/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  : [f7/9]
1. recursive  : [f4/9,f7_loop_cont/10]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f19/5]
4. non_recursive  : [f4_loop_cont/6]
5. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f7/9
1. SCC is partially evaluated into f4/9
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f4_loop_cont/6
5. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f7/9 
* CE 12 is refined into CE [13] 
* CE 11 is refined into CE [14] 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 8 is refined into CE [17] 


### Cost equations --> "Loop" of f7/9 
* CEs [15] --> Loop 13 
* CEs [16] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [13] --> Loop 16 
* CEs [14] --> Loop 17 

### Ranking functions of CR f7(A,B,C,D,F,G,H,I,J) 
* RF of phase [13,14,15]: [B-C]

#### Partial ranking functions of CR f7(A,B,C,D,F,G,H,I,J) 
* Partial RF of phase [13,14,15]:
  - RF of loop [13:1,14:1]:
    -A+B-1
  - RF of loop [13:1,14:1,15:1]:
    B-C


### Specialization of cost equations f4/9 
* CE 4 is refined into CE [18] 
* CE 2 is refined into CE [19,20] 
* CE 5 is refined into CE [21] 
* CE 3 is refined into CE [22,23] 


### Cost equations --> "Loop" of f4/9 
* CEs [23] --> Loop 18 
* CEs [22] --> Loop 19 
* CEs [18] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [19] --> Loop 22 
* CEs [21] --> Loop 23 

### Ranking functions of CR f4(A,B,C,D,F,G,H,I,J) 
* RF of phase [18]: [-A+B-1]

#### Partial ranking functions of CR f4(A,B,C,D,F,G,H,I,J) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    -A+B-1


### Specialization of cost equations f4_loop_cont/6 
* CE 6 is refined into CE [24] 
* CE 7 is refined into CE [25] 


### Cost equations --> "Loop" of f4_loop_cont/6 
* CEs [24] --> Loop 24 
* CEs [25] --> Loop 25 

### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [26,27,28,29,30,31,32,33,34] 


### Cost equations --> "Loop" of f0/5 
* CEs [30] --> Loop 26 
* CEs [29,33,34] --> Loop 27 
* CEs [28] --> Loop 28 
* CEs [32] --> Loop 29 
* CEs [26,31] --> Loop 30 
* CEs [27] --> Loop 31 

### Ranking functions of CR f0(A,B,C,D,F) 

#### Partial ranking functions of CR f0(A,B,C,D,F) 


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

#### Cost of chains of f7(A,B,C,D,F,G,H,I,J):
* Chain [[13,14,15],17]: 2*it(13)+1*it(15)+0
  Such that:aux(1) =< -A+B
aux(2) =< B-I
aux(5) =< B-C
it(13) =< aux(1)
it(13) =< aux(2)
it(13) =< aux(5)
it(15) =< aux(5)

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

* Chain [[13,14,15],16]: 2*it(13)+1*it(15)+0
  Such that:aux(1) =< -A+B
aux(6) =< B-C
it(13) =< aux(1)
it(13) =< aux(6)
it(15) =< aux(6)

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

* Chain [17]: 0
  with precondition: [F=2,C=B,J=D,A+1=G,C=H,C=I,C>=A+1] 

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


#### Cost of chains of f4(A,B,C,D,F,G,H,I,J):
* Chain [[18],23]: 1*it(18)+2*s(11)+1*s(12)+0
  Such that:aux(7) =< B
aux(11) =< -A+B
aux(7) =< aux(11)
it(18) =< aux(11)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(11)
s(11) =< s(13)
s(12) =< s(13)

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [[18],22]: 1*it(18)+2*s(11)+1*s(12)+0
  Such that:aux(7) =< B
aux(12) =< -A+B
aux(7) =< aux(12)
it(18) =< aux(12)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(12)
s(11) =< s(13)
s(12) =< s(13)

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [[18],21]: 4*it(18)+2*s(11)+1*s(12)+0
  Such that:aux(7) =< B
aux(14) =< -A+B
it(18) =< aux(14)
aux(7) =< aux(14)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(14)
s(11) =< s(13)
s(12) =< s(13)

  with precondition: [F=3,A>=0,B>=A+3] 

* Chain [[18],20]: 1*it(18)+2*s(11)+1*s(12)+0
  Such that:aux(7) =< B
aux(15) =< -A+B
aux(7) =< aux(15)
it(18) =< aux(15)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(15)
s(11) =< s(13)
s(12) =< s(13)

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

* Chain [[18],19,23]: 1*it(18)+2*s(11)+1*s(12)+1
  Such that:aux(7) =< B
aux(16) =< -A+B
aux(7) =< aux(16)
it(18) =< aux(16)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(16)
s(11) =< s(13)
s(12) =< s(13)

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [[18],19,20]: 1*it(18)+2*s(11)+1*s(12)+1
  Such that:aux(7) =< B
aux(17) =< -A+B
aux(7) =< aux(17)
it(18) =< aux(17)
aux(8) =< aux(7)+1
s(13) =< it(18)*aux(7)
s(15) =< it(18)*aux(8)
s(11) =< s(15)
s(11) =< aux(17)
s(11) =< s(13)
s(12) =< s(13)

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

* Chain [23]: 0
  with precondition: [F=3,A>=0] 

* Chain [22]: 0
  with precondition: [F=3,A>=0,B>=A+1] 

* Chain [21]: 3*s(18)+0
  Such that:aux(13) =< -A+B
s(18) =< aux(13)

  with precondition: [F=3,A>=0,B>=A+2] 

* Chain [20]: 0
  with precondition: [F=4,I=C,J=D,A=G,B=H,A>=0,A>=B] 

* Chain [19,23]: 1
  with precondition: [F=3,B=A+1,B>=1] 

* Chain [19,20]: 1
  with precondition: [F=4,B=A+1,B=G,B=H,B=I,D=J,B>=1] 


#### Cost of chains of f4_loop_cont(A,B,C,D,E,F):
* Chain [25]: 0
  with precondition: [A=3] 

* Chain [24]: 0
  with precondition: [A=4] 


#### Cost of chains of f0(A,B,C,D,F):
* Chain [31]: 0
  with precondition: [] 

* Chain [30]: 1
  with precondition: [B=1] 

* Chain [29]: 0
  with precondition: [0>=B] 

* Chain [28]: 0
  with precondition: [B>=1] 

* Chain [27]: 8*s(49)+10*s(53)+5*s(54)+1
  Such that:aux(23) =< B
s(49) =< aux(23)
s(50) =< aux(23)+1
s(51) =< s(49)*aux(23)
s(52) =< s(49)*s(50)
s(53) =< s(52)
s(53) =< aux(23)
s(53) =< s(51)
s(54) =< s(51)

  with precondition: [B>=2] 

* Chain [26]: 4*s(73)+2*s(77)+1*s(78)+0
  Such that:aux(24) =< B
s(73) =< aux(24)
s(74) =< aux(24)+1
s(75) =< s(73)*aux(24)
s(76) =< s(73)*s(74)
s(77) =< s(76)
s(77) =< aux(24)
s(77) =< s(75)
s(78) =< s(75)

  with precondition: [B>=3] 


Closed-form bounds of f0(A,B,C,D,F): 
-------------------------------------
* Chain [31] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [B=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [29] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [28] with precondition: [B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [B>=2] 
    - Upper bound: 18*B+1+5*B*B 
    - Complexity: n^2 
* Chain [26] with precondition: [B>=3] 
    - Upper bound: 6*B+B*B 
    - Complexity: n^2 

### Maximum cost of f0(A,B,C,D,F): max([1,nat(B)*12+1+nat(B)*4*nat(B)+(nat(B)*nat(B)+nat(B)*6)]) 
Asymptotic class: n^2 
* Total analysis performed in 450 ms.