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

#### Computed strongly connected components 
0. recursive  : [f16/8]
1. recursive  : [f10/13,f16_loop_cont/14]
2. non_recursive  : [exit_location/1]
3. recursive  : [f25/1]
4. non_recursive  : [f25_loop_cont/2]
5. non_recursive  : [f10_loop_cont/8]
6. non_recursive  : [f0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f16/8
1. SCC is partially evaluated into f10/13
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f25/1
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f10_loop_cont/8
6. SCC is partially evaluated into f0/7

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

### Specialization of cost equations f16/8 
* CE 10 is refined into CE [13] 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of f16/8 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR f16(A,D,E,F,H,I,J,K) 

#### Partial ranking functions of CR f16(A,D,E,F,H,I,J,K) 


### Specialization of cost equations f10/13 
* CE 4 is refined into CE [16] 
* CE 2 is refined into CE [17,18,19] 
* CE 5 is refined into CE [20] 
* CE 3 is refined into CE [21,22] 


### Cost equations --> "Loop" of f10/13 
* CEs [22] --> Loop 16 
* CEs [21] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17,18] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [19] --> Loop 21 

### Ranking functions of CR f10(A,B,C,D,E,F,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR f10(A,B,C,D,E,F,H,I,J,K,L,M,N) 


### Specialization of cost equations f25/1 
* CE 12 is refined into CE [23] 
* CE 11 is refined into CE [24] 


### Cost equations --> "Loop" of f25/1 
* CEs [24] --> Loop 22 
* CEs [23] --> Loop 23 

### Ranking functions of CR f25(H) 

#### Partial ranking functions of CR f25(H) 


### Specialization of cost equations f10_loop_cont/8 
* CE 7 is refined into CE [25,26] 
* CE 6 is refined into CE [27] 


### Cost equations --> "Loop" of f10_loop_cont/8 
* CEs [25] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [26] --> Loop 26 

### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f0/7 
* CE 1 is refined into CE [28,29,30,31,32,33,34,35,36,37] 


### Cost equations --> "Loop" of f0/7 
* CEs [31,33,34,35,36,37] --> Loop 27 
* CEs [28,29,30,32] --> Loop 28 

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

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


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

#### Cost of chains of f16(A,D,E,F,H,I,J,K):
* Chain [[13]]...: 1*it(13)+0
  with precondition: [0>=A,D>=1,H>=2,3>=H] 

* Chain [[13],14]: 1*it(13)+0
  with precondition: [H=3,0>=A,D>=1] 

* Chain [15]: 0
  with precondition: [H=2,J=0,K=I,0>=A,0>=D] 

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


#### Cost of chains of f10(A,B,C,D,E,F,H,I,J,K,L,M,N):
* Chain [[16,17]]...: 3*it(16)+0
  with precondition: [0>=A,B=0] 

* Chain [[16,17],21]...: 4*it(16)+0
  with precondition: [B=0,H=3,0>=A] 

* Chain [[16,17],20]: 3*it(16)+0
  with precondition: [B=0,H=3,0>=A] 

* Chain [[16,17],19]: 4*aux(1)+0
  with precondition: [B=0,H=3,0>=A] 

* Chain [[16,17],18]: 3*it(16)+0
  with precondition: [B=0,H=4,J=0,K=L,0>=A,I>=1] 

* Chain [21]...: 1*s(4)+0
  with precondition: [B=0,H=3,0>=A] 

* Chain [20]: 0
  with precondition: [B=0,H=3] 

* Chain [19]: 1*aux(1)+0
  with precondition: [B=0,H=3,0>=A] 

* Chain [18]: 0
  with precondition: [B=0,H=4,J=0,K=C,L=D,M=E,N=F,A=I,A>=1] 


#### Cost of chains of f25(H):
* Chain [[22]]...: 1*it(22)+0
  with precondition: [H=3] 

* Chain [[22],23]: 1*it(22)+0
  with precondition: [H=3] 

* Chain [23]: 0
  with precondition: [H=3] 


#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H):
* Chain [26]...: 1*s(12)+0
  with precondition: [A=4] 

* Chain [25]: 0
  with precondition: [A=3] 

* Chain [24]: 1*s(13)+0
  with precondition: [A=4] 


#### Cost of chains of f0(A,B,C,D,E,F,H):
* Chain [28]: 1*aux(5)+0
  with precondition: [] 

* Chain [27]...: 1*aux(6)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,H): 
-------------------------------------
* Chain [28] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [27]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,H): inf 
Asymptotic class: infinity 
* Total analysis performed in 110 ms.

