/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  : [l1/7]
1. non_recursive  : [exit_location/1]
2. recursive  : [l3/5]
3. recursive  : [l2/3,l3_loop_cont/4]
4. non_recursive  : [l2_loop_cont/2]
5. non_recursive  : [l1_loop_cont/6]
6. non_recursive  : [l0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/7
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l3/5
3. SCC is partially evaluated into l2/3
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into l1_loop_cont/6
6. SCC is partially evaluated into l0/5

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

### Specialization of cost equations l1/7 
* CE 4 is refined into CE [13] 
* CE 3 is refined into CE [14] 
* CE 2 is refined into CE [15] 


### Cost equations --> "Loop" of l1/7 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR l1(A,B,C,E,F,G,H) 
* RF of phase [13]: [B]

#### Partial ranking functions of CR l1(A,B,C,E,F,G,H) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    B


### Specialization of cost equations l3/5 
* CE 12 is refined into CE [16] 
* CE 11 is refined into CE [17] 
* CE 10 is refined into CE [18] 


### Cost equations --> "Loop" of l3/5 
* CEs [18] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR l3(C,D,E,F,G) 
* RF of phase [16]: [D]

#### Partial ranking functions of CR l3(C,D,E,F,G) 
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    D


### Specialization of cost equations l2/3 
* CE 7 is refined into CE [19,20] 
* CE 9 is refined into CE [21] 
* CE 8 is refined into CE [22] 


### Cost equations --> "Loop" of l2/3 
* CEs [22] --> Loop 19 
* CEs [19,20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR l2(C,D,E) 
* RF of phase [19]: [C]

#### Partial ranking functions of CR l2(C,D,E) 
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    C


### Specialization of cost equations l1_loop_cont/6 
* CE 5 is refined into CE [23] 
* CE 6 is refined into CE [24,25,26] 


### Cost equations --> "Loop" of l1_loop_cont/6 
* CEs [23] --> Loop 22 
* CEs [26] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations l0/5 
* CE 1 is refined into CE [27,28,29,30,31,32] 


### Cost equations --> "Loop" of l0/5 
* CEs [29] --> Loop 26 
* CEs [27,28,32] --> Loop 27 
* CEs [30] --> Loop 28 
* CEs [31] --> Loop 29 

### Ranking functions of CR l0(A,B,C,D,E) 

#### Partial ranking functions of CR l0(A,B,C,D,E) 


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

#### Cost of chains of l1(A,B,C,E,F,G,H):
* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< -A+F

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

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< B

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

* Chain [15]: 0
  with precondition: [E=2,A=F,B=G,A=H,0>=B,A>=0] 

* Chain [14]: 0
  with precondition: [E=3,A>=0] 


#### Cost of chains of l3(C,D,E,F,G):
* Chain [[16],18]: 1*it(16)+0
  Such that:it(16) =< D

  with precondition: [E=2,G=0,C=F+1,D>=1,C>=D] 

* Chain [[16],17]: 1*it(16)+0
  Such that:it(16) =< D

  with precondition: [E=3,D>=1,C>=D] 

* Chain [17]: 0
  with precondition: [E=3,C>=1,C>=D] 


#### Cost of chains of l2(C,D,E):
* Chain [[19],21]: 1*it(19)+1*s(3)+0
  Such that:aux(3) =< C
it(19) =< aux(3)
s(3) =< it(19)*aux(3)

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

* Chain [[19],20]: 2*it(19)+1*s(3)+0
  Such that:aux(4) =< C
it(19) =< aux(4)
s(3) =< it(19)*aux(4)

  with precondition: [E=3,C>=2] 

* Chain [21]: 0
  with precondition: [E=3] 

* Chain [20]: 1*s(4)+0
  Such that:s(4) =< C

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


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F):
* Chain [25]: 0
  with precondition: [A=2] 

* Chain [24]: 2*s(10)+1*s(11)+0
  Such that:s(9) =< D
s(10) =< s(9)
s(11) =< s(10)*s(9)

  with precondition: [A=2,D>=1] 

* Chain [23]: 2*s(13)+1*s(14)+0
  Such that:s(12) =< D
s(13) =< s(12)
s(14) =< s(13)*s(12)

  with precondition: [A=2,D>=2] 

* Chain [22]: 0
  with precondition: [A=3] 


#### Cost of chains of l0(A,B,C,D,E):
* Chain [29]: 0
  with precondition: [] 

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

* Chain [27]: 5*s(15)+1*s(19)+0
  Such that:aux(7) =< B
s(15) =< aux(7)
s(19) =< s(15)*aux(7)

  with precondition: [B>=1] 

* Chain [26]: 3*s(21)+1*s(24)+0
  Such that:aux(8) =< B
s(21) =< aux(8)
s(24) =< s(21)*aux(8)

  with precondition: [B>=2] 


Closed-form bounds of l0(A,B,C,D,E): 
-------------------------------------
* Chain [29] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [28] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [B>=1] 
    - Upper bound: 5*B+B*B 
    - Complexity: n^2 
* Chain [26] with precondition: [B>=2] 
    - Upper bound: 3*B+B*B 
    - Complexity: n^2 

### Maximum cost of l0(A,B,C,D,E): nat(B)*nat(B)+nat(B)*5 
Asymptotic class: n^2 
* Total analysis performed in 198 ms.