/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_random2d_1/4,eval_random2d_2/5,eval_random2d_LeafBlock1_in/5,eval_random2d_LeafBlock3_in/5,eval_random2d_LeafBlock5_in/5,eval_random2d_LeafBlock_in/5,eval_random2d_NewDefault_in/5,eval_random2d_NodeBlock7_in/5,eval_random2d_NodeBlock9_in/5,eval_random2d_NodeBlock_in/5,eval_random2d_bb1_in/3,eval_random2d_bb2_in/3,eval_random2d_bb3_in/5,eval_random2d_bb4_in/5,eval_random2d_bb5_in/5,eval_random2d_bb6_in/5,eval_random2d_bb7_in/5]
1. non_recursive  : [eval_random2d_stop/1]
2. non_recursive  : [eval_random2d_bb8_in/1]
3. non_recursive  : [eval_random2d_bb1_in_loop_cont/2]
4. non_recursive  : [eval_random2d_bb0_in/2]
5. non_recursive  : [eval_random2d_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_random2d_bb1_in/3
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_random2d_bb0_in/2
5. SCC is partially evaluated into eval_random2d_start/2

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

### Specialization of cost equations eval_random2d_bb1_in/3 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 


### Cost equations --> "Loop" of eval_random2d_bb1_in/3 
* CEs [6] --> Loop 5 
* CEs [5] --> Loop 6 

### Ranking functions of CR eval_random2d_bb1_in(V_N,V_i_0,B) 
* RF of phase [5]: [V_N-V_i_0]

#### Partial ranking functions of CR eval_random2d_bb1_in(V_N,V_i_0,B) 
* Partial RF of phase [5]:
  - RF of loop [5:1]:
    V_N-V_i_0


### Specialization of cost equations eval_random2d_bb0_in/2 
* CE 2 is refined into CE [7,8] 


### Cost equations --> "Loop" of eval_random2d_bb0_in/2 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_random2d_bb0_in(V_N,B) 

#### Partial ranking functions of CR eval_random2d_bb0_in(V_N,B) 


### Specialization of cost equations eval_random2d_start/2 
* CE 1 is refined into CE [9,10] 


### Cost equations --> "Loop" of eval_random2d_start/2 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_random2d_start(V_N,B) 

#### Partial ranking functions of CR eval_random2d_start(V_N,B) 


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

#### Cost of chains of eval_random2d_bb1_in(V_N,V_i_0,B):
* Chain [[5],6]: 1*it(5)+0
  Such that:it(5) =< V_N-V_i_0

  with precondition: [B=2,V_i_0>=0,V_N>=V_i_0+1] 

* Chain [6]: 0
  with precondition: [B=2,V_i_0>=0,V_i_0>=V_N] 


#### Cost of chains of eval_random2d_bb0_in(V_N,B):
* Chain [8]: 0
  with precondition: [0>=V_N] 

* Chain [7]: 1*s(1)+0
  Such that:s(1) =< V_N

  with precondition: [V_N>=1] 


#### Cost of chains of eval_random2d_start(V_N,B):
* Chain [10]: 0
  with precondition: [0>=V_N] 

* Chain [9]: 1*s(2)+0
  Such that:s(2) =< V_N

  with precondition: [V_N>=1] 


Closed-form bounds of eval_random2d_start(V_N,B): 
-------------------------------------
* Chain [10] with precondition: [0>=V_N] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [9] with precondition: [V_N>=1] 
    - Upper bound: V_N 
    - Complexity: n 

### Maximum cost of eval_random2d_start(V_N,B): nat(V_N) 
Asymptotic class: n 
* Total analysis performed in 98 ms.