/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [lbl72/7]
1. recursive  : [lbl62/8,lbl72_loop_cont/9]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/7]
4. non_recursive  : [lbl62_loop_cont/8]
5. non_recursive  : [start/7]
6. non_recursive  : [start0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl72/7
1. SCC is partially evaluated into lbl62/8
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl62_loop_cont/8
5. SCC is partially evaluated into start/7
6. SCC is partially evaluated into start0/7

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

### Specialization of cost equations lbl72/7 
* CE 13 is refined into CE [14] 
* CE 12 is refined into CE [15] 
* CE 11 is refined into CE [16] 


### Cost equations --> "Loop" of lbl72/7 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR lbl72(A,B,D,F,G,H,I) 

#### Partial ranking functions of CR lbl72(A,B,D,F,G,H,I) 


### Specialization of cost equations lbl62/8 
* CE 8 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 6 is refined into CE [19] 
* CE 7 is refined into CE [20] 
* CE 5 is refined into CE [21] 


### Cost equations --> "Loop" of lbl62/8 
* CEs [20] --> Loop 17 
* CEs [21] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [18] --> Loop 20 
* CEs [19] --> Loop 21 

### Ranking functions of CR lbl62(A,B,D,F,G,H,I,J) 

#### Partial ranking functions of CR lbl62(A,B,D,F,G,H,I,J) 
* Partial RF of phase [17,18]:
  - RF of loop [17:1]:
    B depends on loops [18:1] 
  - RF of loop [18:1]:
    -B+1 depends on loops [17:1] 
    D-1


### Specialization of cost equations lbl62_loop_cont/8 
* CE 9 is refined into CE [22] 
* CE 10 is refined into CE [23] 


### Cost equations --> "Loop" of lbl62_loop_cont/8 
* CEs [22] --> Loop 22 
* CEs [23] --> Loop 23 

### Ranking functions of CR lbl62_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR lbl62_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations start/7 
* CE 3 is refined into CE [24,25,26,27,28] 
* CE 2 is refined into CE [29] 


### Cost equations --> "Loop" of start/7 
* CEs [26,28] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [29] --> Loop 26 
* CEs [24,25] --> Loop 27 

### 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 [30,31,32,33] 


### Cost equations --> "Loop" of start0/7 
* CEs [33] --> Loop 28 
* CEs [32] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [30] --> Loop 31 

### 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 lbl72(A,B,D,F,G,H,I):
* Chain [16]: 0
  with precondition: [B=0,D=0,G=2,H=0,I=0,F=A,F>=1] 

* Chain [15]: 0
  with precondition: [B=0,G=3,F=A,F=H+1,D=I,D>=1,F>=D+1] 

* Chain [14]: 0
  with precondition: [B=0,G=4,F=A,D>=0,F>=D+1] 


#### Cost of chains of lbl62(A,B,D,F,G,H,I,J):
* Chain [[17,18],21]: 1*it(17)+1*it(18)+0
  Such that:it(18) =< D
aux(23) =< B
aux(24) =< J
aux(17) =< aux(24)
aux(17) =< aux(24)
aux(18) =< it(18)*aux(17)
aux(1) =< it(18)*aux(17)
aux(12) =< it(18)*aux(24)
aux(1) =< it(18)*aux(24)
aux(3) =< aux(18)
aux(3) =< aux(12)
it(17) =< aux(1)+aux(23)
it(17) =< aux(3)+aux(23)

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

* Chain [[17,18],20]: 1*it(17)+1*it(18)+0
  Such that:it(18) =< D
aux(25) =< B
aux(26) =< F
aux(17) =< aux(26)
aux(17) =< aux(26)
aux(18) =< it(18)*aux(17)
aux(1) =< it(18)*aux(17)
aux(12) =< it(18)*aux(26)
aux(1) =< it(18)*aux(26)
aux(3) =< aux(18)
aux(3) =< aux(12)
it(17) =< aux(1)+aux(25)
it(17) =< aux(3)+aux(25)

  with precondition: [G=4,A=F,A>=2,B>=0,D>=1,A>=B+1,A>=D,B+D>=2] 

* Chain [[17,18],19]: 1*it(17)+1*it(18)+0
  Such that:aux(4) =< A
it(18) =< D
aux(27) =< B
aux(28) =< F
aux(4) =< aux(27)
aux(17) =< aux(28)
aux(17) =< aux(28)
aux(18) =< it(18)*aux(17)
aux(1) =< it(18)*aux(17)
aux(12) =< it(18)*aux(28)
aux(1) =< it(18)*aux(28)
aux(3) =< aux(18)
aux(3) =< aux(12)
it(17) =< aux(1)+aux(27)
it(17) =< aux(3)+aux(4)

  with precondition: [G=4,A=F,A>=2,B>=0,D>=1,A>=B+1,A>=D,B+D>=2] 

* Chain [21]: 0
  with precondition: [B=0,D=1,G=2,F=A,F=H,F=J,F>=1] 

* Chain [20]: 0
  with precondition: [B=0,G=4,F=A,D>=1,F>=D] 

* Chain [19]: 0
  with precondition: [G=4,F=A,B>=0,D>=1,F>=B+1,F>=D] 


#### Cost of chains of lbl62_loop_cont(A,B,C,D,E,F,G,H):
* Chain [23]: 0
  with precondition: [A=2,F>=1] 

* Chain [22]: 0
  with precondition: [A=4,F>=1] 


#### Cost of chains of start(A,B,C,D,E,F,G):
* Chain [27]: 0
  with precondition: [A=1,F=1,C=B,E=D] 

* Chain [26]: 0
  with precondition: [F=A,C=B,E=D,0>=F] 

* Chain [25]: 0
  with precondition: [F=A,C=B,E=D,F>=1] 

* Chain [24]: 3*s(20)+3*s(28)+0
  Such that:aux(34) =< F
s(20) =< aux(34)
s(23) =< aux(34)
s(23) =< aux(34)
s(24) =< s(20)*s(23)
s(25) =< s(20)*s(23)
s(26) =< s(20)*aux(34)
s(25) =< s(20)*aux(34)
s(27) =< s(24)
s(27) =< s(26)
s(28) =< s(25)+aux(34)
s(28) =< s(27)+aux(34)

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


#### Cost of chains of start0(A,B,C,D,E,F,G):
* Chain [31]: 0
  with precondition: [A=1] 

* Chain [30]: 0
  with precondition: [0>=A] 

* Chain [29]: 0
  with precondition: [A>=1] 

* Chain [28]: 3*s(42)+3*s(48)+0
  Such that:s(41) =< A
s(42) =< s(41)
s(43) =< s(41)
s(43) =< s(41)
s(44) =< s(42)*s(43)
s(45) =< s(42)*s(43)
s(46) =< s(42)*s(41)
s(45) =< s(42)*s(41)
s(47) =< s(44)
s(47) =< s(46)
s(48) =< s(45)+s(41)
s(48) =< s(47)+s(41)

  with precondition: [A>=2] 


Closed-form bounds of start0(A,B,C,D,E,F,G): 
-------------------------------------
* Chain [31] with precondition: [A=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [28] with precondition: [A>=2] 
    - Upper bound: 3*A*A+6*A 
    - Complexity: n^2 

### Maximum cost of start0(A,B,C,D,E,F,G): nat(A)*3*nat(A)+nat(A)*6 
Asymptotic class: n^2 
* Total analysis performed in 378 ms.