/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  : [eval/6]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [eval_loop_cont/2]
3. non_recursive  : [start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval/6
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into start/6

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

### Specialization of cost equations eval/6 
* CE 6 is refined into CE [7] 
* CE 3 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 2 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of eval/6 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [10] --> Loop 9 
* CEs [11] --> Loop 10 
* CEs [7] --> Loop 11 

### Ranking functions of CR eval(A,B,C,D,E,F) 
* RF of phase [7,9]: [A-B+C-D-1]
* RF of phase [8]: [C-D]
* RF of phase [10]: [A-B]

#### Partial ranking functions of CR eval(A,B,C,D,E,F) 
* Partial RF of phase [7,9]:
  - RF of loop [7:1]:
    C-D
  - RF of loop [9:1]:
    A-B
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    C-D
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    A-B


### Specialization of cost equations start/6 
* CE 1 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of start/6 
* CEs [15] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [12] --> Loop 15 

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

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


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

#### Cost of chains of eval(A,B,C,D,E,F):
* Chain [[10],11]: 1*it(10)+0
  Such that:it(10) =< A-B

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

* Chain [[8],11]: 1*it(8)+0
  Such that:it(8) =< C-D

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

* Chain [[7,9],[10],11]: 1*it(7)+2*it(9)+0
  Such that:it(7) =< C-D
aux(3) =< A-B
aux(4) =< A-B+C-D
it(9) =< aux(3)
it(9) =< aux(4)
it(7) =< aux(4)

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

* Chain [[7,9],[8],11]: 2*it(7)+1*it(9)+0
  Such that:it(9) =< A-B
aux(5) =< A-B+C-D
aux(6) =< C-D
it(7) =< aux(5)
it(7) =< aux(6)
it(9) =< aux(5)

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

* Chain [[7,9],11]: 1*it(7)+1*it(9)+0
  Such that:it(9) =< A-B
it(7) =< C-D
aux(7) =< A-B+C-D
it(7) =< aux(7)
it(9) =< aux(7)

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

* Chain [11]: 0
  with precondition: [F=2] 


#### Cost of chains of start(A,B,C,D,E,F):
* Chain [15]: 0
  with precondition: [] 

* Chain [14]: 1*s(12)+0
  Such that:s(12) =< C-D

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

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

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

* Chain [12]: 4*s(17)+4*s(18)+0
  Such that:s(14) =< A-B
s(15) =< A-B+C-D
s(16) =< C-D
s(17) =< s(14)
s(18) =< s(16)
s(18) =< s(15)
s(17) =< s(15)

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


Closed-form bounds of start(A,B,C,D,E,F): 
-------------------------------------
* Chain [15] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [14] with precondition: [B>=A,C>=D+1] 
    - Upper bound: C-D 
    - Complexity: n 
* Chain [13] with precondition: [A>=B+1,D>=C] 
    - Upper bound: A-B 
    - Complexity: n 
* Chain [12] with precondition: [A>=B+1,C>=D+1] 
    - Upper bound: 4*A-4*B+4*C-4*D 
    - Complexity: n 

### Maximum cost of start(A,B,C,D,E,F): max([nat(C-D),nat(C-D)*4+nat(A-B)*3+nat(A-B)]) 
Asymptotic class: n 
* Total analysis performed in 212 ms.