/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^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(A,C,D,E) 
* RF of phase [12]: [A-C+1]

#### Partial ranking functions of CR evalfbb2in(A,C,D,E) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    A-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 [19,20] 


### Cost equations --> "Loop" of evalfbb4in/6 
* CEs [19] --> Loop 15 
* CEs [20] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [18] --> Loop 20 

### Ranking functions of CR evalfbb4in(A,B,C,D,E,F) 
* RF of phase [15]: [B]
* RF of phase [16]: [B]

#### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    B
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    B


### Specialization of cost equations evalfbb4in_loop_cont/5 
* CE 7 is refined into CE [21] 
* CE 8 is refined into CE [22] 


### Cost equations --> "Loop" of evalfbb4in_loop_cont/5 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 

### 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 [23,24,25,26,27,28,29,30,31] 


### Cost equations --> "Loop" of evalfentryin/4 
* CEs [27] --> Loop 23 
* CEs [26,30] --> Loop 24 
* CEs [28] --> Loop 25 
* CEs [25] --> Loop 26 
* CEs [24,29] --> Loop 27 
* CEs [31] --> Loop 28 
* CEs [23] --> Loop 29 

### 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 [32,33,34,35,36,37,38] 


### Cost equations --> "Loop" of evalfstart/4 
* CEs [38] --> Loop 30 
* CEs [37] --> Loop 31 
* CEs [36] --> Loop 32 
* CEs [35] --> Loop 33 
* CEs [34] --> Loop 34 
* CEs [33] --> Loop 35 
* CEs [32] --> Loop 36 

### 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(A,C,D,E):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< -C+E

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

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

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

* Chain [14]: 0
  with precondition: [D=2,C=E,C>=1,C>=A+1] 

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


#### Cost of chains of evalfbb4in(A,B,C,D,E,F):
* Chain [[16],20]: 1*it(16)+0
  Such that:it(16) =< B

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

* Chain [[16],18]: 1*it(16)+0
  Such that:it(16) =< B

  with precondition: [D=3,0>=A,B>=2] 

* Chain [[16],17]: 1*it(16)+0
  Such that:it(16) =< B

  with precondition: [D=4,E=0,F=1,0>=A,B>=1] 

* Chain [[15],20]: 1*it(15)+1*s(3)+0
  Such that:aux(1) =< A
it(15) =< B
s(3) =< it(15)*aux(1)

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

* Chain [[15],19]: 1*it(15)+1*s(3)+1*s(4)+0
  Such that:it(15) =< B
aux(2) =< A
s(4) =< aux(2)
s(3) =< it(15)*aux(2)

  with precondition: [D=3,A>=1,B>=2] 

* Chain [[15],18]: 1*it(15)+1*s(3)+0
  Such that:aux(1) =< A
it(15) =< B
s(3) =< it(15)*aux(1)

  with precondition: [D=3,A>=1,B>=2] 

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

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

* Chain [20]: 0
  with precondition: [D=3] 

* Chain [19]: 1*s(4)+0
  Such that:s(4) =< A

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

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

* Chain [17]: 0
  with precondition: [D=4,F=C,B=E,0>=B] 


#### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E):
* Chain [22]: 0
  with precondition: [A=3] 

* Chain [21]: 0
  with precondition: [A=4] 


#### Cost of chains of evalfentryin(A,B,C,D):
* Chain [29]: 0
  with precondition: [] 

* Chain [28]: 0
  with precondition: [0>=A] 

* Chain [27]: 2*s(16)+0
  Such that:aux(6) =< A
s(16) =< aux(6)

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

* Chain [26]: 1*s(18)+0
  Such that:s(18) =< A

  with precondition: [0>=B,A>=2] 

* Chain [25]: 0
  with precondition: [A>=1] 

* Chain [24]: 2*s(19)+1*s(21)+2*s(22)+0
  Such that:aux(7) =< A
aux(8) =< B
s(19) =< aux(7)
s(21) =< aux(8)
s(22) =< s(19)*aux(8)

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

* Chain [23]: 2*s(28)+2*s(29)+1*s(30)+0
  Such that:s(27) =< A
s(26) =< B
s(28) =< s(27)
s(29) =< s(28)*s(26)
s(30) =< s(26)

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


#### Cost of chains of evalfstart(A,B,C,D):
* Chain [36]: 0
  with precondition: [] 

* Chain [35]: 0
  with precondition: [0>=A] 

* Chain [34]: 2*s(32)+0
  Such that:s(31) =< A
s(32) =< s(31)

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

* Chain [33]: 1*s(33)+0
  Such that:s(33) =< A

  with precondition: [0>=B,A>=2] 

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

* Chain [31]: 2*s(36)+1*s(37)+2*s(38)+0
  Such that:s(34) =< A
s(35) =< B
s(36) =< s(34)
s(37) =< s(35)
s(38) =< s(36)*s(35)

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

* Chain [30]: 2*s(41)+2*s(42)+1*s(43)+0
  Such that:s(39) =< A
s(40) =< B
s(41) =< s(39)
s(42) =< s(41)*s(40)
s(43) =< s(40)

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


Closed-form bounds of evalfstart(A,B,C,D): 
-------------------------------------
* Chain [36] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=B,A>=1] 
    - Upper bound: 2*A 
    - Complexity: n 
* Chain [33] with precondition: [0>=B,A>=2] 
    - Upper bound: A 
    - Complexity: n 
* Chain [32] with precondition: [A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [A>=1,B>=1] 
    - Upper bound: 2*A*B+2*A+B 
    - Complexity: n^2 
* Chain [30] with precondition: [A>=2,B>=1] 
    - Upper bound: 2*A*B+2*A+B 
    - Complexity: n^2 

### Maximum cost of evalfstart(A,B,C,D): nat(A)*2*nat(B)+nat(B)+nat(A)+nat(A) 
Asymptotic class: n^2 
* Total analysis performed in 238 ms.