/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_bb2_in/5,eval_foo_bb3_in/5]
1. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in_loop_cont/4]
2. non_recursive  : [eval_foo_stop/1]
3. non_recursive  : [eval_foo_bb4_in/1]
4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
5. non_recursive  : [eval_foo_bb0_in/3]
6. non_recursive  : [eval_foo_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb2_in/5
1. SCC is partially evaluated into eval_foo_bb1_in/3
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/3
6. SCC is partially evaluated into eval_foo_start/4

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

### Specialization of cost equations eval_foo_bb2_in/5 
* CE 9 is refined into CE [10] 
* CE 8 is refined into CE [11] 


### Cost equations --> "Loop" of eval_foo_bb2_in/5 
* CEs [11] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR eval_foo_bb2_in(V__13,V__1,V__0,B,C) 
* RF of phase [10]: [V__0,-V__13+V__0+1]

#### Partial ranking functions of CR eval_foo_bb2_in(V__13,V__1,V__0,B,C) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V__0
    -V__13+V__0+1


### Specialization of cost equations eval_foo_bb1_in/3 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13,14] 


### Cost equations --> "Loop" of eval_foo_bb1_in/3 
* CEs [14] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR eval_foo_bb1_in(V__13,V__1,B) 
* RF of phase [12]: [V__13]

#### Partial ranking functions of CR eval_foo_bb1_in(V__13,V__1,B) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V__13


### Specialization of cost equations eval_foo_bb0_in/3 
* CE 5 is refined into CE [15,16,17,18] 
* CE 4 is refined into CE [19,20,21] 
* CE 3 is refined into CE [22,23,24] 
* CE 2 is refined into CE [25,26] 


### Cost equations --> "Loop" of eval_foo_bb0_in/3 
* CEs [17] --> Loop 15 
* CEs [23] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [21] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [25] --> Loop 20 
* CEs [24] --> Loop 21 
* CEs [26] --> Loop 22 
* CEs [15] --> Loop 23 
* CEs [22] --> Loop 24 
* CEs [16] --> Loop 25 
* CEs [19] --> Loop 26 

### 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/4 
* CE 1 is refined into CE [27,28,29,30,31,32,33,34,35,36,37,38] 


### Cost equations --> "Loop" of eval_foo_start/4 
* CEs [38] --> Loop 27 
* CEs [37] --> Loop 28 
* CEs [36] --> Loop 29 
* CEs [35] --> Loop 30 
* CEs [34] --> Loop 31 
* CEs [33] --> Loop 32 
* CEs [32] --> Loop 33 
* CEs [31] --> Loop 34 
* CEs [30] --> Loop 35 
* CEs [29] --> Loop 36 
* CEs [28] --> Loop 37 
* CEs [27] --> Loop 38 

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

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


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

#### Cost of chains of eval_foo_bb2_in(V__13,V__1,V__0,B,C):
* Chain [[10],11]: 1*it(10)+0
  Such that:it(10) =< -V__13+V__0+1

  with precondition: [B=2,C>=0,V__1>=V__0,V__13>=C+1,V__0>=V__13+C] 

* Chain [11]: 0
  with precondition: [B=2,V__0=C,V__0>=0,V__13>=V__0+1,V__1>=V__0] 


#### Cost of chains of eval_foo_bb1_in(V__13,V__1,B):
* Chain [[12],14]: 1*it(12)+1*s(3)+0
  Such that:it(12) =< V__13
s(3) =< V__13+V__1

  with precondition: [B=3,V__13>=1,V__1>=V__13] 

* Chain [14]: 0
  with precondition: [V__13=0,B=3,V__1>=0] 

* Chain [13,[12],14]: 1*it(12)+1*s(3)+1
  Such that:s(3) =< V__13+V__1
it(12) =< V__1

  with precondition: [B=3,V__1>=1,V__13>=V__1+1] 

* Chain [13,14]: 1
  with precondition: [V__1=0,B=3,V__13>=1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
* Chain [26]: 1
  with precondition: [V_x=0,0>=V_y+1] 

* Chain [25]: 1
  with precondition: [V_x=0,V_y>=1] 

* Chain [24]: 0
  with precondition: [V_y=0,0>=V_x+1] 

* Chain [23]: 0
  with precondition: [V_y=0,V_x>=0] 

* Chain [22]: 1*s(4)+1*s(5)+1
  Such that:s(5) =< -V_x
s(4) =< -V_x-V_y

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

* Chain [21]: 1*s(6)+1*s(7)+1
  Such that:s(7) =< -V_x
s(6) =< -V_x+V_y

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

* Chain [20]: 1*s(8)+1*s(9)+0
  Such that:s(9) =< -V_x-V_y
s(8) =< -V_y

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

* Chain [19]: 1*s(10)+1*s(11)+0
  Such that:s(11) =< V_x-V_y
s(10) =< -V_y

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

* Chain [18]: 1*s(12)+1*s(13)+1
  Such that:s(13) =< V_x
s(12) =< V_x-V_y

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

* Chain [17]: 1*s(14)+1*s(15)+1
  Such that:s(15) =< V_x
s(14) =< V_x+V_y

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

* Chain [16]: 1*s(16)+1*s(17)+0
  Such that:s(17) =< -V_x+V_y
s(16) =< V_y

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

* Chain [15]: 1*s(18)+1*s(19)+0
  Such that:s(19) =< V_x+V_y
s(18) =< V_y

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


#### Cost of chains of eval_foo_start(V_r,V_x,V_y,B):
* Chain [38]: 1
  with precondition: [V_x=0,0>=V_y+1] 

* Chain [37]: 1
  with precondition: [V_x=0,V_y>=1] 

* Chain [36]: 0
  with precondition: [V_y=0,0>=V_x+1] 

* Chain [35]: 0
  with precondition: [V_y=0,V_x>=0] 

* Chain [34]: 1*s(20)+1*s(21)+1
  Such that:s(20) =< -V_x
s(21) =< -V_x-V_y

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

* Chain [33]: 1*s(22)+1*s(23)+1
  Such that:s(22) =< -V_x
s(23) =< -V_x+V_y

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

* Chain [32]: 1*s(24)+1*s(25)+0
  Such that:s(24) =< -V_x-V_y
s(25) =< -V_y

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

* Chain [31]: 1*s(26)+1*s(27)+0
  Such that:s(26) =< V_x-V_y
s(27) =< -V_y

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

* Chain [30]: 1*s(28)+1*s(29)+1
  Such that:s(28) =< V_x
s(29) =< V_x-V_y

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

* Chain [29]: 1*s(30)+1*s(31)+1
  Such that:s(30) =< V_x
s(31) =< V_x+V_y

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

* Chain [28]: 1*s(32)+1*s(33)+0
  Such that:s(32) =< -V_x+V_y
s(33) =< V_y

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

* Chain [27]: 1*s(34)+1*s(35)+0
  Such that:s(34) =< V_x+V_y
s(35) =< V_y

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


Closed-form bounds of eval_foo_start(V_r,V_x,V_y,B): 
-------------------------------------
* Chain [38] with precondition: [V_x=0,0>=V_y+1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [37] with precondition: [V_x=0,V_y>=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [36] with precondition: [V_y=0,0>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [V_y=0,V_x>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=V_x+1,V_x>=V_y+1] 
    - Upper bound: -2*V_x-V_y+1 
    - Complexity: n 
* Chain [33] with precondition: [0>=V_x+1,V_x+V_y>=1] 
    - Upper bound: -2*V_x+V_y+1 
    - Complexity: n 
* Chain [32] with precondition: [0>=V_y+1,V_y>=V_x] 
    - Upper bound: -V_x-2*V_y 
    - Complexity: n 
* Chain [31] with precondition: [0>=V_y+1,V_x+V_y>=0] 
    - Upper bound: V_x-2*V_y 
    - Complexity: n 
* Chain [30] with precondition: [V_x>=1,0>=V_x+V_y+1] 
    - Upper bound: 2*V_x-V_y+1 
    - Complexity: n 
* Chain [29] with precondition: [V_x>=1,V_y>=V_x+1] 
    - Upper bound: 2*V_x+V_y+1 
    - Complexity: n 
* Chain [28] with precondition: [V_y>=1,0>=V_x+V_y] 
    - Upper bound: -V_x+2*V_y 
    - Complexity: n 
* Chain [27] with precondition: [V_y>=1,V_x>=V_y] 
    - Upper bound: V_x+2*V_y 
    - Complexity: n 

### Maximum cost of eval_foo_start(V_r,V_x,V_y,B): max([max([max([max([1,nat(-V_y)+max([nat(V_x-V_y),nat(-V_x-V_y)])]),nat(-V_x)+1+max([nat(-V_x+V_y),nat(-V_x-V_y)])]),nat(V_y)+max([nat(V_x+V_y),nat(-V_x+V_y)])]),nat(V_x)+1+max([nat(V_x+V_y),nat(V_x-V_y)])]) 
Asymptotic class: n 
* Total analysis performed in 203 ms.