/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_jama_ex2_bb2_in/4,eval_jama_ex2_bb3_in/4]
1. recursive  : [eval_jama_ex2_bb1_in/3,eval_jama_ex2_bb2_in_loop_cont/5,eval_jama_ex2_bb4_in/4]
2. non_recursive  : [eval_jama_ex2_stop/1]
3. non_recursive  : [eval_jama_ex2_bb5_in/1]
4. non_recursive  : [eval_jama_ex2_bb1_in_loop_cont/2]
5. non_recursive  : [eval_jama_ex2_bb0_in/2]
6. non_recursive  : [eval_jama_ex2_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_jama_ex2_bb2_in/4
1. SCC is partially evaluated into eval_jama_ex2_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_jama_ex2_bb0_in/2
6. SCC is partially evaluated into eval_jama_ex2_start/2

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

### Specialization of cost equations eval_jama_ex2_bb2_in/4 
* CE 6 is refined into CE [7] 
* CE 5 is refined into CE [8] 


### Cost equations --> "Loop" of eval_jama_ex2_bb2_in/4 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_jama_ex2_bb2_in(V_i_0,V_j_0,B,C) 
* RF of phase [7]: [V_i_0-V_j_0+1]

#### Partial ranking functions of CR eval_jama_ex2_bb2_in(V_i_0,V_j_0,B,C) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    V_i_0-V_j_0+1


### Specialization of cost equations eval_jama_ex2_bb1_in/3 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of eval_jama_ex2_bb1_in/3 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_jama_ex2_bb1_in(V_n,V_i_0,B) 
* RF of phase [9]: [V_n-V_i_0+1]

#### Partial ranking functions of CR eval_jama_ex2_bb1_in(V_n,V_i_0,B) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V_n-V_i_0+1


### Specialization of cost equations eval_jama_ex2_bb0_in/2 
* CE 2 is refined into CE [11,12] 


### Cost equations --> "Loop" of eval_jama_ex2_bb0_in/2 
* CEs [12] --> Loop 11 
* CEs [11] --> Loop 12 

### Ranking functions of CR eval_jama_ex2_bb0_in(V_n,B) 

#### Partial ranking functions of CR eval_jama_ex2_bb0_in(V_n,B) 


### Specialization of cost equations eval_jama_ex2_start/2 
* CE 1 is refined into CE [13,14] 


### Cost equations --> "Loop" of eval_jama_ex2_start/2 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_jama_ex2_start(V_n,B) 

#### Partial ranking functions of CR eval_jama_ex2_start(V_n,B) 


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

#### Cost of chains of eval_jama_ex2_bb2_in(V_i_0,V_j_0,B,C):
* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -V_j_0+C

  with precondition: [B=2,V_i_0+1=C,V_j_0>=1,V_i_0>=V_j_0] 


#### Cost of chains of eval_jama_ex2_bb1_in(V_n,V_i_0,B):
* Chain [[9],10]: 1*it(9)+1*s(3)+0
  Such that:aux(1) =< V_n+1
it(9) =< V_n-V_i_0+1
s(3) =< it(9)*aux(1)

  with precondition: [B=3,V_i_0>=1,V_n>=V_i_0] 

* Chain [10]: 0
  with precondition: [B=3,V_i_0>=1,V_i_0>=V_n+1] 


#### Cost of chains of eval_jama_ex2_bb0_in(V_n,B):
* Chain [12]: 0
  with precondition: [0>=V_n] 

* Chain [11]: 1*s(5)+1*s(6)+0
  Such that:s(5) =< V_n
s(4) =< V_n+1
s(6) =< s(5)*s(4)

  with precondition: [V_n>=1] 


#### Cost of chains of eval_jama_ex2_start(V_n,B):
* Chain [14]: 0
  with precondition: [0>=V_n] 

* Chain [13]: 1*s(7)+1*s(9)+0
  Such that:s(7) =< V_n
s(8) =< V_n+1
s(9) =< s(7)*s(8)

  with precondition: [V_n>=1] 


Closed-form bounds of eval_jama_ex2_start(V_n,B): 
-------------------------------------
* Chain [14] with precondition: [0>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [13] with precondition: [V_n>=1] 
    - Upper bound: (V_n+1)*V_n+V_n 
    - Complexity: n^2 

### Maximum cost of eval_jama_ex2_start(V_n,B): nat(V_n+1)*nat(V_n)+nat(V_n) 
Asymptotic class: n^2 
* Total analysis performed in 91 ms.