/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/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/3]

#### 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/3

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

### Specialization of cost equations eval_foo_bb1_in/3 
* 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/3 
* CEs [7] --> Loop 6 
* CEs [8] --> Loop 7 
* CEs [6] --> Loop 8 

### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
* RF of phase [6]: [V__01+1]
* RF of phase [7]: [V__0+1]

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


### Specialization of cost equations eval_foo_bb0_in/3 
* CE 2 is refined into CE [9,10,11] 


### Cost equations --> "Loop" of eval_foo_bb0_in/3 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

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

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


### Specialization of cost equations eval_foo_start/3 
* CE 1 is refined into CE [12,13,14] 


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

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

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


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

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

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

* Chain [[6],[7],8]: 1*it(6)+1*s(1)+0
  Such that:it([[7],8]) =< 1
aux(8) =< V__01
it(6) =< V__01+1
aux(14) =< V__0+1
aux(10) =< aux(8)
aux(9) =< it(6)*aux(8)
aux(1) =< it(6)*aux(8)
aux(11) =< it(6)*aux(10)
aux(3) =< aux(9)
aux(1) =< it(6)*aux(10)
aux(3) =< aux(11)
s(1) =< aux(1)+aux(14)
aux(5) =< aux(14)+aux(3)
s(1) =< aux(3)+aux(14)
s(1) =< it([[7],8])*aux(5)

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

* Chain [8]: 0
  with precondition: [B=2,0>=V__0+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
* Chain [11]: 0
  with precondition: [0>=V_x+1] 

* Chain [10]: 1*s(2)+0
  Such that:s(2) =< V_x+1

  with precondition: [0>=V_y+1,V_x>=0] 

* Chain [9]: 1*s(5)+1*s(12)+0
  Such that:s(3) =< 1
s(6) =< V_x+1
s(4) =< V_y
s(5) =< V_y+1
s(7) =< s(4)
s(8) =< s(5)*s(4)
s(9) =< s(5)*s(4)
s(10) =< s(5)*s(7)
s(11) =< s(8)
s(9) =< s(5)*s(7)
s(11) =< s(10)
s(12) =< s(9)+s(6)
s(13) =< s(6)+s(11)
s(12) =< s(11)+s(6)
s(12) =< s(3)*s(13)

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


#### Cost of chains of eval_foo_start(V_x,V_y,B):
* Chain [14]: 0
  with precondition: [0>=V_x+1] 

* Chain [13]: 1*s(14)+0
  Such that:s(14) =< V_x+1

  with precondition: [0>=V_y+1,V_x>=0] 

* Chain [12]: 1*s(18)+1*s(24)+0
  Such that:s(15) =< 1
s(16) =< V_x+1
s(17) =< V_y
s(18) =< V_y+1
s(19) =< s(17)
s(20) =< s(18)*s(17)
s(21) =< s(18)*s(17)
s(22) =< s(18)*s(19)
s(23) =< s(20)
s(21) =< s(18)*s(19)
s(23) =< s(22)
s(24) =< s(21)+s(16)
s(25) =< s(16)+s(23)
s(24) =< s(23)+s(16)
s(24) =< s(15)*s(25)

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


Closed-form bounds of eval_foo_start(V_x,V_y,B): 
-------------------------------------
* Chain [14] with precondition: [0>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [13] with precondition: [0>=V_y+1,V_x>=0] 
    - Upper bound: V_x+1 
    - Complexity: n 
* Chain [12] with precondition: [V_x>=0,V_y>=0] 
    - Upper bound: V_x+1+(V_y+1)*V_y+(V_y+1) 
    - Complexity: n^2 

### Maximum cost of eval_foo_start(V_x,V_y,B): nat(V_y+1)*nat(V_y)+nat(V_y+1)+nat(V_x+1) 
Asymptotic class: n^2 
* Total analysis performed in 106 ms.