/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_foo_bb3_in/3,eval_foo_bb4_in/3]
1. recursive  : [eval_foo_bb1_in/2,eval_foo_bb2_in/2,eval_foo_bb3_in_loop_cont/4,eval_foo_bb5_in/3]
2. non_recursive  : [eval_foo_stop/1]
3. non_recursive  : [eval_foo_bb6_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/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb3_in/3
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/5

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

### Specialization of cost equations eval_foo_bb3_in/3 
* CE 6 is refined into CE [7] 
* CE 5 is refined into CE [8] 


### Cost equations --> "Loop" of eval_foo_bb3_in/3 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_foo_bb3_in(V__01,B,C) 
* RF of phase [7]: [V__01-1]

#### Partial ranking functions of CR eval_foo_bb3_in(V__01,B,C) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    V__01-1


### 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__0,B) 
* RF of phase [10]: [V__0-1]

#### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V__0-1


### Specialization of cost equations eval_foo_bb0_in/2 
* CE 2 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of eval_foo_bb0_in/2 
* CEs [15] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [12] --> Loop 15 

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

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


### Specialization of cost equations eval_foo_start/5 
* CE 1 is refined into CE [16,17,18,19] 


### Cost equations --> "Loop" of eval_foo_start/5 
* CEs [19] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [16] --> Loop 19 

### Ranking functions of CR eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B) 

#### Partial ranking functions of CR eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B) 


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

#### Cost of chains of eval_foo_bb3_in(V__01,B,C):
* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< V__01-C

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

* Chain [8]: 0
  with precondition: [B=2,V__01=C,1>=V__01,V__01>=0] 


#### Cost of chains of eval_foo_bb1_in(V__0,B):
* Chain [[10],11]: 1*it(10)+0
  Such that:it(10) =< V__0

  with precondition: [B=3,3>=V__0,V__0>=2] 

* Chain [11]: 0
  with precondition: [B=3,1>=V__0] 

* Chain [9,[10],11]: 1*it(10)+1*s(1)+1
  Such that:it(10) =< 2
s(1) =< V__0

  with precondition: [B=3,V__0>=5] 

* Chain [9,11]: 1*s(1)+1
  Such that:s(1) =< V__0

  with precondition: [B=3,V__0>=4] 


#### Cost of chains of eval_foo_bb0_in(V_x,B):
* Chain [15]: 1*s(2)+0
  Such that:s(2) =< V_x

  with precondition: [3>=V_x,V_x>=2] 

* Chain [14]: 0
  with precondition: [1>=V_x] 

* Chain [13]: 1*s(3)+1
  Such that:s(3) =< V_x

  with precondition: [V_x>=4] 

* Chain [12]: 1*s(4)+1*s(5)+1
  Such that:s(4) =< 2
s(5) =< V_x

  with precondition: [V_x>=5] 


#### Cost of chains of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B):
* Chain [19]: 1*s(6)+0
  Such that:s(6) =< V_x

  with precondition: [3>=V_x,V_x>=2] 

* Chain [18]: 0
  with precondition: [1>=V_x] 

* Chain [17]: 1*s(7)+1
  Such that:s(7) =< V_x

  with precondition: [V_x>=4] 

* Chain [16]: 1*s(8)+1*s(9)+1
  Such that:s(8) =< 2
s(9) =< V_x

  with precondition: [V_x>=5] 


Closed-form bounds of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B): 
-------------------------------------
* Chain [19] with precondition: [3>=V_x,V_x>=2] 
    - Upper bound: V_x 
    - Complexity: n 
* Chain [18] with precondition: [1>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [V_x>=4] 
    - Upper bound: V_x+1 
    - Complexity: n 
* Chain [16] with precondition: [V_x>=5] 
    - Upper bound: V_x+3 
    - Complexity: n 

### Maximum cost of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B): nat(V_x)+3 
Asymptotic class: n 
* Total analysis performed in 88 ms.