is refined into CE [23,24,25] 


### Cost equations --> "Loop" of eval_sipma91_start/2 
* CEs [25] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [23] --> Loop 25 

### Ranking functions of CR eval_sipma91_start(V_x,B) 

#### Partial ranking functions of CR eval_sipma91_start(V_x,B) 


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

#### Cost of chains of eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D):
* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< -V_y1_0/11+101/11

  with precondition: [B=3,D+11*V_y2_0=11*C+V_y1_0,V_y2_0>=1,C>=V_y2_0+1,V_y1_0+11*C>=11*V_y2_0+101,11*V_y2_0+111>=11*C+V_y1_0] 


#### Cost of chains of eval_sipma91_bb3_in(V_y2_1,V_y1_1,B):
* Chain [[13,14],15,16]: 1*it(13)+1*it(14)+1
  Such that:it(13) =< V_y2_1
aux(3) =< -V_y1_1+111
it(14) =< it(13)*9+aux(3)

  with precondition: [B=2,V_y2_1>=2] 

* Chain [16]: 0
  with precondition: [B=2,1>=V_y2_1] 

* Chain [15,16]: 1
  with precondition: [V_y2_1=2,B=2,V_y1_1>=111] 


#### Cost of chains of eval_sipma91_bb1_in_loop_cont(A,B,C,D):
* Chain [19]: 1
  with precondition: [A=3,B=2,C>=111] 

* Chain [18]: 0
  with precondition: [A=3,1>=B] 

* Chain [17]: 1*s(1)+1*s(3)+1
  Such that:s(1) =< B
s(2) =< -C+111
s(3) =< s(1)*9+s(2)

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


#### Cost of chains of eval_sipma91_bb0_in(V_x,B):
* Chain [22]: 1*s(4)+1
  Such that:s(4) =< 1/11

  with precondition: [V_x=100] 

* Chain [21]: 1*s(5)+1*s(6)+1*s(8)+1
  Such that:s(7) =< 10
s(5) =< -V_x/11+101/11
s(6) =< -V_x/11+122/11
aux(5) =< -V_x+122
s(6) =< aux(5)
s(7) =< aux(5)
s(8) =< s(6)*9+s(7)

  with precondition: [100>=V_x] 

* Chain [20]: 0
  with precondition: [V_x>=101] 


#### Cost of chains of eval_sipma91_start(V_x,B):
* Chain [25]: 1*s(9)+1
  Such that:s(9) =< 1/11

  with precondition: [V_x=100] 

* Chain [24]: 1*s(11)+1*s(12)+1*s(14)+1
  Such that:s(10) =< 10
s(13) =< -V_x+122
s(11) =< -V_x/11+101/11
s(12) =< -V_x/11+122/11
s(12) =< s(13)
s(10) =< s(13)
s(14) =< s(12)*9+s(10)

  with precondition: [100>=V_x] 

* Chain [23]: 0
  with precondition: [V_x>=101] 


Closed-form bounds of eval_sipma91_start(V_x,B): 
-------------------------------------
* Chain [25] with precondition: [V_x=100] 
    - Upper bound: 12/11 
    - Complexity: constant 
* Chain [24] with precondition: [100>=V_x] 
    - Upper bound: -V_x+1442/11 
    - Complexity: n 
* Chain [23] with precondition: [V_x>=101] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_sipma91_start(V_x,B): max([12/11,nat(-V_x/11+101/11)+11+nat(-V_x/11+122/11)*10]) 
Asymptotic class: n 
* Total analysis performed in 159 ms.