/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /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_4/10,eval_wcet1_5/10,eval_wcet1_bb1_in/10,eval_wcet1_bb2_in/10,eval_wcet1_bb3_in/10,eval_wcet1_bb4_in/10]
1. non_recursive  : [eval_wcet1_stop/6]
2. non_recursive  : [eval_wcet1_bb5_in/6]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval_wcet1_bb1_in_loop_cont/7]
5. non_recursive  : [eval_wcet1_3/6]
6. non_recursive  : [eval_wcet1_2/6]
7. non_recursive  : [eval_wcet1_1/6]
8. non_recursive  : [eval_wcet1_0/6]
9. non_recursive  : [eval_wcet1_bb0_in/6]
10. non_recursive  : [eval_wcet1_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_wcet1_bb1_in/10
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_bb1_in_loop_cont/7
5. SCC is partially evaluated into eval_wcet1_3/6
6. SCC is completely evaluated into other SCCs
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 partially evaluated into eval_wcet1_start/6

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

### Specialization of cost equations eval_wcet1_bb1_in/10 
* CE 11 is refined into CE [15] 
* CE 7 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 10 is refined into CE [18] 
* CE 12 is refined into CE [19] 
* CE 5 is refined into CE [20] 
* CE 9 is refined into CE [21] 
* CE 4 is discarded (unfeasible) 
* CE 8 is refined into CE [22] 


### Cost equations --> "Loop" of eval_wcet1_bb1_in/10 
* CEs [20] --> Loop 15 
* CEs [21] --> Loop 16 
* CEs [22] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [15] --> Loop 19 
* CEs [16] --> Loop 20 
* CEs [18] --> Loop 21 
* CEs [17] --> Loop 22 

### Ranking functions of CR eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F) 
* RF of phase [15,16,17]: [V_i_0-1]

#### Partial ranking functions of CR eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F) 
* Partial RF of phase [15,16,17]:
  - RF of loop [15:1]:
    -V_j_0+V_n-1 depends on loops [16:1,17:1] 
  - RF of loop [15:1,16:1,17:1]:
    V_i_0-1
  - RF of loop [16:1]:
    V_j_0-1 depends on loops [15:1] 


### Specialization of cost equations eval_wcet1_bb1_in_loop_cont/7 
* CE 14 is refined into CE [23] 
* CE 13 is refined into CE [24] 


### Cost equations --> "Loop" of eval_wcet1_bb1_in_loop_cont/7 
* CEs [23] --> Loop 23 
* CEs [24] --> Loop 24 

### Ranking functions of CR eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations eval_wcet1_3/6 
* CE 3 is refined into CE [25,26,27,28,29,30,31,32] 
* CE 2 is refined into CE [33] 


### Cost equations --> "Loop" of eval_wcet1_3/6 
* CEs [32] --> Loop 25 
* CEs [28,29,30,31] --> Loop 26 
* CEs [27] --> Loop 27 
* CEs [33] --> Loop 28 
* CEs [25,26] --> Loop 29 

### Ranking functions of CR eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 

#### Partial ranking functions of CR eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 


### Specialization of cost equations eval_wcet1_start/6 
* CE 1 is refined into CE [34,35,36,37,38] 


### Cost equations --> "Loop" of eval_wcet1_start/6 
* CEs [38] --> Loop 30 
* CEs [37] --> Loop 31 
* CEs [36] --> Loop 32 
* CEs [35] --> Loop 33 
* CEs [34] --> Loop 34 

### Ranking functions of CR eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 

#### Partial ranking functions of CR eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 


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

#### Cost of chains of eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F):
* Chain [[15,16,17],22]: 3*it(15)+0
  Such that:aux(7) =< V_i_0
it(15) =< aux(7)

  with precondition: [B=3,D=1,F=0,V_i_0+V_j_0=V_n,V_i_0+V_j_0=E+1,V_i_0>=2,V_j_0>=0,C>=1] 

* Chain [[15,16,17],21]: 3*it(15)+0
  Such that:aux(8) =< V_i_0
it(15) =< aux(8)

  with precondition: [B=3,D=1,F=0,0>=C,1>=E,V_i_0>=2,V_j_0>=0,E>=0,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1] 

* Chain [[15,16,17],20]: 3*it(15)+0
  Such that:aux(9) =< V_i_0
it(15) =< aux(9)

  with precondition: [B=3,D=1,E+1=F,V_i_0>=2,V_j_0>=0,C>=1,E>=0,V_n>=E+2,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1,V_i_0+V_j_0>=E+1] 

* Chain [[15,16,17],19]: 3*it(15)+0
  Such that:aux(10) =< V_i_0
it(15) =< aux(10)

  with precondition: [B=3,D=1,E=F+1,0>=C,V_i_0>=2,V_j_0>=0,E>=2,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1,V_i_0+V_j_0>=E+1] 

* Chain [[15,16,17],18]: 3*it(15)+0
  Such that:aux(11) =< V_i_0
it(15) =< aux(11)

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

* Chain [22]: 0
  with precondition: [V_i_0=1,B=3,D=1,F=0,V_n=V_j_0+1,V_n=E+1,V_n>=1,C>=1] 

* Chain [21]: 0
  with precondition: [V_i_0=1,B=3,D=1,F=0,V_j_0=E,1>=V_j_0,0>=C,V_j_0>=0,V_n>=V_j_0+1] 

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


#### Cost of chains of eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G):
* Chain [24]: 0
  with precondition: [A=2,F>=1] 

* Chain [23]: 0
  with precondition: [A=3,F>=1] 


#### Cost of chains of eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B):
* Chain [29]: 0
  with precondition: [V_n=1] 

* Chain [28]: 0
  with precondition: [0>=V_n] 

* Chain [27]: 0
  with precondition: [V_n>=1] 

* Chain [26]: 12*s(2)+0
  Such that:aux(12) =< V_n
s(2) =< aux(12)

  with precondition: [V_n>=2] 

* Chain [25]: 3*s(10)+0
  Such that:s(9) =< V_n
s(10) =< s(9)

  with precondition: [V_n>=3] 


#### Cost of chains of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B):
* Chain [34]: 0
  with precondition: [V_n=1] 

* Chain [33]: 0
  with precondition: [0>=V_n] 

* Chain [32]: 0
  with precondition: [V_n>=1] 

* Chain [31]: 12*s(12)+0
  Such that:s(11) =< V_n
s(12) =< s(11)

  with precondition: [V_n>=2] 

* Chain [30]: 3*s(14)+0
  Such that:s(13) =< V_n
s(14) =< s(13)

  with precondition: [V_n>=3] 


Closed-form bounds of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B): 
-------------------------------------
* Chain [34] with precondition: [V_n=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [0>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [V_n>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [V_n>=2] 
    - Upper bound: 12*V_n 
    - Complexity: n 
* Chain [30] with precondition: [V_n>=3] 
    - Upper bound: 3*V_n 
    - Complexity: n 

### Maximum cost of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B): nat(V_n)*12 
Asymptotic class: n 
* Total analysis performed in 435 ms.