/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  : [f2/13]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f4/7]
3. non_recursive  : [f2_loop_cont/8]
4. non_recursive  : [f3/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/13
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f2_loop_cont/8
4. SCC is partially evaluated into f3/7

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

### Specialization of cost equations f2/13 
* CE 5 is refined into CE [8] 
* CE 3 is refined into CE [9] 
* CE 4 is refined into CE [10] 
* CE 2 is refined into CE [11] 


### Cost equations --> "Loop" of f2/13 
* CEs [11] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR f2(A,B,C,D,E,F,I,J,K,L,M,N,O) 
* RF of phase [8]: [A,B]

#### Partial ranking functions of CR f2(A,B,C,D,E,F,I,J,K,L,M,N,O) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A
    B


### Specialization of cost equations f2_loop_cont/8 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of f2_loop_cont/8 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f3/7 
* CE 1 is refined into CE [14,15,16,17,18,19] 


### Cost equations --> "Loop" of f3/7 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [19] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR f3(A,B,C,D,E,F,I) 

#### Partial ranking functions of CR f3(A,B,C,D,E,F,I) 


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

#### Cost of chains of f2(A,B,C,D,E,F,I,J,K,L,M,N,O):
* Chain [[8],11]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [I=2,J=0,L=1,N+1=0,A+K=B,A+M=B+1,A>=1,B>=A+1] 

* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A-J

  with precondition: [I=2,M=1,A=B+J,A+1=B+L,A=B+N+1,0>=K,B>=1,A>=B] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< A
it(8) =< B

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

* Chain [11]: 0
  with precondition: [I=2,L=C,M=D,N=E,A=J,B=K,0>=A,B>=1] 

* Chain [10]: 0
  with precondition: [I=2,J=A,L=C,M=D,N=E,0>=B,0>=K] 

* Chain [9]: 0
  with precondition: [I=3] 


#### Cost of chains of f2_loop_cont(A,B,C,D,E,F,G,H):
* Chain [13]: 0
  with precondition: [A=2] 

* Chain [12]: 0
  with precondition: [A=3] 


#### Cost of chains of f3(A,B,C,D,E,F,I):
* Chain [19]: 0
  with precondition: [] 

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

* Chain [17]: 0
  with precondition: [0>=B] 

* Chain [16]: 1*s(1)+0
  Such that:s(1) =< A
s(1) =< B

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

* Chain [15]: 1*s(2)+0
  Such that:s(2) =< A

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

* Chain [14]: 1*s(3)+0
  Such that:s(3) =< B

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


Closed-form bounds of f3(A,B,C,D,E,F,I): 
-------------------------------------
* Chain [19] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [0>=A,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [A>=1,B>=1] 
    - Upper bound: A 
    - Complexity: n 
* Chain [15] with precondition: [A>=1,B>=A+1] 
    - Upper bound: A 
    - Complexity: n 
* Chain [14] with precondition: [B>=1,A>=B] 
    - Upper bound: B 
    - Complexity: n 

### Maximum cost of f3(A,B,C,D,E,F,I): max([nat(A),nat(B)]) 
Asymptotic class: n 
* Total analysis performed in 175 ms.