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

#### Computed strongly connected components 
0. recursive  : [f31/5]
1. non_recursive  : [exit_location/1]
2. recursive  : [f42/10]
3. recursive  : [f39/11,f42_loop_cont/12]
4. recursive  : [f53/8]
5. non_recursive  : [f59/8]
6. recursive  : [f63/4]
7. non_recursive  : [f63_loop_cont/9]
8. non_recursive  : [f53_loop_cont/9]
9. non_recursive  : [f39_loop_cont/9]
10. non_recursive  : [f31_loop_cont/9]
11. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f31/5
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f42/10
3. SCC is partially evaluated into f39/11
4. SCC is partially evaluated into f53/8
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into f63/4
7. SCC is partially evaluated into f63_loop_cont/9
8. SCC is partially evaluated into f53_loop_cont/9
9. SCC is partially evaluated into f39_loop_cont/9
10. SCC is partially evaluated into f31_loop_cont/9
11. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f31/5 
* CE 6 is refined into CE [30] 
* CE 5 is refined into CE [31] 
* CE 3 is discarded (unfeasible) 
* CE 4 is refined into CE [32] 
* CE 2 is refined into CE [33] 


### Cost equations --> "Loop" of f31/5 
* CEs [32] --> Loop 30 
* CEs [33] --> Loop 31 
* CEs [30] --> Loop 32 
* CEs [31] --> Loop 33 

### Ranking functions of CR f31(A,C,D,J,K) 
* RF of phase [30]: [-D+5]

#### Partial ranking functions of CR f31(A,C,D,J,K) 
* Partial RF of phase [30]:
  - RF of loop [30:1]:
    -D+5


### Specialization of cost equations f42/10 
* CE 17 is refined into CE [34] 
* CE 16 is refined into CE [35] 
* CE 15 is refined into CE [36] 


### Cost equations --> "Loop" of f42/10 
* CEs [36] --> Loop 34 
* CEs [34] --> Loop 35 
* CEs [35] --> Loop 36 

### Ranking functions of CR f42(B,D,E,F,G,J,K,L,M,N) 
* RF of phase [34]: [-E+7]

#### Partial ranking functions of CR f42(B,D,E,F,G,J,K,L,M,N) 
* Partial RF of phase [34]:
  - RF of loop [34:1]:
    -E+7


### Specialization of cost equations f39/11 
* CE 11 is refined into CE [37] 
* CE 9 is refined into CE [38,39] 
* CE 12 is refined into CE [40] 
* CE 10 is refined into CE [41] 


### Cost equations --> "Loop" of f39/11 
* CEs [41] --> Loop 37 
* CEs [37] --> Loop 38 
* CEs [38,39] --> Loop 39 
* CEs [40] --> Loop 40 

### Ranking functions of CR f39(A,B,D,E,F,G,J,K,L,M,N) 
* RF of phase [37]: [-D+5]

#### Partial ranking functions of CR f39(A,B,D,E,F,G,J,K,L,M,N) 
* Partial RF of phase [37]:
  - RF of loop [37:1]:
    -D+5


### Specialization of cost equations f53/8 
* CE 20 is refined into CE [42] 
* CE 18 is refined into CE [43] 
* CE 21 is refined into CE [44] 
* CE 19 is refined into CE [45] 


### Cost equations --> "Loop" of f53/8 
* CEs [45] --> Loop 41 
* CEs [42] --> Loop 42 
* CEs [43] --> Loop 43 
* CEs [44] --> Loop 44 

### Ranking functions of CR f53(B,D,F,G,J,K,L,M) 
* RF of phase [41]: [-D+7]

#### Partial ranking functions of CR f53(B,D,F,G,J,K,L,M) 
* Partial RF of phase [41]:
  - RF of loop [41:1]:
    -D+7


### Specialization of cost equations f63/4 
* CE 26 is refined into CE [46] 
* CE 27 is refined into CE [47] 
* CE 25 is refined into CE [48] 


### Cost equations --> "Loop" of f63/4 
* CEs [48] --> Loop 45 
* CEs [46] --> Loop 46 
* CEs [47] --> Loop 47 

### Ranking functions of CR f63(A,D,J,K) 
* RF of phase [45]: [-D+5]

#### Partial ranking functions of CR f63(A,D,J,K) 
* Partial RF of phase [45]:
  - RF of loop [45:1]:
    -D+5


### Specialization of cost equations f63_loop_cont/9 
* CE 28 is refined into CE [49] 
* CE 29 is refined into CE [50] 


### Cost equations --> "Loop" of f63_loop_cont/9 
* CEs [49] --> Loop 48 
* CEs [50] --> Loop 49 

### Ranking functions of CR f63_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f63_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f53_loop_cont/9 
* CE 24 is refined into CE [51,52,53,54] 
* CE 22 is refined into CE [55] 
* CE 23 is refined into CE [56] 


### Cost equations --> "Loop" of f53_loop_cont/9 
* CEs [54] --> Loop 50 
* CEs [52,53] --> Loop 51 
* CEs [51] --> Loop 52 
* CEs [55] --> Loop 53 
* CEs [56] --> Loop 54 

### Ranking functions of CR f53_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f53_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f39_loop_cont/9 
* CE 14 is refined into CE [57,58,59,60,61,62,63,64] 
* CE 13 is refined into CE [65] 


### Cost equations --> "Loop" of f39_loop_cont/9 
* CEs [61,62] --> Loop 55 
* CEs [60] --> Loop 56 
* CEs [58,59,63,64] --> Loop 57 
* CEs [57] --> Loop 58 
* CEs [65] --> Loop 59 

### Ranking functions of CR f39_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f39_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f31_loop_cont/9 
* CE 7 is refined into CE [66] 
* CE 8 is refined into CE [67,68,69,70,71,72,73,74,75] 


### Cost equations --> "Loop" of f31_loop_cont/9 
* CEs [66] --> Loop 60 
* CEs [73,74,75] --> Loop 61 
* CEs [69] --> Loop 62 
* CEs [68,70,71,72] --> Loop 63 
* CEs [67] --> Loop 64 

### Ranking functions of CR f31_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f31_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [76,77,78,79,80] 


### Cost equations --> "Loop" of f0/8 
* CEs [76,77,78,79,80] --> Loop 65 

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

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


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

#### Cost of chains of f31(A,C,D,J,K):
* Chain [32]: 0
  with precondition: [A=5,C=0,J=3,D>=0] 

* Chain [31,[30],33]: 1*it(30)+1
  Such that:it(30) =< 4

  with precondition: [A=5,C=0,D=0,J=2,K=0] 

* Chain [31,[30],32]: 1*it(30)+1
  Such that:it(30) =< 4

  with precondition: [A=5,C=0,D=0,J=3] 

* Chain [31,32]: 1
  with precondition: [A=5,C=0,D=0,J=3] 


#### Cost of chains of f42(B,D,E,F,G,J,K,L,M,N):
* Chain [[34],36]: 1*it(34)+0
  Such that:it(34) =< -E+7

  with precondition: [B=7,J=2,L=7,D+1=K,4>=D,6>=E,E>=0] 

* Chain [[34],35]: 1*it(34)+0
  Such that:it(34) =< -E+7

  with precondition: [B=7,J=3,4>=D,6>=E,E>=0] 

* Chain [35]: 0
  with precondition: [B=7,J=3,4>=D,E>=0] 


#### Cost of chains of f39(A,B,D,E,F,G,J,K,L,M,N):
* Chain [[37],40]: 1*it(37)+1*s(4)+0
  Such that:aux(4) =< -D+5
it(37) =< aux(4)
s(4) =< aux(4)*7

  with precondition: [A=5,B=7,J=3,4>=D] 

* Chain [[37],39]: 1*it(37)+1*s(4)+7
  Such that:aux(3) =< -D+4
aux(2) =< -D+5
aux(1) =< aux(2)
it(37) =< aux(2)
aux(1) =< aux(3)
it(37) =< aux(3)
s(4) =< aux(1)*7

  with precondition: [A=5,B=7,J=3,3>=D] 

* Chain [[37],38]: 1*it(37)+1*s(4)+0
  Such that:aux(5) =< -D+5
it(37) =< aux(5)
s(4) =< aux(5)*7

  with precondition: [A=5,B=7,J=6,K=0,L=7,4>=D] 

* Chain [40]: 0
  with precondition: [A=5,B=7,J=3] 

* Chain [39]: 7
  with precondition: [A=5,B=7,J=3,4>=D] 

* Chain [38]: 0
  with precondition: [A=5,B=7,J=6,K=0,L=E,M=F,N=G,D>=5] 


#### Cost of chains of f53(B,D,F,G,J,K,L,M):
* Chain [[41],44]: 1*it(41)+0
  Such that:it(41) =< -D+7

  with precondition: [B=7,J=3,6>=D] 

* Chain [[41],43]: 1*it(41)+0
  Such that:it(41) =< -D+K

  with precondition: [B=7,J=4,6>=K,K>=D+1] 

* Chain [[41],42]: 1*it(41)+0
  Such that:it(41) =< -D+7

  with precondition: [B=7,J=5,K=0,6>=D] 

* Chain [44]: 0
  with precondition: [B=7,J=3] 

* Chain [43]: 0
  with precondition: [B=7,J=4,D=K,6>=D] 

* Chain [42]: 0
  with precondition: [B=7,J=5,K=0,L=F,M=G,D>=7] 


#### Cost of chains of f63(A,D,J,K):
* Chain [[45],47]: 1*it(45)+0
  Such that:it(45) =< -D+5

  with precondition: [A=5,J=3,4>=D] 

* Chain [[45],46]: 1*it(45)+0
  Such that:it(45) =< -D+5

  with precondition: [A=5,J=4,K=5,4>=D] 

* Chain [47]: 0
  with precondition: [A=5,J=3] 

* Chain [46]: 0
  with precondition: [A=5,J=4,D=K,D>=5] 


#### Cost of chains of f63_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [49]: 0
  with precondition: [A=3,B=5,C=7,D=0] 

* Chain [48]: 0
  with precondition: [A=4,B=5,C=7,D=0] 


#### Cost of chains of f53_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [54]: 0
  with precondition: [A=3,B=5,C=7,D=0] 

* Chain [53]: 0
  with precondition: [A=4,B=5,C=7,D=0] 

* Chain [52]: 0
  with precondition: [A=5,B=5,C=7,D=0] 

* Chain [51]: 2*s(9)+0
  Such that:aux(6) =< -E+5
s(9) =< aux(6)

  with precondition: [A=5,B=5,C=7,D=0,4>=E] 

* Chain [50]: 0
  with precondition: [A=5,B=5,C=7,D=0,E>=5] 


#### Cost of chains of f39_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [59]: 0
  with precondition: [A=3,B=5,C=7,D=0] 

* Chain [58]: 0
  with precondition: [A=6,B=5,C=7,D=0] 

* Chain [57]: 3*s(11)+2*s(15)+0
  Such that:s(14) =< 5
aux(7) =< -E+7
s(11) =< aux(7)
s(15) =< s(14)

  with precondition: [A=6,B=5,C=7,D=0,6>=E] 

* Chain [56]: 1*s(16)+0
  Such that:s(16) =< -E+6

  with precondition: [A=6,B=5,C=7,D=0,5>=E] 

* Chain [55]: 10
  with precondition: [A=6,B=5,C=7,D=0,E>=7] 


#### Cost of chains of f31_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [64]: 0
  with precondition: [A=2,B=5,C=7,D=0] 

* Chain [63]: 4*s(20)+4*s(21)+3*s(30)+2*s(31)+1*s(35)+7
  Such that:s(28) =< 5
s(35) =< 6
s(29) =< 7
aux(8) =< -E+5
s(30) =< s(29)
s(31) =< s(28)
s(20) =< aux(8)
s(21) =< aux(8)*7

  with precondition: [A=2,B=5,C=7,D=0,4>=E] 

* Chain [62]: 1*s(39)+1*s(40)+7
  Such that:s(36) =< -E+4
s(37) =< -E+5
s(38) =< s(37)
s(39) =< s(37)
s(38) =< s(36)
s(39) =< s(36)
s(40) =< s(38)*7

  with precondition: [A=2,B=5,C=7,D=0,3>=E] 

* Chain [61]: 37
  with precondition: [A=2,B=5,C=7,D=0,E>=5] 

* Chain [60]: 0
  with precondition: [A=3,B=5,C=7,D=0] 


#### Cost of chains of f0(A,B,C,D,E,F,G,J):
* Chain [65]: 257
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,J): 
-------------------------------------
* Chain [65] with precondition: [] 
    - Upper bound: 257 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,J): 257 
Asymptotic class: constant 
* Total analysis performed in 271 ms.

