/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_foo_bb1_in/3,eval_foo_bb2_in/3]
1. non_recursive  : [eval_foo_stop/1]
2. non_recursive  : [eval_foo_bb3_in/1]
3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
4. non_recursive  : [eval_foo_bb0_in/3]
5. non_recursive  : [eval_foo_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_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_foo_bb0_in/3
5. SCC is partially evaluated into eval_foo_start/4

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

### Specialization of cost equations eval_foo_bb1_in/3 
* CE 7 is refined into CE [8] 
* CE 5 is refined into CE [9] 
* CE 6 is refined into CE [10] 


### Cost equations --> "Loop" of eval_foo_bb1_in/3 
* CEs [9] --> Loop 8 
* CEs [10] --> Loop 9 
* CEs [8] --> Loop 10 

### Ranking functions of CR eval_foo_bb1_in(V_m,V__0,B) 
* RF of phase [8]: [V__0,-V_m+V__0+1]
* RF of phase [9]: [V__0]

#### Partial ranking functions of CR eval_foo_bb1_in(V_m,V__0,B) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V__0
    -V_m+V__0+1
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V__0


### Specialization of cost equations eval_foo_bb0_in/3 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12,13] 
* CE 2 is refined into CE [14] 


### Cost equations --> "Loop" of eval_foo_bb0_in/3 
* CEs [11] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 


### Specialization of cost equations eval_foo_start/4 
* CE 1 is refined into CE [15,16,17,18] 


### Cost equations --> "Loop" of eval_foo_start/4 
* CEs [18] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [15] --> Loop 18 

### Ranking functions of CR eval_foo_start(V_i,V_m,V_n,B) 

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


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

#### Cost of chains of eval_foo_bb1_in(V_m,V__0,B):
* Chain [[8],[9],10]: 1*it(8)+1*it(9)+0
  Such that:it(9) =< -V_m+V__0
it(8) =< -V_m+V__0+1
it(9) =< V_m

  with precondition: [B=2,V_m>=2,V__0>=V_m+1] 

* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -V_m+V__0+1

  with precondition: [B=2,V_m>=1,V__0>=V_m] 


#### Cost of chains of eval_foo_bb0_in(V_m,V_n,B):
* Chain [14]: 0
  with precondition: [0>=V_m] 

* Chain [13]: 1*s(1)+0
  Such that:s(1) =< -V_m+V_n+1

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

* Chain [12]: 1*s(2)+1*s(3)+0
  Such that:s(2) =< -V_m+V_n
s(3) =< -V_m+V_n+1
s(2) =< V_m

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

* Chain [11]: 0
  with precondition: [V_m>=V_n] 


#### Cost of chains of eval_foo_start(V_i,V_m,V_n,B):
* Chain [18]: 0
  with precondition: [0>=V_m] 

* Chain [17]: 1*s(4)+0
  Such that:s(4) =< -V_m+V_n+1

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

* Chain [16]: 1*s(5)+1*s(6)+0
  Such that:s(5) =< -V_m+V_n
s(6) =< -V_m+V_n+1
s(5) =< V_m

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

* Chain [15]: 0
  with precondition: [V_m>=V_n] 


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

### Maximum cost of eval_foo_start(V_i,V_m,V_n,B): nat(-V_m+V_n+1)+nat(-V_m+V_n) 
Asymptotic class: n 
* Total analysis performed in 94 ms.