/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  : [evalcyclicbb3in/5,evalcyclicbb4in/5,evalcyclicbbin/5]
1. non_recursive  : [evalcyclicstop/4]
2. non_recursive  : [evalcyclicreturnin/4]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evalcyclicbb3in_loop_cont/5]
5. non_recursive  : [evalcyclicentryin/4]
6. non_recursive  : [evalcyclicstart/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalcyclicbb3in/5
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 evalcyclicbb3in_loop_cont/5
5. SCC is partially evaluated into evalcyclicentryin/4
6. SCC is partially evaluated into evalcyclicstart/4

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

### Specialization of cost equations evalcyclicbb3in/5 
* CE 10 is refined into CE [13] 
* CE 4 is refined into CE [14] 
* CE 3 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 5 is refined into CE [18] 
* CE 8 is discarded (unfeasible) 
* CE 7 is refined into CE [19] 


### Cost equations --> "Loop" of evalcyclicbb3in/5 
* CEs [18] --> Loop 13 
* CEs [17] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [13] --> Loop 16 
* CEs [14] --> Loop 17 
* CEs [15] --> Loop 18 
* CEs [16] --> Loop 19 

### Ranking functions of CR evalcyclicbb3in(A,B,C,E,F) 
* RF of phase [13]: [B-C+1]
* RF of phase [14]: [A-C,B-C-1]

#### Partial ranking functions of CR evalcyclicbb3in(A,B,C,E,F) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    B-C+1
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    A-C
    B-C-1


### Specialization of cost equations evalcyclicbb3in_loop_cont/5 
* CE 12 is refined into CE [20] 
* CE 11 is refined into CE [21] 


### Cost equations --> "Loop" of evalcyclicbb3in_loop_cont/5 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR evalcyclicbb3in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR evalcyclicbb3in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations evalcyclicentryin/4 
* CE 2 is refined into CE [22,23,24,25,26,27,28,29,30] 


### Cost equations --> "Loop" of evalcyclicentryin/4 
* CEs [27] --> Loop 22 
* CEs [23,24,30] --> Loop 23 
* CEs [25,26,28,29] --> Loop 24 
* CEs [22] --> Loop 25 

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

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


### Specialization of cost equations evalcyclicstart/4 
* CE 1 is refined into CE [31,32,33,34] 


### Cost equations --> "Loop" of evalcyclicstart/4 
* CEs [34] --> Loop 26 
* CEs [33] --> Loop 27 
* CEs [32] --> Loop 28 
* CEs [31] --> Loop 29 

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

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


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

#### Cost of chains of evalcyclicbb3in(A,B,C,E,F):
* Chain [[13],18]: 1*it(13)+0
  Such that:it(13) =< -C+F

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

* Chain [[13],16]: 1*it(13)+0
  Such that:it(13) =< B-C+1

  with precondition: [E=3,A>=0,C>=A+1,B>=C] 

* Chain [[13],15,[14],19]: 1*it(13)+1*it(14)+1
  Such that:it(13) =< B-C+1
it(14) =< F

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

* Chain [[13],15,[14],17]: 1*it(13)+1*it(14)+1
  Such that:it(13) =< B-C+1
it(14) =< F

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

* Chain [[13],15,[14],16]: 1*it(13)+1*it(14)+1
  Such that:it(14) =< A
it(13) =< B-C+1

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

* Chain [[13],15,19]: 1*it(13)+1
  Such that:it(13) =< B-C+1

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

* Chain [[13],15,17]: 1*it(13)+1
  Such that:it(13) =< B-C+1

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

* Chain [[13],15,16]: 1*it(13)+1
  Such that:it(13) =< B-C+1

  with precondition: [E=3,A>=0,C>=A+1,B>=C] 

* Chain [18]: 0
  with precondition: [E=2,C=F,A>=0,B>=A+1,C>=A+1] 

* Chain [16]: 0
  with precondition: [E=3,A>=0,C>=0,B>=A+1] 


#### Cost of chains of evalcyclicbb3in_loop_cont(A,B,C,D,E):
* Chain [21]: 0
  with precondition: [A=2,B>=0,C>=B+1] 

* Chain [20]: 0
  with precondition: [A=3,B>=0,C>=B+1] 


#### Cost of chains of evalcyclicentryin(A,B,C,E):
* Chain [25]: 1*s(3)+1
  Such that:s(3) =< B

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

* Chain [24]: 3*s(4)+1
  Such that:aux(2) =< -A+B
s(4) =< aux(2)

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

* Chain [23]: 3*s(7)+2*s(9)+1
  Such that:aux(3) =< -A+B
aux(4) =< A
s(7) =< aux(3)
s(9) =< aux(4)

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

* Chain [22]: 1*s(12)+1*s(13)+1
  Such that:s(12) =< -A+B
s(13) =< A

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


#### Cost of chains of evalcyclicstart(A,B,C,E):
* Chain [29]: 1*s(14)+1
  Such that:s(14) =< B

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

* Chain [28]: 3*s(16)+1
  Such that:s(15) =< -A+B
s(16) =< s(15)

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

* Chain [27]: 3*s(19)+2*s(20)+1
  Such that:s(17) =< -A+B
s(18) =< A
s(19) =< s(17)
s(20) =< s(18)

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

* Chain [26]: 1*s(21)+1*s(22)+1
  Such that:s(21) =< -A+B
s(22) =< A

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


Closed-form bounds of evalcyclicstart(A,B,C,E): 
-------------------------------------
* Chain [29] with precondition: [A=0,B>=1] 
    - Upper bound: B+1 
    - Complexity: n 
* Chain [28] with precondition: [A>=0,B>=A+1] 
    - Upper bound: -3*A+3*B+1 
    - Complexity: n 
* Chain [27] with precondition: [A>=1,B>=A+1] 
    - Upper bound: -A+3*B+1 
    - Complexity: n 
* Chain [26] with precondition: [A>=2,B>=A+1] 
    - Upper bound: B+1 
    - Complexity: n 

### Maximum cost of evalcyclicstart(A,B,C,E): -A+3*B+1 
Asymptotic class: n 
* Total analysis performed in 338 ms.