/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. recursive  : [evaleasy2bb1in/3,evaleasy2bbin/3]
1. non_recursive  : [evaleasy2stop/2]
2. non_recursive  : [evaleasy2returnin/2]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evaleasy2bb1in_loop_cont/3]
5. non_recursive  : [evaleasy2entryin/2]
6. non_recursive  : [evaleasy2start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evaleasy2bb1in/3
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into evaleasy2bb1in_loop_cont/3
5. SCC is partially evaluated into evaleasy2entryin/2
6. SCC is partially evaluated into evaleasy2start/2

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

### Specialization of cost equations evaleasy2bb1in/3 
* 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 evaleasy2bb1in/3 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR evaleasy2bb1in(A,B,C) 
* RF of phase [8]: [A]

#### Partial ranking functions of CR evaleasy2bb1in(A,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A


### Specialization of cost equations evaleasy2bb1in_loop_cont/3 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of evaleasy2bb1in_loop_cont/3 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR evaleasy2bb1in_loop_cont(A,B,C) 

#### Partial ranking functions of CR evaleasy2bb1in_loop_cont(A,B,C) 


### Specialization of cost equations evaleasy2entryin/2 
* CE 2 is refined into CE [13,14,15,16] 


### Cost equations --> "Loop" of evaleasy2entryin/2 
* CEs [13,16] --> Loop 13 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR evaleasy2entryin(A,B) 

#### Partial ranking functions of CR evaleasy2entryin(A,B) 


### Specialization of cost equations evaleasy2start/2 
* CE 1 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of evaleasy2start/2 
* CEs [19] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR evaleasy2start(A,B) 

#### Partial ranking functions of CR evaleasy2start(A,B) 


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

#### Cost of chains of evaleasy2bb1in(A,B,C):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [B=2,C=0,A>=1] 

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

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

* Chain [10]: 0
  with precondition: [B=2,A=C,0>=A] 

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


#### Cost of chains of evaleasy2bb1in_loop_cont(A,B,C):
* Chain [12]: 0
  with precondition: [A=2] 

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


#### Cost of chains of evaleasy2entryin(A,B):
* Chain [15]: 0
  with precondition: [] 

* Chain [14]: 0
  with precondition: [0>=A] 

* Chain [13]: 2*s(1)+0
  Such that:aux(1) =< A
s(1) =< aux(1)

  with precondition: [A>=1] 


#### Cost of chains of evaleasy2start(A,B):
* Chain [18]: 0
  with precondition: [] 

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

* Chain [16]: 2*s(4)+0
  Such that:s(3) =< A
s(4) =< s(3)

  with precondition: [A>=1] 


Closed-form bounds of evaleasy2start(A,B): 
-------------------------------------
* Chain [18] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [A>=1] 
    - Upper bound: 2*A 
    - Complexity: n 

### Maximum cost of evaleasy2start(A,B): nat(A)*2 
Asymptotic class: n 
* Total analysis performed in 52 ms.