/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_Loopus2015_ex2_bb2_in/4,eval_Loopus2015_ex2_bb3_in/4]
1. recursive  : [eval_Loopus2015_ex2_bb4_in/2,eval_Loopus2015_ex2_bb5_in/2]
2. non_recursive  : [eval_Loopus2015_ex2_stop/1]
3. non_recursive  : [eval_Loopus2015_ex2_bb6_in/1]
4. non_recursive  : [eval_Loopus2015_ex2_bb4_in_loop_cont/2]
5. non_recursive  : [eval_Loopus2015_ex2_bb2_in_loop_cont/3]
6. non_recursive  : [eval_Loopus2015_ex2_1/5]
7. non_recursive  : [eval_Loopus2015_ex2_0/4]
8. non_recursive  : [eval_Loopus2015_ex2_bb1_in/4]
9. non_recursive  : [eval_Loopus2015_ex2_bb0_in/4]
10. non_recursive  : [eval_Loopus2015_ex2_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_Loopus2015_ex2_bb2_in/4
1. SCC is partially evaluated into eval_Loopus2015_ex2_bb4_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_Loopus2015_ex2_bb2_in_loop_cont/3
6. SCC is partially evaluated into eval_Loopus2015_ex2_1/5
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into eval_Loopus2015_ex2_bb0_in/4
10. SCC is partially evaluated into eval_Loopus2015_ex2_start/4

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

### Specialization of cost equations eval_Loopus2015_ex2_bb2_in/4 
* CE 9 is refined into CE [13] 
* CE 8 is refined into CE [14] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_bb2_in/4 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_Loopus2015_ex2_bb2_in(V_x_1,V_y_0,B,C) 
* RF of phase [13]: [V_y_0]

#### Partial ranking functions of CR eval_Loopus2015_ex2_bb2_in(V_x_1,V_y_0,B,C) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    V_y_0


### Specialization of cost equations eval_Loopus2015_ex2_bb4_in/2 
* CE 12 is refined into CE [15] 
* CE 11 is refined into CE [16] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_bb4_in/2 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR eval_Loopus2015_ex2_bb4_in(V_z_0,B) 
* RF of phase [15]: [V_z_0]

#### Partial ranking functions of CR eval_Loopus2015_ex2_bb4_in(V_z_0,B) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    V_z_0


### Specialization of cost equations eval_Loopus2015_ex2_bb2_in_loop_cont/3 
* CE 10 is refined into CE [17,18] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_bb2_in_loop_cont/3 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR eval_Loopus2015_ex2_bb2_in_loop_cont(A,B,C) 

#### Partial ranking functions of CR eval_Loopus2015_ex2_bb2_in_loop_cont(A,B,C) 


### Specialization of cost equations eval_Loopus2015_ex2_1/5 
* CE 6 is refined into CE [19,20,21] 
* CE 7 is refined into CE [22,23,24] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_1/5 
* CEs [21] --> Loop 19 
* CEs [24] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [19] --> Loop 24 

### Ranking functions of CR eval_Loopus2015_ex2_1(V_n,V_m1,V_m2,V_3,B) 

#### Partial ranking functions of CR eval_Loopus2015_ex2_1(V_n,V_m1,V_m2,V_3,B) 


### Specialization of cost equations eval_Loopus2015_ex2_bb0_in/4 
* CE 5 is refined into CE [25,26,27,28,29,30] 
* CE 4 is refined into CE [31] 
* CE 3 is refined into CE [32] 
* CE 2 is refined into CE [33] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_bb0_in/4 
* CEs [29,30] --> Loop 25 
* CEs [31] --> Loop 26 
* CEs [32] --> Loop 27 
* CEs [33] --> Loop 28 
* CEs [28] --> Loop 29 
* CEs [27] --> Loop 30 
* CEs [26] --> Loop 31 
* CEs [25] --> Loop 32 

### Ranking functions of CR eval_Loopus2015_ex2_bb0_in(V_n,V_m1,V_m2,B) 

#### Partial ranking functions of CR eval_Loopus2015_ex2_bb0_in(V_n,V_m1,V_m2,B) 


### Specialization of cost equations eval_Loopus2015_ex2_start/4 
* CE 1 is refined into CE [34,35,36,37,38,39,40,41] 


### Cost equations --> "Loop" of eval_Loopus2015_ex2_start/4 
* CEs [41] --> Loop 33 
* CEs [40] --> Loop 34 
* CEs [39] --> Loop 35 
* CEs [38] --> Loop 36 
* CEs [37] --> Loop 37 
* CEs [36] --> Loop 38 
* CEs [35] --> Loop 39 
* CEs [34] --> Loop 40 

### Ranking functions of CR eval_Loopus2015_ex2_start(V_n,V_m1,V_m2,B) 

#### Partial ranking functions of CR eval_Loopus2015_ex2_start(V_n,V_m1,V_m2,B) 


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

#### Cost of chains of eval_Loopus2015_ex2_bb2_in(V_x_1,V_y_0,B,C):
* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< -V_x_1/2+C/2

  with precondition: [B=3,V_x_1+2*V_y_0=C,V_x_1>=0,V_y_0>=1] 

* Chain [14]: 0
  with precondition: [V_y_0=0,B=3,V_x_1=C,V_x_1>=0] 


#### Cost of chains of eval_Loopus2015_ex2_bb4_in(V_z_0,B):
* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< V_z_0

  with precondition: [B=2,V_z_0>=1] 

* Chain [16]: 0
  with precondition: [B=2,0>=V_z_0] 


#### Cost of chains of eval_Loopus2015_ex2_bb2_in_loop_cont(A,B,C):
* Chain [18]: 0
  with precondition: [A=3,0>=B] 

* Chain [17]: 1*s(1)+0
  Such that:s(1) =< B

  with precondition: [A=3,B>=1] 


#### Cost of chains of eval_Loopus2015_ex2_1(V_n,V_m1,V_m2,V_3,B):
* Chain [24]: 0
  with precondition: [V_n=0,V_m1=0,V_m2>=0,V_3>=1] 

* Chain [23]: 0
  with precondition: [V_n=0,V_m2=0,0>=V_3,V_m1>=0] 

* Chain [22]: 1*s(2)+0
  Such that:s(2) =< V_m2

  with precondition: [V_n=0,0>=V_3,V_m1>=0,V_m2>=1] 

* Chain [21]: 1*s(3)+0
  Such that:s(3) =< V_m1

  with precondition: [V_n=0,V_m1>=1,V_m2>=0,V_3>=1] 

* Chain [20]: 1*s(4)+1*s(5)+0
  Such that:s(4) =< V_n
s(5) =< 2*V_n+V_m2

  with precondition: [0>=V_3,V_n>=1,V_m1>=0,V_m2>=0] 

* Chain [19]: 1*s(6)+1*s(7)+0
  Such that:s(6) =< V_n
s(7) =< 2*V_n+V_m1

  with precondition: [V_n>=1,V_m1>=0,V_m2>=0,V_3>=1] 


#### Cost of chains of eval_Loopus2015_ex2_bb0_in(V_n,V_m1,V_m2,B):
* Chain [32]: 0
  with precondition: [V_n=0,V_m1=0,V_m2>=0] 

* Chain [31]: 0
  with precondition: [V_n=0,V_m2=0,V_m1>=0] 

* Chain [30]: 1*s(8)+0
  Such that:s(8) =< V_m2

  with precondition: [V_n=0,V_m1>=0,V_m2>=1] 

* Chain [29]: 1*s(9)+0
  Such that:s(9) =< V_m1

  with precondition: [V_n=0,V_m1>=1,V_m2>=0] 

* Chain [28]: 0
  with precondition: [0>=V_n+1] 

* Chain [27]: 0
  with precondition: [0>=V_m1+1] 

* Chain [26]: 0
  with precondition: [0>=V_m2+1] 

* Chain [25]: 2*s(10)+1*s(11)+1*s(13)+0
  Such that:s(13) =< 2*V_n+V_m1
s(11) =< 2*V_n+V_m2
aux(1) =< V_n
s(10) =< aux(1)

  with precondition: [V_n>=1,V_m1>=0,V_m2>=0] 


#### Cost of chains of eval_Loopus2015_ex2_start(V_n,V_m1,V_m2,B):
* Chain [40]: 0
  with precondition: [V_n=0,V_m1=0,V_m2>=0] 

* Chain [39]: 0
  with precondition: [V_n=0,V_m2=0,V_m1>=0] 

* Chain [38]: 1*s(14)+0
  Such that:s(14) =< V_m2

  with precondition: [V_n=0,V_m1>=0,V_m2>=1] 

* Chain [37]: 1*s(15)+0
  Such that:s(15) =< V_m1

  with precondition: [V_n=0,V_m1>=1,V_m2>=0] 

* Chain [36]: 0
  with precondition: [0>=V_n+1] 

* Chain [35]: 0
  with precondition: [0>=V_m1+1] 

* Chain [34]: 0
  with precondition: [0>=V_m2+1] 

* Chain [33]: 1*s(16)+1*s(17)+2*s(19)+0
  Such that:s(18) =< V_n
s(16) =< 2*V_n+V_m1
s(17) =< 2*V_n+V_m2
s(19) =< s(18)

  with precondition: [V_n>=1,V_m1>=0,V_m2>=0] 


Closed-form bounds of eval_Loopus2015_ex2_start(V_n,V_m1,V_m2,B): 
-------------------------------------
* Chain [40] with precondition: [V_n=0,V_m1=0,V_m2>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [V_n=0,V_m2=0,V_m1>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [38] with precondition: [V_n=0,V_m1>=0,V_m2>=1] 
    - Upper bound: V_m2 
    - Complexity: n 
* Chain [37] with precondition: [V_n=0,V_m1>=1,V_m2>=0] 
    - Upper bound: V_m1 
    - Complexity: n 
* Chain [36] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [0>=V_m1+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=V_m2+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [V_n>=1,V_m1>=0,V_m2>=0] 
    - Upper bound: 6*V_n+V_m1+V_m2 
    - Complexity: n 

### Maximum cost of eval_Loopus2015_ex2_start(V_n,V_m1,V_m2,B): max([nat(V_m1),nat(V_m2),nat(V_n)*2+nat(2*V_n+V_m1)+nat(2*V_n+V_m2)]) 
Asymptotic class: n 
* Total analysis performed in 160 ms.