/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_wcet1_0/4,eval_wcet1_1/5,eval_wcet1_bb1_in/4,eval_wcet1_bb2_in/5,eval_wcet1_bb3_in/5,eval_wcet1_bb4_in/6]
1. non_recursive  : [eval_wcet1_stop/1]
2. non_recursive  : [eval_wcet1_bb5_in/1]
3. non_recursive  : [eval_wcet1_bb1_in_loop_cont/2]
4. non_recursive  : [eval_wcet1_bb0_in/2]
5. non_recursive  : [eval_wcet1_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_wcet1_bb1_in/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_wcet1_bb0_in/2
5. SCC is partially evaluated into eval_wcet1_start/2

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

### Specialization of cost equations eval_wcet1_bb1_in/4 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 11 is refined into CE [14] 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 5 is refined into CE [17] 
* CE 4 is discarded (unfeasible) 
* CE 8 is refined into CE [18] 


### Cost equations --> "Loop" of eval_wcet1_bb1_in/4 
* CEs [16] --> Loop 12 
* CEs [17] --> Loop 13 
* CEs [18] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [12] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [13] --> Loop 18 

### Ranking functions of CR eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B) 
* RF of phase [12,13,14]: [V_i_0-1]

#### Partial ranking functions of CR eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B) 
* Partial RF of phase [12,13,14]:
  - RF of loop [12:1]:
    V_j_0-1 depends on loops [13:1] 
  - RF of loop [12:1,13:1,14:1]:
    V_i_0-1
  - RF of loop [13:1]:
    V_n-V_j_0-1 depends on loops [12:1,14:1] 


### Specialization of cost equations eval_wcet1_bb0_in/2 
* CE 3 is refined into CE [19,20,21,22,23,24] 
* CE 2 is refined into CE [25] 


### Cost equations --> "Loop" of eval_wcet1_bb0_in/2 
* CEs [23] --> Loop 19 
* CEs [21,22,24] --> Loop 20 
* CEs [25] --> Loop 21 
* CEs [19,20] --> Loop 22 

### Ranking functions of CR eval_wcet1_bb0_in(V_n,B) 

#### Partial ranking functions of CR eval_wcet1_bb0_in(V_n,B) 


### Specialization of cost equations eval_wcet1_start/2 
* CE 1 is refined into CE [26,27,28,29] 


### Cost equations --> "Loop" of eval_wcet1_start/2 
* CEs [29] --> Loop 23 
* CEs [28] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [26] --> Loop 26 

### Ranking functions of CR eval_wcet1_start(V_n,B) 

#### Partial ranking functions of CR eval_wcet1_start(V_n,B) 


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

#### Cost of chains of eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B):
* Chain [[12,13,14],18]: 3*it(12)+0
  Such that:aux(7) =< V_i_0
it(12) =< aux(7)

  with precondition: [B=2,V_i_0+V_j_0=V_n,V_j_0>=0,V_n>=V_j_0+2] 

* Chain [[12,13,14],17]: 3*it(12)+0
  Such that:aux(8) =< V_i_0
it(12) =< aux(8)

  with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_i_0>=V_j_0,V_n>=V_i_0+V_j_0] 

* Chain [[12,13,14],16]: 3*it(12)+0
  Such that:aux(9) =< V_i_0
it(12) =< aux(9)

  with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_n>=V_i_0+V_j_0] 

* Chain [[12,13,14],15]: 3*it(12)+0
  Such that:aux(10) =< V_i_0
it(12) =< aux(10)

  with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_i_0+V_j_0>=3,V_n>=V_i_0+V_j_0] 

* Chain [18]: 0
  with precondition: [V_i_0=1,B=2,V_n=V_j_0+1,V_n>=1] 

* Chain [17]: 0
  with precondition: [V_i_0=1,B=2,1>=V_j_0,V_j_0>=0,V_n>=V_j_0+1] 


#### Cost of chains of eval_wcet1_bb0_in(V_n,B):
* Chain [22]: 0
  with precondition: [V_n=1] 

* Chain [21]: 0
  with precondition: [0>=V_n] 

* Chain [20]: 9*s(2)+0
  Such that:aux(11) =< V_n
s(2) =< aux(11)

  with precondition: [V_n>=2] 

* Chain [19]: 3*s(8)+0
  Such that:s(7) =< V_n
s(8) =< s(7)

  with precondition: [V_n>=3] 


#### Cost of chains of eval_wcet1_start(V_n,B):
* Chain [26]: 0
  with precondition: [V_n=1] 

* Chain [25]: 0
  with precondition: [0>=V_n] 

* Chain [24]: 9*s(10)+0
  Such that:s(9) =< V_n
s(10) =< s(9)

  with precondition: [V_n>=2] 

* Chain [23]: 3*s(12)+0
  Such that:s(11) =< V_n
s(12) =< s(11)

  with precondition: [V_n>=3] 


Closed-form bounds of eval_wcet1_start(V_n,B): 
-------------------------------------
* Chain [26] with precondition: [V_n=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [0>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24] with precondition: [V_n>=2] 
    - Upper bound: 9*V_n 
    - Complexity: n 
* Chain [23] with precondition: [V_n>=3] 
    - Upper bound: 3*V_n 
    - Complexity: n 

### Maximum cost of eval_wcet1_start(V_n,B): nat(V_n)*9 
Asymptotic class: n 
* Total analysis performed in 211 ms.