/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_foo_bb2_in/4,eval_foo_bb3_in/4]
1. recursive  : [eval_foo_bb1_in/2,eval_foo_bb2_in_loop_cont/4,eval_foo_bb4_in/3]
2. non_recursive  : [eval_foo_stop/1]
3. non_recursive  : [eval_foo_bb5_in/1]
4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
5. non_recursive  : [eval_foo_bb0_in/2]
6. non_recursive  : [eval_foo_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb2_in/4
1. SCC is partially evaluated into eval_foo_bb1_in/2
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_foo_bb0_in/2
6. SCC is partially evaluated into eval_foo_start/4

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

### Specialization of cost equations eval_foo_bb2_in/4 
* CE 6 is refined into CE [7] 
* CE 5 is refined into CE [8] 


### Cost equations --> "Loop" of eval_foo_bb2_in/4 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_foo_bb2_in(V__01,V__02,B,C) 
* RF of phase [7]: [V__01-V__02]

#### Partial ranking functions of CR eval_foo_bb2_in(V__01,V__02,B,C) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    V__01-V__02


### Specialization of cost equations eval_foo_bb1_in/2 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10,11] 


### Cost equations --> "Loop" of eval_foo_bb1_in/2 
* CEs [11] --> Loop 9 
* CEs [10] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR eval_foo_bb1_in(V__01,B) 
* RF of phase [9]: [V__01]

#### Partial ranking functions of CR eval_foo_bb1_in(V__01,B) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V__01


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


### Cost equations --> "Loop" of eval_foo_bb0_in/2 
* CEs [14] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR eval_foo_bb0_in(V_i,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_i,B) 


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


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

### Ranking functions of CR eval_foo_start(V_c,V_i,V_j,B) 

#### Partial ranking functions of CR eval_foo_start(V_c,V_i,V_j,B) 


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

#### Cost of chains of eval_foo_bb2_in(V__01,V__02,B,C):
* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -V__02+C

  with precondition: [B=2,V__01=C,V__02>=0,V__01>=V__02+1] 

* Chain [8]: 0
  with precondition: [B=2,V__02=V__01,V__02=C,V__02>=0] 


#### Cost of chains of eval_foo_bb1_in(V__01,B):
* Chain [[9],10,11]: 1*it(9)+1*s(3)+1
  Such that:aux(3) =< V__01
it(9) =< aux(3)
s(3) =< it(9)*aux(3)

  with precondition: [B=3,V__01>=1] 

* Chain [11]: 0
  with precondition: [B=3,0>=V__01+1] 

* Chain [10,11]: 1
  with precondition: [V__01=0,B=3] 


#### Cost of chains of eval_foo_bb0_in(V_i,B):
* Chain [14]: 1
  with precondition: [V_i=0] 

* Chain [13]: 0
  with precondition: [0>=V_i+1] 

* Chain [12]: 1*s(5)+1*s(6)+1
  Such that:s(4) =< V_i
s(5) =< s(4)
s(6) =< s(5)*s(4)

  with precondition: [V_i>=1] 


#### Cost of chains of eval_foo_start(V_c,V_i,V_j,B):
* Chain [17]: 1
  with precondition: [V_i=0] 

* Chain [16]: 0
  with precondition: [0>=V_i+1] 

* Chain [15]: 1*s(8)+1*s(9)+1
  Such that:s(7) =< V_i
s(8) =< s(7)
s(9) =< s(8)*s(7)

  with precondition: [V_i>=1] 


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

### Maximum cost of eval_foo_start(V_c,V_i,V_j,B): max([1,nat(V_i)+1+nat(V_i)*nat(V_i)]) 
Asymptotic class: n^2 
* Total analysis performed in 88 ms.