/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval_speedSingleSingle2_3/9,eval_speedSingleSingle2_4/9,eval_speedSingleSingle2_bb1_in/9,eval_speedSingleSingle2_bb2_in/9,eval_speedSingleSingle2_bb3_in/9,eval_speedSingleSingle2_bb4_in/9,eval_speedSingleSingle2_bb5_in/9]
1. non_recursive  : [eval_speedSingleSingle2_stop/6]
2. non_recursive  : [eval_speedSingleSingle2_bb6_in/6]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval_speedSingleSingle2_bb1_in_loop_cont/7]
5. non_recursive  : [eval_speedSingleSingle2_2/6]
6. non_recursive  : [eval_speedSingleSingle2_1/6]
7. non_recursive  : [eval_speedSingleSingle2_0/6]
8. non_recursive  : [eval_speedSingleSingle2_bb0_in/6]
9. non_recursive  : [eval_speedSingleSingle2_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_speedSingleSingle2_bb1_in/9
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_speedSingleSingle2_bb1_in_loop_cont/7
5. SCC is partially evaluated into eval_speedSingleSingle2_2/6
6. SCC is completely evaluated into other SCCs
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into eval_speedSingleSingle2_start/6

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

### Specialization of cost equations eval_speedSingleSingle2_bb1_in/9 
* CE 9 is refined into CE [12] 
* CE 7 is refined into CE [13] 
* CE 8 is refined into CE [14] 
* CE 5 is refined into CE [15] 
* CE 6 is refined into CE [16] 


### Cost equations --> "Loop" of eval_speedSingleSingle2_bb1_in/9 
* CEs [16] --> Loop 12 
* CEs [15] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [13] --> Loop 15 
* CEs [14] --> Loop 16 

### Ranking functions of CR eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E) 
* RF of phase [12]: [V_m-V_x_0,V_m-V_y_0]
* RF of phase [13]: [V_n-V_x_0,V_n-V_y_0]

#### Partial ranking functions of CR eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V_m-V_x_0
    V_m-V_y_0
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    V_n-V_x_0
    V_n-V_y_0


### Specialization of cost equations eval_speedSingleSingle2_bb1_in_loop_cont/7 
* CE 11 is refined into CE [17] 
* CE 10 is refined into CE [18] 


### Cost equations --> "Loop" of eval_speedSingleSingle2_bb1_in_loop_cont/7 
* CEs [17] --> Loop 17 
* CEs [18] --> Loop 18 

### Ranking functions of CR eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations eval_speedSingleSingle2_2/6 
* CE 4 is refined into CE [19,20,21,22,23,24,25,26,27,28,29,30] 
* CE 2 is refined into CE [31] 
* CE 3 is refined into CE [32] 


### Cost equations --> "Loop" of eval_speedSingleSingle2_2/6 
* CEs [22,26,30] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [24,28] --> Loop 21 
* CEs [19,27] --> Loop 22 
* CEs [31] --> Loop 23 
* CEs [32] --> Loop 24 
* CEs [21,25,29] --> Loop 25 
* CEs [20] --> Loop 26 

### Ranking functions of CR eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B) 

#### Partial ranking functions of CR eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B) 


### Specialization of cost equations eval_speedSingleSingle2_start/6 
* CE 1 is refined into CE [33,34,35,36,37,38,39,40] 


### Cost equations --> "Loop" of eval_speedSingleSingle2_start/6 
* CEs [40] --> Loop 27 
* CEs [39] --> Loop 28 
* CEs [38] --> Loop 29 
* CEs [37] --> Loop 30 
* CEs [36] --> Loop 31 
* CEs [35] --> Loop 32 
* CEs [34] --> Loop 33 
* CEs [33] --> Loop 34 

### Ranking functions of CR eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B) 

#### Partial ranking functions of CR eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B) 


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

#### Cost of chains of eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E):
* Chain [[13],[12],16]: 1*it(12)+1*it(13)+0
  Such that:it(12) =< -V_n+D
it(13) =< V_n-V_x_0

  with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_x_0>=0,D>=V_n+1,V_n>=V_x_0+1,V_m>=D] 

* Chain [[13],[12],15]: 1*it(12)+1*it(13)+0
  Such that:it(12) =< -V_n+D
it(13) =< V_n-V_y_0

  with precondition: [B=2,V_x_0=V_y_0,V_m=D,V_m=E,V_x_0>=0,C>=1,V_m>=V_n+1,V_n>=V_x_0+1] 

* Chain [[13],[12],14]: 1*it(12)+1*it(13)+0
  Such that:it(12) =< V_m-V_n
it(13) =< V_n-V_y_0

  with precondition: [B=3,V_x_0=V_y_0,V_x_0>=0,V_m>=V_n+1,V_n>=V_x_0+1] 

* Chain [[13],16]: 1*it(13)+0
  Such that:it(13) =< -V_y_0+D

  with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_m>=0,V_x_0>=0,D>=V_x_0+1,V_n>=D] 

* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< -V_y_0+D

  with precondition: [B=2,V_x_0=V_y_0,V_n=D,V_n=E,V_m>=0,V_x_0>=0,C>=1,V_n>=V_m,V_n>=V_x_0+1] 

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< V_n-V_y_0

  with precondition: [B=3,V_x_0=V_y_0,V_m>=0,V_x_0>=0,V_n>=V_x_0+1] 

* Chain [[12],16]: 1*it(12)+0
  Such that:it(12) =< -V_y_0+D

  with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_n>=0,V_x_0>=V_n,D>=V_x_0+1,V_m>=D] 

* Chain [[12],15]: 1*it(12)+0
  Such that:it(12) =< -V_y_0+D

  with precondition: [B=2,V_x_0=V_y_0,V_m=D,V_m=E,V_n>=0,C>=1,V_x_0>=V_n,V_m>=V_x_0+1] 

* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< V_m-V_y_0

  with precondition: [B=3,V_x_0=V_y_0,V_n>=0,V_x_0>=V_n,V_m>=V_x_0+1] 

* Chain [16]: 0
  with precondition: [B=2,V_y_0=V_x_0,V_y_0=D,V_y_0=E,0>=C,V_m>=0,V_n>=0,V_y_0>=0,V_m+V_n>=V_y_0] 

* Chain [15]: 0
  with precondition: [B=2,V_y_0=V_x_0,V_y_0=D,V_y_0=E,C>=1,V_y_0>=V_m,V_y_0>=V_n,V_m+V_n>=V_y_0] 

* Chain [14]: 0
  with precondition: [B=3,V_y_0=V_x_0,V_m>=0,V_n>=0,V_y_0>=0,V_m+V_n>=V_y_0] 


#### Cost of chains of eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G):
* Chain [18]: 0
  with precondition: [A=2,C>=0,D>=0] 

* Chain [17]: 0
  with precondition: [A=3,C>=0,D>=0] 


#### Cost of chains of eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B):
* Chain [26]: 0
  with precondition: [V_m=0,V_n=0] 

* Chain [25]: 3*s(1)+0
  Such that:aux(1) =< V_m
s(1) =< aux(1)

  with precondition: [V_n=0,V_m>=1] 

* Chain [24]: 0
  with precondition: [0>=V_m+1] 

* Chain [23]: 0
  with precondition: [0>=V_n+1] 

* Chain [22]: 0
  with precondition: [V_m>=0,V_n>=0] 

* Chain [21]: 2*s(4)+0
  Such that:aux(2) =< V_n
s(4) =< aux(2)

  with precondition: [V_m>=0,V_n>=1] 

* Chain [20]: 1*s(6)+0
  Such that:s(6) =< V_n

  with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 

* Chain [19]: 3*s(7)+3*s(8)+0
  Such that:aux(3) =< V_m-V_n
aux(4) =< V_n
s(7) =< aux(3)
s(8) =< aux(4)

  with precondition: [V_n>=1,V_m>=V_n+1] 


#### Cost of chains of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B):
* Chain [34]: 0
  with precondition: [V_m=0,V_n=0] 

* Chain [33]: 3*s(14)+0
  Such that:s(13) =< V_m
s(14) =< s(13)

  with precondition: [V_n=0,V_m>=1] 

* Chain [32]: 0
  with precondition: [0>=V_m+1] 

* Chain [31]: 0
  with precondition: [0>=V_n+1] 

* Chain [30]: 0
  with precondition: [V_m>=0,V_n>=0] 

* Chain [29]: 2*s(16)+0
  Such that:s(15) =< V_n
s(16) =< s(15)

  with precondition: [V_m>=0,V_n>=1] 

* Chain [28]: 1*s(17)+0
  Such that:s(17) =< V_n

  with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 

* Chain [27]: 3*s(20)+3*s(21)+0
  Such that:s(18) =< V_m-V_n
s(19) =< V_n
s(20) =< s(18)
s(21) =< s(19)

  with precondition: [V_n>=1,V_m>=V_n+1] 


Closed-form bounds of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B): 
-------------------------------------
* Chain [34] with precondition: [V_m=0,V_n=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [V_n=0,V_m>=1] 
    - Upper bound: 3*V_m 
    - Complexity: n 
* Chain [32] with precondition: [0>=V_m+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [V_m>=0,V_n>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [V_m>=0,V_n>=1] 
    - Upper bound: 2*V_n 
    - Complexity: n 
* Chain [28] with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 
    - Upper bound: V_n 
    - Complexity: n 
* Chain [27] with precondition: [V_n>=1,V_m>=V_n+1] 
    - Upper bound: 3*V_m 
    - Complexity: n 

### Maximum cost of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B): max([nat(V_m)*3,nat(V_m-V_n)*3+nat(V_n)+nat(V_n)+nat(V_n)]) 
Asymptotic class: n 
* Total analysis performed in 456 ms.