/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_bb1_in/4,eval_foo_bb2_in/4]
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/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/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/4 
* CE 5 is refined into CE [6] 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 


### Cost equations --> "Loop" of eval_foo_bb1_in/4 
* CEs [7] --> Loop 6 
* CEs [8] --> Loop 7 
* CEs [6] --> Loop 8 

### Ranking functions of CR eval_foo_bb1_in(V_N,V__01,V__0,B) 

#### Partial ranking functions of CR eval_foo_bb1_in(V_N,V__01,V__0,B) 
* Partial RF of phase [6,7]:
  - RF of loop [6:1]:
    V__01 depends on loops [7:1] 
  - RF of loop [7:1]:
    V__0
    -V__01+1 depends on loops [6:1] 


### Specialization of cost equations eval_foo_bb0_in/3 
* CE 2 is refined into CE [9,10] 


### Cost equations --> "Loop" of eval_foo_bb0_in/3 
* CEs [10] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_foo_bb0_in(V_j,V_N,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_j,V_N,B) 


### Specialization of cost equations eval_foo_start/4 
* CE 1 is refined into CE [11,12] 


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

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

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


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

#### Cost of chains of eval_foo_bb1_in(V_N,V__01,V__0,B):
* Chain [[6,7],8]: 1*it(6)+1*it(7)+0
  Such that:aux(7) =< V_N
aux(2) =< V__01
it(7) =< V__0
aux(1) =< it(7)*aux(7)
it(6) =< aux(1)+aux(2)

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

* Chain [8]: 0
  with precondition: [B=2,0>=V__0,V_N>=V__0] 


#### Cost of chains of eval_foo_bb0_in(V_j,V_N,B):
* Chain [10]: 0
  with precondition: [0>=V_N] 

* Chain [9]: 1*s(3)+1*s(5)+0
  Such that:s(2) =< V_j
aux(8) =< V_N
s(3) =< aux(8)
s(4) =< s(3)*aux(8)
s(5) =< s(4)+s(2)

  with precondition: [V_N>=1] 


#### Cost of chains of eval_foo_start(V_i,V_j,V_N,B):
* Chain [12]: 0
  with precondition: [0>=V_N] 

* Chain [11]: 1*s(8)+1*s(10)+0
  Such that:s(6) =< V_j
s(7) =< V_N
s(8) =< s(7)
s(9) =< s(8)*s(7)
s(10) =< s(9)+s(6)

  with precondition: [V_N>=1] 


Closed-form bounds of eval_foo_start(V_i,V_j,V_N,B): 
-------------------------------------
* Chain [12] with precondition: [0>=V_N] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [11] with precondition: [V_N>=1] 
    - Upper bound: nat(V_j)+V_N+V_N*V_N 
    - Complexity: n^2 

### Maximum cost of eval_foo_start(V_i,V_j,V_N,B): nat(V_N)+nat(V_j)+nat(V_N)*nat(V_N) 
Asymptotic class: n^2 
* Total analysis performed in 90 ms.