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


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


WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [lbl43/8]
1. recursive  : [lbl13/11,lbl31/11,lbl43_loop_cont/12]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/11]
4. non_recursive  : [lbl31_loop_cont/12]
5. non_recursive  : [start/11]
6. non_recursive  : [start0/11]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl43/8
1. SCC is partially evaluated into lbl31/11
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl31_loop_cont/12
5. SCC is partially evaluated into start/11
6. SCC is partially evaluated into start0/11

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

### Specialization of cost equations lbl43/8 
* CE 14 is refined into CE [15] 
* CE 13 is refined into CE [16] 
* CE 12 is refined into CE [17] 


### Cost equations --> "Loop" of lbl43/8 
* CEs [17] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR lbl43(A,D,F,G,I,L,M,N) 
* RF of phase [15]: [G+1]

#### Partial ranking functions of CR lbl43(A,D,F,G,I,L,M,N) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    G+1


### Specialization of cost equations lbl31/11 
* CE 7 is refined into CE [18] 
* CE 6 is refined into CE [19,20] 
* CE 8 is refined into CE [21,22] 
* CE 9 is refined into CE [23] 
* CE 4 is refined into CE [24,25] 
* CE 5 is refined into CE [26] 


### Cost equations --> "Loop" of lbl31/11 
* CEs [26] --> Loop 18 
* CEs [25] --> Loop 19 
* CEs [24] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [19] --> Loop 22 
* CEs [18] --> Loop 23 
* CEs [22] --> Loop 24 
* CEs [21,23] --> Loop 25 

### Ranking functions of CR lbl31(A,B,D,F,G,I,L,M,N,O,P) 
* RF of phase [18,19,20]: [A-I-1,F-I-1]

#### Partial ranking functions of CR lbl31(A,B,D,F,G,I,L,M,N,O,P) 
* Partial RF of phase [18,19,20]:
  - RF of loop [18:1,19:1,20:1]:
    A-I-1
    F-I-1


### Specialization of cost equations lbl31_loop_cont/12 
* CE 10 is refined into CE [27] 
* CE 11 is refined into CE [28] 


### Cost equations --> "Loop" of lbl31_loop_cont/12 
* CEs [27] --> Loop 26 
* CEs [28] --> Loop 27 

### Ranking functions of CR lbl31_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 

#### Partial ranking functions of CR lbl31_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 


### Specialization of cost equations start/11 
* CE 3 is refined into CE [29,30,31,32,33,34] 
* CE 2 is refined into CE [35] 


### Cost equations --> "Loop" of start/11 
* CEs [30,32,33,34] --> Loop 28 
* CEs [29] --> Loop 29 
* CEs [35] --> Loop 30 
* CEs [31] --> Loop 31 

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

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


### Specialization of cost equations start0/11 
* CE 1 is refined into CE [36,37,38,39] 


### Cost equations --> "Loop" of start0/11 
* CEs [39] --> Loop 32 
* CEs [38] --> Loop 33 
* CEs [37] --> Loop 34 
* CEs [36] --> Loop 35 

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

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


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

#### Cost of chains of lbl43(A,D,F,G,I,L,M,N):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< G-M

  with precondition: [L=2,A=F,I+1=N,M+1>=0,I>=G+2,A>=I+1,G>=M+1] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< G+1

  with precondition: [L=3,A=F,G>=0,I>=G+2,A>=I+1] 

* Chain [17]: 0
  with precondition: [L=2,F=A,G=M,I+1=N,G+1>=0,I>=G+2,F>=I+1] 

* Chain [16]: 0
  with precondition: [L=3,F=A,G+1>=0,I>=G+2,F>=I+1] 


#### Cost of chains of lbl31(A,B,D,F,G,I,L,M,N,O,P):
* Chain [[18,19,20],25]: 3*it(18)+1*s(3)+0
  Such that:aux(1) =< F
aux(6) =< F-I
it(18) =< aux(6)
s(3) =< it(18)*aux(1)

  with precondition: [L=3,A=F,I>=1,A>=I+2] 

* Chain [[18,19,20],24]: 3*it(18)+1*s(3)+1*s(4)+0
  Such that:aux(7) =< F
aux(8) =< F-I
s(4) =< aux(7)
it(18) =< aux(8)
s(3) =< it(18)*aux(7)

  with precondition: [L=3,A=F,I>=1,A>=I+2] 

* Chain [[18,19,20],23]: 3*it(18)+1*s(3)+0
  Such that:aux(1) =< P
aux(9) =< -I+P
it(18) =< aux(9)
s(3) =< it(18)*aux(1)

  with precondition: [L=4,A=F,A=N+1,A=O+2,A=P,I>=1,A>=I+2] 

* Chain [[18,19,20],22]: 3*it(18)+1*s(3)+0
  Such that:aux(1) =< P
aux(10) =< -I+P
it(18) =< aux(10)
s(3) =< it(18)*aux(1)

  with precondition: [L=4,A=F,A=N+1,A=O+3,A=P,I>=1,A>=I+2] 

* Chain [[18,19,20],21]: 3*it(18)+1*s(3)+1*s(5)+0
  Such that:aux(11) =< A
aux(12) =< A-I
s(5) =< aux(11)
it(18) =< aux(12)
s(3) =< it(18)*aux(11)

  with precondition: [L=4,A=F,A=N+1,A=P,I>=1,O+1>=0,A>=I+2,A>=O+4] 

* Chain [25]: 0
  with precondition: [L=3,F=A,I>=1,F>=I+1] 

* Chain [23]: 0
  with precondition: [L=4,F=A,M=B,F=I+1,F=N+1,F=O+2,F=P,F>=2] 


#### Cost of chains of lbl31_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [27]: 0
  with precondition: [A=3,G=B,G>=2] 

* Chain [26]: 0
  with precondition: [A=4,G=B,G>=2] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I,J,L):
* Chain [31]: 0
  with precondition: [A=2,F=2,C=B,E=D,H=G,J=I] 

* Chain [30]: 0
  with precondition: [F=A,C=B,E=D,H=G,J=I,1>=F] 

* Chain [29]: 0
  with precondition: [F=A,C=B,E=D,H=G,J=I,F>=2] 

* Chain [28]: 17*s(17)+5*s(19)+0
  Such that:aux(19) =< F
s(17) =< aux(19)
s(19) =< s(17)*aux(19)

  with precondition: [F=A,C=B,E=D,H=G,J=I,F>=3] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,L):
* Chain [35]: 0
  with precondition: [A=2] 

* Chain [34]: 0
  with precondition: [1>=A] 

* Chain [33]: 0
  with precondition: [A>=2] 

* Chain [32]: 17*s(34)+5*s(35)+0
  Such that:s(33) =< A
s(34) =< s(33)
s(35) =< s(34)*s(33)

  with precondition: [A>=3] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,L): 
-------------------------------------
* Chain [35] with precondition: [A=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [1>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [A>=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [A>=3] 
    - Upper bound: 5*A*A+17*A 
    - Complexity: n^2 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,L): nat(A)*5*nat(A)+nat(A)*17 
Asymptotic class: n^2 
* Total analysis performed in 588 ms.