/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_Loopus2015_ex1_bb3_in/7,eval_Loopus2015_ex1_bb4_in/7]
1. recursive  : [eval_Loopus2015_ex1_2/5,eval_Loopus2015_ex1_3/6,eval_Loopus2015_ex1_bb1_in/3,eval_Loopus2015_ex1_bb2_in/3,eval_Loopus2015_ex1_bb3_in_loop_cont/4]
2. non_recursive  : [eval_Loopus2015_ex1_stop/1]
3. non_recursive  : [eval_Loopus2015_ex1_bb5_in/1]
4. non_recursive  : [eval_Loopus2015_ex1_bb1_in_loop_cont/2]
5. non_recursive  : [eval_Loopus2015_ex1_bb0_in/2]
6. non_recursive  : [eval_Loopus2015_ex1_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_Loopus2015_ex1_bb3_in/7
1. SCC is partially evaluated into eval_Loopus2015_ex1_bb1_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_Loopus2015_ex1_bb0_in/2
6. SCC is partially evaluated into eval_Loopus2015_ex1_start/2

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

### Specialization of cost equations eval_Loopus2015_ex1_bb3_in/7 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 


### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb3_in/7 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C) 
* RF of phase [8]: [V_p_0]

#### Partial ranking functions of CR eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V_p_0


### Specialization of cost equations eval_Loopus2015_ex1_bb1_in/3 
* CE 5 is refined into CE [10] 
* CE 4 is refined into CE [11,12] 
* CE 3 is refined into CE [13] 


### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb1_in/3 
* CEs [13] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B) 
* RF of phase [10,11,12]: [V_x_0]

#### Partial ranking functions of CR eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B) 


### Specialization of cost equations eval_Loopus2015_ex1_bb0_in/2 
* CE 2 is refined into CE [14,15] 


### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb0_in/2 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR eval_Loopus2015_ex1_bb0_in(V_n,B) 

#### Partial ranking functions of CR eval_Loopus2015_ex1_bb0_in(V_n,B) 


### Specialization of cost equations eval_Loopus2015_ex1_start/2 
* CE 1 is refined into CE [16,17] 


### Cost equations --> "Loop" of eval_Loopus2015_ex1_start/2 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_Loopus2015_ex1_start(V_n,B) 

#### Partial ranking functions of CR eval_Loopus2015_ex1_start(V_n,B) 


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

#### Cost of chains of eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C):
* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< V_p_0

  with precondition: [B=2,C=0,V_r_0+1=V_2,V_x_0>=1,V_3>=1,V_p_0>=1,V_r_0+1>=V_p_0] 

* Chain [9]: 0
  with precondition: [B=2,C=0,V_2=V_r_0+1,0>=V_p_0,V_x_0>=1,V_3>=1,V_2>=V_p_0] 


#### Cost of chains of eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B):
* Chain [[10,11,12],13]: 2*it(10)+1*s(3)+0
  Such that:s(3) =< V_r_0+V_x_0
aux(3) =< V_x_0
it(10) =< aux(3)

  with precondition: [B=3,V_r_0>=0,V_x_0>=1] 

* Chain [13]: 0
  with precondition: [B=3,0>=V_x_0,V_r_0>=0] 


#### Cost of chains of eval_Loopus2015_ex1_bb0_in(V_n,B):
* Chain [15]: 0
  with precondition: [0>=V_n] 

* Chain [14]: 3*s(4)+0
  Such that:aux(4) =< V_n
s(4) =< aux(4)

  with precondition: [V_n>=1] 


#### Cost of chains of eval_Loopus2015_ex1_start(V_n,B):
* Chain [17]: 0
  with precondition: [0>=V_n] 

* Chain [16]: 3*s(8)+0
  Such that:s(7) =< V_n
s(8) =< s(7)

  with precondition: [V_n>=1] 


Closed-form bounds of eval_Loopus2015_ex1_start(V_n,B): 
-------------------------------------
* Chain [17] with precondition: [0>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [V_n>=1] 
    - Upper bound: 3*V_n 
    - Complexity: n 

### Maximum cost of eval_Loopus2015_ex1_start(V_n,B): nat(V_n)*3 
Asymptotic class: n 
* Total analysis performed in 143 ms.