/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. non_recursive  : [end/5]
1. recursive  : [eval3/5]
2. recursive  : [eval11/4,eval5/4,eval7/4,eval9/4]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [eval5_loop_cont/2]
5. non_recursive  : [eval3_loop_cont/6]
6. non_recursive  : [eval1/5]
7. non_recursive  : [eval0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into eval3/5
2. SCC is partially evaluated into eval5/4
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval3_loop_cont/6
6. SCC is partially evaluated into eval1/5
7. SCC is partially evaluated into eval0/5

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

### Specialization of cost equations eval3/5 
* CE 5 is refined into CE [13] 
* CE 6 is refined into CE [14] 
* CE 4 is refined into CE [15] 


### Cost equations --> "Loop" of eval3/5 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR eval3(A,C,E,F,G) 
* RF of phase [13]: [-A/11+101/11]

#### Partial ranking functions of CR eval3(A,C,E,F,G) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    -A/11+101/11


### Specialization of cost equations eval5/4 
* CE 12 is refined into CE [16] 
* CE 10 is refined into CE [17] 
* CE 11 is refined into CE [18] 
* CE 9 is refined into CE [19] 


### Cost equations --> "Loop" of eval5/4 
* CEs [17] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [16] --> Loop 19 

### Ranking functions of CR eval5(A,C,D,E) 

#### Partial ranking functions of CR eval5(A,C,D,E) 
* Partial RF of phase [16,17]:
  - RF of loop [16:1]:
    -A+111 depends on loops [17:1] 
  - RF of loop [17:1]:
    A/9-110/9 depends on loops [16:1] 
    C-1


### Specialization of cost equations eval3_loop_cont/6 
* CE 8 is refined into CE [20,21,22] 
* CE 7 is refined into CE [23] 


### Cost equations --> "Loop" of eval3_loop_cont/6 
* CEs [22] --> Loop 20 
* CEs [21] --> Loop 21 
* CEs [20] --> Loop 22 
* CEs [23] --> Loop 23 

### Ranking functions of CR eval3_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR eval3_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations eval1/5 
* CE 2 is refined into CE [24] 
* CE 3 is refined into CE [25,26,27,28,29] 


### Cost equations --> "Loop" of eval1/5 
* CEs [24] --> Loop 24 
* CEs [25,26,28,29] --> Loop 25 
* CEs [27] --> Loop 26 

### Ranking functions of CR eval1(A,B,C,D,E) 

#### Partial ranking functions of CR eval1(A,B,C,D,E) 


### Specialization of cost equations eval0/5 
* CE 1 is refined into CE [30,31,32] 


### Cost equations --> "Loop" of eval0/5 
* CEs [32] --> Loop 27 
* CEs [31] --> Loop 28 
* CEs [30] --> Loop 29 

### Ranking functions of CR eval0(A,B,C,D,E) 

#### Partial ranking functions of CR eval0(A,B,C,D,E) 


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

#### Cost of chains of eval3(A,C,E,F,G):
* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< -A/11+101/11

  with precondition: [E=2,100>=A,C>=1] 

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< -A/11+101/11

  with precondition: [E=3,A+11*G=11*C+F,111>=F,C>=1,F>=101,F>=A+11] 

* Chain [15]: 0
  with precondition: [E=2,C>=1,11*C+89>=A] 


#### Cost of chains of eval5(A,C,D,E):
* Chain [[16,17],19]: 1*it(16)+1*it(17)+0
  Such that:aux(1) =< -A+111
it(17) =< C
it(16) =< it(17)*9+aux(1)

  with precondition: [E=2,C>=2] 

* Chain [[16,17],18,19]: 1*it(16)+1*it(17)+1
  Such that:aux(1) =< -A+111
it(17) =< C
it(16) =< it(17)*9+aux(1)

  with precondition: [E=2,C>=2] 

* Chain [19]: 0
  with precondition: [E=2] 

* Chain [18,19]: 1
  with precondition: [C=2,E=2,A>=111] 


#### Cost of chains of eval3_loop_cont(A,B,C,D,E,F):
* Chain [23]: 0
  with precondition: [A=2,100>=C] 

* Chain [22]: 1
  with precondition: [A=3,D=2,100>=C,B>=111] 

* Chain [21]: 0
  with precondition: [A=3,100>=C] 

* Chain [20]: 2*s(9)+2*s(10)+1
  Such that:s(7) =< -B+111
s(8) =< D
s(9) =< s(8)
s(10) =< s(9)*9+s(7)

  with precondition: [A=3,100>=C,D>=2] 


#### Cost of chains of eval1(A,B,C,D,E):
* Chain [26]: 1*s(11)+1
  Such that:s(11) =< 1/11

  with precondition: [A=100,B=100,C=1] 

* Chain [25]: 2*s(12)+1*s(14)+2*s(17)+2*s(18)+1
  Such that:s(15) =< 10
aux(7) =< -B+122
s(14) =< -B/11+101/11
s(16) =< -B/11+122/11
aux(8) =< -A/11+101/11
s(12) =< aux(8)
s(15) =< aux(7)
s(16) =< aux(7)
s(17) =< s(16)
s(18) =< s(17)*9+s(15)

  with precondition: [C=1,B=A,100>=B] 

* Chain [24]: 0
  with precondition: [C=1,B=A,B>=101] 


#### Cost of chains of eval0(A,B,C,D,E):
* Chain [29]: 1*s(19)+1
  Such that:s(19) =< 1/11

  with precondition: [B=100] 

* Chain [28]: 3*s(22)+2*s(26)+2*s(27)+1
  Such that:s(20) =< 10
s(21) =< -B+122
s(23) =< -B/11+122/11
aux(9) =< -B/11+101/11
s(22) =< aux(9)
s(20) =< s(21)
s(23) =< s(21)
s(26) =< s(23)
s(27) =< s(26)*9+s(20)

  with precondition: [100>=B] 

* Chain [27]: 0
  with precondition: [B>=101] 


Closed-form bounds of eval0(A,B,C,D,E): 
-------------------------------------
* Chain [29] with precondition: [B=100] 
    - Upper bound: 12/11 
    - Complexity: constant 
* Chain [28] with precondition: [100>=B] 
    - Upper bound: -23/11*B+2974/11 
    - Complexity: n 
* Chain [27] with precondition: [B>=101] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval0(A,B,C,D,E): max([12/11,nat(-B/11+101/11)*3+21+nat(-B/11+122/11)*20]) 
Asymptotic class: n 
* Total analysis performed in 223 ms.