/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_peed_pldi09_fig4_4_bb1_in/3,eval_peed_pldi09_fig4_4_bb2_in/3]
1. non_recursive  : [eval_peed_pldi09_fig4_4_stop/1]
2. non_recursive  : [eval_peed_pldi09_fig4_4_bb3_in/1]
3. non_recursive  : [eval_peed_pldi09_fig4_4_bb1_in_loop_cont/2]
4. non_recursive  : [eval_peed_pldi09_fig4_4_bb0_in/3]
5. non_recursive  : [eval_peed_pldi09_fig4_4_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_peed_pldi09_fig4_4_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_peed_pldi09_fig4_4_bb0_in/3
5. SCC is partially evaluated into eval_peed_pldi09_fig4_4_start/3

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

### Specialization of cost equations eval_peed_pldi09_fig4_4_bb1_in/3 
* CE 6 is refined into CE [7] 
* CE 4 is refined into CE [8] 
* CE 5 is refined into CE [9] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_bb1_in/3 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [7] --> Loop 9 

### Ranking functions of CR eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B) 
* RF of phase [7]: [V_i_0,-V_m+V_i_0+1]
* RF of phase [8]: [V_i_0]

#### Partial ranking functions of CR eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    V_i_0
    -V_m+V_i_0+1
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V_i_0


### Specialization of cost equations eval_peed_pldi09_fig4_4_bb0_in/3 
* CE 3 is refined into CE [10,11,12,13] 
* CE 2 is refined into CE [14] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_bb0_in/3 
* CEs [12] --> Loop 10 
* CEs [11] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [10] --> Loop 14 

### Ranking functions of CR eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B) 

#### Partial ranking functions of CR eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B) 


### Specialization of cost equations eval_peed_pldi09_fig4_4_start/3 
* CE 1 is refined into CE [15,16,17,18,19] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_start/3 
* CEs [19] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [17] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [15] --> Loop 19 

### Ranking functions of CR eval_peed_pldi09_fig4_4_start(V_n,V_m,B) 

#### Partial ranking functions of CR eval_peed_pldi09_fig4_4_start(V_n,V_m,B) 


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

#### Cost of chains of eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B):
* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< V_i_0

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

* Chain [[7],[8],9]: 1*it(7)+1*it(8)+0
  Such that:it(8) =< -V_m+V_i_0
it(7) =< -V_m+V_i_0+1
it(8) =< V_m

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

* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -V_m+V_i_0+1

  with precondition: [B=2,V_m>=1,V_i_0>=V_m] 

* Chain [9]: 0
  with precondition: [B=2,0>=V_i_0,V_m>=1] 


#### Cost of chains of eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B):
* Chain [14]: 0
  with precondition: [0>=V_n,V_m>=1] 

* Chain [13]: 0
  with precondition: [0>=V_m] 

* Chain [12]: 1*s(1)+0
  Such that:s(1) =< V_n

  with precondition: [V_n>=1,V_m>=V_n+1] 

* Chain [11]: 1*s(2)+0
  Such that:s(2) =< V_n-V_m+1

  with precondition: [V_m>=1,V_n>=V_m] 

* Chain [10]: 1*s(3)+1*s(4)+0
  Such that:s(3) =< V_n-V_m
s(4) =< V_n-V_m+1
s(3) =< V_m

  with precondition: [V_m>=2,V_n>=V_m+1] 


#### Cost of chains of eval_peed_pldi09_fig4_4_start(V_n,V_m,B):
* Chain [19]: 0
  with precondition: [0>=V_n,V_m>=1] 

* Chain [18]: 0
  with precondition: [0>=V_m] 

* Chain [17]: 1*s(5)+0
  Such that:s(5) =< V_n

  with precondition: [V_n>=1,V_m>=V_n+1] 

* Chain [16]: 1*s(6)+0
  Such that:s(6) =< V_n-V_m+1

  with precondition: [V_m>=1,V_n>=V_m] 

* Chain [15]: 1*s(7)+1*s(8)+0
  Such that:s(7) =< V_n-V_m
s(8) =< V_n-V_m+1
s(7) =< V_m

  with precondition: [V_m>=2,V_n>=V_m+1] 


Closed-form bounds of eval_peed_pldi09_fig4_4_start(V_n,V_m,B): 
-------------------------------------
* Chain [19] with precondition: [0>=V_n,V_m>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [0>=V_m] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [V_n>=1,V_m>=V_n+1] 
    - Upper bound: V_n 
    - Complexity: n 
* Chain [16] with precondition: [V_m>=1,V_n>=V_m] 
    - Upper bound: V_n-V_m+1 
    - Complexity: n 
* Chain [15] with precondition: [V_m>=2,V_n>=V_m+1] 
    - Upper bound: 2*V_n-2*V_m+1 
    - Complexity: n 

### Maximum cost of eval_peed_pldi09_fig4_4_start(V_n,V_m,B): max([nat(V_n),nat(V_n-V_m)+nat(V_n-V_m+1)]) 
Asymptotic class: n 
* Total analysis performed in 100 ms.