/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [lbl71/10]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [stop/7]
3. non_recursive  : [lbl71_loop_cont/8]
4. non_recursive  : [start/7]
5. non_recursive  : [start0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl71/10
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into lbl71_loop_cont/8
4. SCC is partially evaluated into start/7
5. SCC is partially evaluated into start0/7

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

### Specialization of cost equations lbl71/10 
* CE 6 is refined into CE [9] 
* CE 4 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of lbl71/10 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J) 
* RF of phase [9]: [A+C-D,A-E+F,B]

#### Partial ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    A+C-D
    A-E+F
    B


### Specialization of cost equations lbl71_loop_cont/8 
* CE 8 is refined into CE [12] 
* CE 7 is refined into CE [13] 


### Cost equations --> "Loop" of lbl71_loop_cont/8 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations start/7 
* CE 3 is refined into CE [14,15,16,17] 
* CE 2 is refined into CE [18] 


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

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

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


### Specialization of cost equations start0/7 
* CE 1 is refined into CE [19,20,21,22] 


### Cost equations --> "Loop" of start0/7 
* CEs [22] --> Loop 18 
* CEs [21] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [19] --> Loop 21 

### Ranking functions of CR start0(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 


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

#### Cost of chains of lbl71(A,B,C,D,E,F,G,H,I,J):
* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< B

  with precondition: [G=2,H=0,B+I=C,B+E=J,B+D=A+C,B+E=A+F,B>=1,A>=B+1] 

* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< A+C-D

  with precondition: [G=3,A+F=B+E,C+E=D+F,E>=F+1,A+F>=E+1] 

* Chain [11]: 0
  with precondition: [B=0,G=2,H=0,C=I,A+C=D,A+F=E,A+F=J,A>=1] 

* Chain [10]: 0
  with precondition: [G=3,B+D=A+C,B+E=A+F,B>=0,A>=B+1] 


#### Cost of chains of lbl71_loop_cont(A,B,C,D,E,F,G,H):
* Chain [13]: 0
  with precondition: [A=2,B>=1] 

* Chain [12]: 0
  with precondition: [A=3,B>=1] 


#### Cost of chains of start(A,B,C,D,E,F,G):
* Chain [17]: 0
  with precondition: [A=1,B=1,D=C,F=E] 

* Chain [16]: 0
  with precondition: [B=A,D=C,F=E,0>=B] 

* Chain [15]: 0
  with precondition: [B=A,D=C,F=E,B>=1] 

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

  with precondition: [B=A,D=C,F=E,B>=2] 


#### Cost of chains of start0(A,B,C,D,E,F,G):
* Chain [21]: 0
  with precondition: [A=1] 

* Chain [20]: 0
  with precondition: [0>=A] 

* Chain [19]: 0
  with precondition: [A>=1] 

* Chain [18]: 2*s(4)+0
  Such that:s(3) =< A
s(4) =< s(3)

  with precondition: [A>=2] 


Closed-form bounds of start0(A,B,C,D,E,F,G): 
-------------------------------------
* Chain [21] with precondition: [A=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [20] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [19] with precondition: [A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [A>=2] 
    - Upper bound: 2*A 
    - Complexity: n 

### Maximum cost of start0(A,B,C,D,E,F,G): nat(A)*2 
Asymptotic class: n 
* Total analysis performed in 218 ms.