/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [sumto/4]
1. non_recursive  : [end/3]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [sumto_loop_cont/4]
4. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into sumto/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into sumto_loop_cont/4
4. SCC is partially evaluated into start/3

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

### Specialization of cost equations sumto/4 
* CE 4 is refined into CE [7] 
* CE 2 is refined into CE [8] 
* CE 3 is refined into CE [9] 


### Cost equations --> "Loop" of sumto/4 
* CEs [9] --> Loop 7 
* CEs [7] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR sumto(A,B,C,D) 
* RF of phase [7]: [-A+B+1]

#### Partial ranking functions of CR sumto(A,B,C,D) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -A+B+1


### Specialization of cost equations sumto_loop_cont/4 
* CE 6 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of sumto_loop_cont/4 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

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

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


### Specialization of cost equations start/3 
* CE 1 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of start/3 
* CEs [12] --> Loop 12 
* CEs [13,15] --> Loop 13 
* CEs [14] --> Loop 14 

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

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


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

#### Cost of chains of sumto(A,B,C,D):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -A+B+1

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

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -A+B+1

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

* Chain [9]: 0
  with precondition: [C=2,A=D,A>=B+1] 

* Chain [8]: 0
  with precondition: [C=3] 


#### Cost of chains of sumto_loop_cont(A,B,C,D):
* Chain [11]: 0
  with precondition: [A=2] 

* Chain [10]: 0
  with precondition: [A=3] 


#### Cost of chains of start(A,B,C):
* Chain [14]: 0
  with precondition: [] 

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

  with precondition: [B>=A] 

* Chain [12]: 0
  with precondition: [A>=B+1] 


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [14] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [13] with precondition: [B>=A] 
    - Upper bound: -2*A+2*B+2 
    - Complexity: n 
* Chain [12] with precondition: [A>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of start(A,B,C): nat(-A+B+1)*2 
Asymptotic class: n 
* Total analysis performed in 57 ms.