/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_random1d_2/6,eval_random1d_3/6,eval_random1d_bb1_in/6,eval_random1d_bb2_in/6]
1. non_recursive  : [eval_random1d_stop/4]
2. non_recursive  : [eval_random1d_bb3_in/4]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval_random1d_bb1_in_loop_cont/5]
5. non_recursive  : [eval_random1d_1/4]
6. non_recursive  : [eval_random1d_0/4]
7. non_recursive  : [eval_random1d_bb0_in/4]
8. non_recursive  : [eval_random1d_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_random1d_bb1_in/6
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_random1d_bb1_in_loop_cont/5
5. SCC is partially evaluated into eval_random1d_1/4
6. SCC is completely evaluated into other SCCs
7. SCC is completely evaluated into other SCCs
8. SCC is partially evaluated into eval_random1d_start/4

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

### Specialization of cost equations eval_random1d_bb1_in/6 
* CE 7 is refined into CE [10] 
* CE 6 is refined into CE [11] 
* CE 5 is refined into CE [12] 
* CE 4 is refined into CE [13] 


### Cost equations --> "Loop" of eval_random1d_bb1_in/6 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D) 
* RF of phase [10,11]: [V_max-V_x_0+1]

#### Partial ranking functions of CR eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1,11:1]:
    V_max-V_x_0+1


### Specialization of cost equations eval_random1d_bb1_in_loop_cont/5 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of eval_random1d_bb1_in_loop_cont/5 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR eval_random1d_bb1_in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR eval_random1d_bb1_in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations eval_random1d_1/4 
* CE 3 is refined into CE [16,17,18] 
* CE 2 is refined into CE [19] 


### Cost equations --> "Loop" of eval_random1d_1/4 
* CEs [16,17,18] --> Loop 16 
* CEs [19] --> Loop 17 

### Ranking functions of CR eval_random1d_1(V_2,V_max,V_x_0,B) 

#### Partial ranking functions of CR eval_random1d_1(V_2,V_max,V_x_0,B) 


### Specialization of cost equations eval_random1d_start/4 
* CE 1 is refined into CE [20,21] 


### Cost equations --> "Loop" of eval_random1d_start/4 
* CEs [21] --> Loop 18 
* CEs [20] --> Loop 19 

### Ranking functions of CR eval_random1d_start(V_2,V_max,V_x_0,B) 

#### Partial ranking functions of CR eval_random1d_start(V_2,V_max,V_x_0,B) 


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

#### Cost of chains of eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D):
* Chain [[10,11],13]: 2*it(10)+0
  Such that:aux(3) =< V_max-V_x_0+1
it(10) =< aux(3)

  with precondition: [B=2,V_max+1=D,V_x_0>=1,V_max>=V_x_0] 

* Chain [[10,11],12]: 2*it(10)+0
  Such that:aux(4) =< V_max-V_x_0+1
it(10) =< aux(4)

  with precondition: [B=3,V_x_0>=1,V_max>=V_x_0] 

* Chain [12]: 0
  with precondition: [B=3,V_max>=1,V_x_0>=1] 


#### Cost of chains of eval_random1d_bb1_in_loop_cont(A,B,C,D,E):
* Chain [15]: 0
  with precondition: [A=2,C>=1] 

* Chain [14]: 0
  with precondition: [A=3,C>=1] 


#### Cost of chains of eval_random1d_1(V_2,V_max,V_x_0,B):
* Chain [17]: 0
  with precondition: [0>=V_max] 

* Chain [16]: 4*s(2)+0
  Such that:aux(5) =< V_max
s(2) =< aux(5)

  with precondition: [V_max>=1] 


#### Cost of chains of eval_random1d_start(V_2,V_max,V_x_0,B):
* Chain [19]: 0
  with precondition: [0>=V_max] 

* Chain [18]: 4*s(6)+0
  Such that:s(5) =< V_max
s(6) =< s(5)

  with precondition: [V_max>=1] 


Closed-form bounds of eval_random1d_start(V_2,V_max,V_x_0,B): 
-------------------------------------
* Chain [19] with precondition: [0>=V_max] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [V_max>=1] 
    - Upper bound: 4*V_max 
    - Complexity: n 

### Maximum cost of eval_random1d_start(V_2,V_max,V_x_0,B): nat(V_max)*4 
Asymptotic class: n 
* Total analysis performed in 119 ms.