/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  : [evalfbb1in/4,evalfbb2in/4,evalfbb3in/4,evalfbbin/4]
1. non_recursive  : [evalfstop/3]
2. non_recursive  : [evalfreturnin/3]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evalfbb3in_loop_cont/4]
5. non_recursive  : [evalfentryin/3]
6. non_recursive  : [evalfstart/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalfbb3in/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 evalfbb3in_loop_cont/4
5. SCC is partially evaluated into evalfentryin/3
6. SCC is partially evaluated into evalfstart/3

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

### Specialization of cost equations evalfbb3in/4 
* CE 8 is refined into CE [11] 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 4 is refined into CE [14] 
* CE 3 is refined into CE [15] 
* CE 5 is refined into CE [16] 


### Cost equations --> "Loop" of evalfbb3in/4 
* CEs [14] --> Loop 11 
* CEs [15] --> Loop 12 
* CEs [16] --> Loop 13 
* CEs [11] --> Loop 14 
* CEs [12] --> Loop 15 
* CEs [13] --> Loop 16 

### Ranking functions of CR evalfbb3in(A,B,C,D) 
* RF of phase [11]: [-B+255]
* RF of phase [12]: [-B+255]
* RF of phase [13]: [B]

#### Partial ranking functions of CR evalfbb3in(A,B,C,D) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    -B+255
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -B+255
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    B


### Specialization of cost equations evalfbb3in_loop_cont/4 
* CE 10 is refined into CE [17] 
* CE 9 is refined into CE [18] 


### Cost equations --> "Loop" of evalfbb3in_loop_cont/4 
* CEs [17] --> Loop 17 
* CEs [18] --> Loop 18 

### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D) 


### Specialization of cost equations evalfentryin/3 
* CE 2 is refined into CE [19,20,21,22,23,24,25,26,27] 


### Cost equations --> "Loop" of evalfentryin/3 
* CEs [24] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [22,27] --> Loop 21 
* CEs [21,26] --> Loop 22 
* CEs [19,20] --> Loop 23 
* CEs [25] --> Loop 24 

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

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


### Specialization of cost equations evalfstart/3 
* CE 1 is refined into CE [28,29,30,31,32,33] 


### Cost equations --> "Loop" of evalfstart/3 
* CEs [33] --> Loop 25 
* CEs [32] --> Loop 26 
* CEs [31] --> Loop 27 
* CEs [30] --> Loop 28 
* CEs [29] --> Loop 29 
* CEs [28] --> Loop 30 

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

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


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

#### Cost of chains of evalfbb3in(A,B,C,D):
* Chain [[13],16]: 1*it(13)+0
  Such that:it(13) =< B

  with precondition: [A=0,C=2,D=0,254>=B,B>=1] 

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

  with precondition: [A=0,C=3,254>=B,B>=1] 

* Chain [[12],15]: 1*it(12)+0
  Such that:it(12) =< -B+255

  with precondition: [C=2,D=255,0>=A+1,254>=B,B>=1] 

* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -B+255

  with precondition: [C=3,0>=A+1,254>=B,B>=1] 

* Chain [[11],15]: 1*it(11)+0
  Such that:it(11) =< -B+255

  with precondition: [C=2,D=255,254>=B,A>=1,B>=1] 

* Chain [[11],14]: 1*it(11)+0
  Such that:it(11) =< -B+255

  with precondition: [C=3,254>=B,A>=1,B>=1] 

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

* Chain [15]: 0
  with precondition: [C=2,B=D,B>=255] 

* Chain [14]: 0
  with precondition: [C=3] 


#### Cost of chains of evalfbb3in_loop_cont(A,B,C,D):
* Chain [18]: 0
  with precondition: [A=2] 

* Chain [17]: 0
  with precondition: [A=3] 


#### Cost of chains of evalfentryin(A,B,C):
* Chain [24]: 0
  with precondition: [] 

* Chain [23]: 2*s(1)+0
  Such that:aux(1) =< A
s(1) =< aux(1)

  with precondition: [B=0,254>=A,A>=1] 

* Chain [22]: 2*s(3)+0
  Such that:aux(2) =< -A+255
s(3) =< aux(2)

  with precondition: [254>=A,0>=B+1,A>=1] 

* Chain [21]: 2*s(5)+0
  Such that:aux(3) =< -A+255
s(5) =< aux(3)

  with precondition: [254>=A,A>=1,B>=1] 

* Chain [20]: 0
  with precondition: [0>=A] 

* Chain [19]: 0
  with precondition: [A>=255] 


#### Cost of chains of evalfstart(A,B,C):
* Chain [30]: 0
  with precondition: [] 

* Chain [29]: 2*s(8)+0
  Such that:s(7) =< A
s(8) =< s(7)

  with precondition: [B=0,254>=A,A>=1] 

* Chain [28]: 2*s(10)+0
  Such that:s(9) =< -A+255
s(10) =< s(9)

  with precondition: [254>=A,0>=B+1,A>=1] 

* Chain [27]: 2*s(12)+0
  Such that:s(11) =< -A+255
s(12) =< s(11)

  with precondition: [254>=A,A>=1,B>=1] 

* Chain [26]: 0
  with precondition: [0>=A] 

* Chain [25]: 0
  with precondition: [A>=255] 


Closed-form bounds of evalfstart(A,B,C): 
-------------------------------------
* Chain [30] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [B=0,254>=A,A>=1] 
    - Upper bound: 2*A 
    - Complexity: n 
* Chain [28] with precondition: [254>=A,0>=B+1,A>=1] 
    - Upper bound: -2*A+510 
    - Complexity: n 
* Chain [27] with precondition: [254>=A,A>=1,B>=1] 
    - Upper bound: -2*A+510 
    - Complexity: n 
* Chain [26] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [A>=255] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of evalfstart(A,B,C): max([nat(A)*2,nat(-A+255)*2]) 
Asymptotic class: n 
* Total analysis performed in 170 ms.