/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_0/4,eval_foo_1/5,eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in/5,eval_foo_bb4_in/5]
1. non_recursive  : [eval_foo_stop/1]
2. non_recursive  : [eval_foo_bb5_in/1]
3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
4. non_recursive  : [eval_foo_bb0_in/4]
5. non_recursive  : [eval_foo_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb1_in/4
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/4
5. SCC is partially evaluated into eval_foo_start/4

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

### Specialization of cost equations eval_foo_bb1_in/4 
* CE 5 is refined into CE [7] 
* CE 6 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of eval_foo_bb1_in/4 
* CEs [9] --> Loop 7 
* CEs [10] --> Loop 8 
* CEs [7] --> Loop 9 
* CEs [8] --> Loop 10 

### Ranking functions of CR eval_foo_bb1_in(V_tx,V__01,V__0,B) 
* RF of phase [7,8]: [-V__01+V__0+1]

#### Partial ranking functions of CR eval_foo_bb1_in(V_tx,V__01,V__0,B) 
* Partial RF of phase [7,8]:
  - RF of loop [7:1,8:1]:
    -V__01+V__0+1


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


### Cost equations --> "Loop" of eval_foo_bb0_in/4 
* CEs [13] --> Loop 11 
* CEs [12] --> Loop 12 
* CEs [11] --> Loop 13 

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

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


### Specialization of cost equations eval_foo_start/4 
* CE 1 is refined into CE [14,15,16] 


### Cost equations --> "Loop" of eval_foo_start/4 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14] --> Loop 16 

### Ranking functions of CR eval_foo_start(V_x,V_y,V_tx,B) 

#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_tx,B) 


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

#### Cost of chains of eval_foo_bb1_in(V_tx,V__01,V__0,B):
* Chain [[7,8],9]: 2*it(7)+0
  Such that:aux(2) =< V_tx-V__01+V__0+1
aux(1) =< -V__01+V__0+1
it(7) =< aux(1)
it(7) =< aux(2)

  with precondition: [B=2,V_tx>=0,V__0>=V__01] 

* Chain [10]: 0
  with precondition: [B=2,0>=V_tx+1] 

* Chain [9]: 0
  with precondition: [B=2,V__01>=V__0+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_tx,B):
* Chain [13]: 0
  with precondition: [0>=V_tx+1] 

* Chain [12]: 2*s(3)+0
  Such that:s(2) =< V_x-V_y+1
s(1) =< V_x-V_y+V_tx+1
s(3) =< s(2)
s(3) =< s(1)

  with precondition: [V_tx>=0,V_x>=V_y] 

* Chain [11]: 0
  with precondition: [V_y>=V_x+1] 


#### Cost of chains of eval_foo_start(V_x,V_y,V_tx,B):
* Chain [16]: 0
  with precondition: [0>=V_tx+1] 

* Chain [15]: 2*s(6)+0
  Such that:s(4) =< V_x-V_y+1
s(5) =< V_x-V_y+V_tx+1
s(6) =< s(4)
s(6) =< s(5)

  with precondition: [V_tx>=0,V_x>=V_y] 

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


Closed-form bounds of eval_foo_start(V_x,V_y,V_tx,B): 
-------------------------------------
* Chain [16] with precondition: [0>=V_tx+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [V_tx>=0,V_x>=V_y] 
    - Upper bound: 2*V_x-2*V_y+2 
    - Complexity: n 
* Chain [14] with precondition: [V_y>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_x,V_y,V_tx,B): nat(V_x-V_y+1)*2 
Asymptotic class: n 
* Total analysis performed in 91 ms.