/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [evalfbb1in/4,evalfbb2in/4]
1. recursive  : [evalfbb2in_loop_cont/7,evalfbb3in/6,evalfbb4in/6]
2. non_recursive  : [evalfstop/4]
3. non_recursive  : [evalfreturnin/4]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [evalfbb4in_loop_cont/5]
6. non_recursive  : [evalfentryin/4]
7. non_recursive  : [evalfstart/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalfbb2in/4
1. SCC is partially evaluated into evalfbb4in/6
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 evalfbb4in_loop_cont/5
6. SCC is partially evaluated into evalfentryin/4
7. SCC is partially evaluated into evalfstart/4

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

### Specialization of cost equations evalfbb2in/4 
* CE 11 is refined into CE [12] 
* CE 10 is refined into CE [13] 
* CE 9 is refined into CE [14] 


### Cost equations --> "Loop" of evalfbb2in/4 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR evalfbb2in(B,C,D,E) 
* RF of phase [12]: [B-C+1]

#### Partial ranking functions of CR evalfbb2in(B,C,D,E) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    B-C+1


### Specialization of cost equations evalfbb4in/6 
* CE 5 is refined into CE [15] 
* CE 3 is refined into CE [16,17] 
* CE 6 is refined into CE [18] 
* CE 4 is refined into CE [19] 


### Cost equations --> "Loop" of evalfbb4in/6 
* CEs [19] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16,17] --> Loop 17 
* CEs [18] --> Loop 18 

### Ranking functions of CR evalfbb4in(A,B,C,D,E,F) 
* RF of phase [15]: [-A+B+1]

#### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -A+B+1


### Specialization of cost equations evalfbb4in_loop_cont/5 
* CE 7 is refined into CE [20] 
* CE 8 is refined into CE [21] 


### Cost equations --> "Loop" of evalfbb4in_loop_cont/5 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 

### Ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations evalfentryin/4 
* CE 2 is refined into CE [22,23,24,25,26] 


### Cost equations --> "Loop" of evalfentryin/4 
* CEs [24] --> Loop 21 
* CEs [23,26] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [22] --> Loop 24 

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

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


### Specialization of cost equations evalfstart/4 
* CE 1 is refined into CE [27,28,29,30] 


### Cost equations --> "Loop" of evalfstart/4 
* CEs [30] --> Loop 25 
* CEs [29] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27] --> Loop 28 

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

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


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

#### Cost of chains of evalfbb2in(B,C,D,E):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -C+E

  with precondition: [D=2,B+1=E,C>=1,B>=C] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< B-C+1

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

* Chain [13]: 0
  with precondition: [D=3,B>=1,C>=1,B+1>=C] 


#### Cost of chains of evalfbb4in(A,B,C,D,E,F):
* Chain [[15],18]: 1*it(15)+1*s(3)+0
  Such that:aux(1) =< B
aux(3) =< -A+B+1
it(15) =< aux(3)
aux(1) =< aux(3)
s(3) =< it(15)*aux(1)

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

* Chain [[15],17]: 2*it(15)+1*s(3)+0
  Such that:aux(1) =< B
aux(4) =< -A+B
aux(5) =< -A+B+1
it(15) =< aux(4)
it(15) =< aux(5)
aux(1) =< aux(5)
s(3) =< it(15)*aux(1)

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

* Chain [[15],16]: 1*it(15)+1*s(3)+0
  Such that:aux(1) =< E
aux(6) =< -A+E
it(15) =< aux(6)
aux(1) =< aux(6)
s(3) =< it(15)*aux(1)

  with precondition: [D=4,B+1=E,B+1=F,A>=1,B>=A] 

* Chain [18]: 0
  with precondition: [D=3,A>=1] 

* Chain [17]: 1*s(4)+0
  Such that:s(4) =< -A+B+1

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

* Chain [16]: 0
  with precondition: [D=4,F=C,A=E,A>=1,A>=B+1] 


#### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E):
* Chain [20]: 0
  with precondition: [A=3] 

* Chain [19]: 0
  with precondition: [A=4] 


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

* Chain [23]: 0
  with precondition: [0>=B] 

* Chain [22]: 3*s(12)+1*s(13)+1*s(17)+0
  Such that:s(14) =< B+1
aux(9) =< B
s(12) =< aux(9)
s(13) =< s(12)*aux(9)
s(14) =< aux(9)
s(17) =< s(12)*s(14)

  with precondition: [B>=1] 

* Chain [21]: 2*s(21)+1*s(22)+0
  Such that:aux(10) =< B
s(21) =< aux(10)
s(22) =< s(21)*aux(10)

  with precondition: [B>=2] 


#### Cost of chains of evalfstart(A,B,C,D):
* Chain [28]: 0
  with precondition: [] 

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

* Chain [26]: 3*s(25)+1*s(26)+1*s(27)+0
  Such that:s(24) =< B
s(23) =< B+1
s(25) =< s(24)
s(26) =< s(25)*s(24)
s(23) =< s(24)
s(27) =< s(25)*s(23)

  with precondition: [B>=1] 

* Chain [25]: 2*s(29)+1*s(30)+0
  Such that:s(28) =< B
s(29) =< s(28)
s(30) =< s(29)*s(28)

  with precondition: [B>=2] 


Closed-form bounds of evalfstart(A,B,C,D): 
-------------------------------------
* Chain [28] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [B>=1] 
    - Upper bound: 3*B+B*B+(B+1)*B 
    - Complexity: n^2 
* Chain [25] with precondition: [B>=2] 
    - Upper bound: 2*B+B*B 
    - Complexity: n^2 

### Maximum cost of evalfstart(A,B,C,D): nat(B+1)*nat(B)+nat(B)+(nat(B)*nat(B)+nat(B)*2) 
Asymptotic class: n^2 
* Total analysis performed in 191 ms.