/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  : [f2/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f4/4]
3. non_recursive  : [f2_loop_cont/5]
4. non_recursive  : [f3/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/7
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/5
4. SCC is partially evaluated into f3/4

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

### Specialization of cost equations f2/7 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of f2/7 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR f2(A,B,C,E,F,G,H) 
* RF of phase [8]: [A]

#### Partial ranking functions of CR f2(A,B,C,E,F,G,H) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A


### Specialization of cost equations f2_loop_cont/5 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f2_loop_cont/5 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

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

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


### Specialization of cost equations f3/4 
* CE 2 is refined into CE [13,14,15,16] 
* CE 1 is refined into CE [17] 


### Cost equations --> "Loop" of f3/4 
* CEs [16] --> Loop 13 
* CEs [14,15] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [13] --> Loop 16 

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

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


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

#### Cost of chains of f2(A,B,C,E,F,G,H):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [E=2,0>=F,B>=1,G>=B+1,F+G>=2,A+B+2>=2*G+F] 

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

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

* Chain [10]: 0
  with precondition: [E=2,A=F,B=G,0>=A,B>=1] 

* Chain [9]: 0
  with precondition: [E=3,B>=1] 


#### Cost of chains of f2_loop_cont(A,B,C,D,E):
* Chain [12]: 0
  with precondition: [A=2] 

* Chain [11]: 0
  with precondition: [A=3] 


#### Cost of chains of f3(A,B,C,E):
* Chain [16]: 0
  with precondition: [0>=A,B>=1] 

* Chain [15]: 0
  with precondition: [0>=B] 

* Chain [14]: 2*s(1)+0
  Such that:aux(1) =< A
s(1) =< aux(1)

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

* Chain [13]: 0
  with precondition: [B>=1] 


Closed-form bounds of f3(A,B,C,E): 
-------------------------------------
* Chain [16] with precondition: [0>=A,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [14] with precondition: [A>=1,B>=1] 
    - Upper bound: 2*A 
    - Complexity: n 
* Chain [13] with precondition: [B>=1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f3(A,B,C,E): nat(A)*2 
Asymptotic class: n 
* Total analysis performed in 84 ms.