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

#### Computed strongly connected components 
0. recursive  : [f15/6]
1. recursive  : [f12/6,f15_loop_cont/7]
2. non_recursive  : [exit_location/1]
3. recursive  : [f30/6]
4. recursive  : [f26/8,f30_loop_cont/9]
5. recursive  : [f23/10,f26_loop_cont/11]
6. non_recursive  : [f52/8]
7. non_recursive  : [f23_loop_cont/9]
8. non_recursive  : [f12_loop_cont/9]
9. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f15/6
1. SCC is partially evaluated into f12/6
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f30/6
4. SCC is partially evaluated into f26/8
5. SCC is partially evaluated into f23/10
6. SCC is completely evaluated into other SCCs
7. SCC is partially evaluated into f23_loop_cont/9
8. SCC is partially evaluated into f12_loop_cont/9
9. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f15/6 
* CE 9 is refined into CE [25] 
* CE 10 is refined into CE [26] 
* CE 8 is refined into CE [27] 


### Cost equations --> "Loop" of f15/6 
* CEs [27] --> Loop 25 
* CEs [25] --> Loop 26 
* CEs [26] --> Loop 27 

### Ranking functions of CR f15(A,D,E,J,K,L) 
* RF of phase [25]: [-E+2]

#### Partial ranking functions of CR f15(A,D,E,J,K,L) 
* Partial RF of phase [25]:
  - RF of loop [25:1]:
    -E+2


### Specialization of cost equations f12/6 
* CE 4 is refined into CE [28] 
* CE 2 is refined into CE [29,30] 
* CE 5 is refined into CE [31] 
* CE 3 is refined into CE [32] 


### Cost equations --> "Loop" of f12/6 
* CEs [32] --> Loop 28 
* CEs [28] --> Loop 29 
* CEs [29,30] --> Loop 30 
* CEs [31] --> Loop 31 

### Ranking functions of CR f12(A,D,E,J,K,L) 
* RF of phase [28]: [-D+2]

#### Partial ranking functions of CR f12(A,D,E,J,K,L) 
* Partial RF of phase [28]:
  - RF of loop [28:1]:
    -D+2


### Specialization of cost equations f30/6 
* CE 24 is refined into CE [33] 
* CE 23 is refined into CE [34] 
* CE 22 is refined into CE [35] 


### Cost equations --> "Loop" of f30/6 
* CEs [35] --> Loop 32 
* CEs [33] --> Loop 33 
* CEs [34] --> Loop 34 

### Ranking functions of CR f30(A,E,F,J,K,L) 
* RF of phase [32]: [-F+2]

#### Partial ranking functions of CR f30(A,E,F,J,K,L) 
* Partial RF of phase [32]:
  - RF of loop [32:1]:
    -F+2


### Specialization of cost equations f26/8 
* CE 20 is refined into CE [36] 
* CE 18 is refined into CE [37,38] 
* CE 21 is refined into CE [39] 
* CE 19 is refined into CE [40] 


### Cost equations --> "Loop" of f26/8 
* CEs [40] --> Loop 35 
* CEs [36] --> Loop 36 
* CEs [37,38] --> Loop 37 
* CEs [39] --> Loop 38 

### Ranking functions of CR f26(A,D,E,F,J,K,L,M) 
* RF of phase [35]: [-E+2]

#### Partial ranking functions of CR f26(A,D,E,F,J,K,L,M) 
* Partial RF of phase [35]:
  - RF of loop [35:1]:
    -E+2


### Specialization of cost equations f23/10 
* CE 14 is refined into CE [41] 
* CE 13 is refined into CE [42] 
* CE 11 is refined into CE [43,44,45] 
* CE 15 is refined into CE [46] 
* CE 12 is refined into CE [47] 


### Cost equations --> "Loop" of f23/10 
* CEs [47] --> Loop 39 
* CEs [41] --> Loop 40 
* CEs [42] --> Loop 41 
* CEs [43,44,45] --> Loop 42 
* CEs [46] --> Loop 43 

### Ranking functions of CR f23(A,D,E,F,G,J,K,L,M,N) 
* RF of phase [39]: [-D+2]

#### Partial ranking functions of CR f23(A,D,E,F,G,J,K,L,M,N) 
* Partial RF of phase [39]:
  - RF of loop [39:1]:
    -D+2


### Specialization of cost equations f23_loop_cont/9 
* CE 16 is refined into CE [48] 
* CE 17 is refined into CE [49] 


### Cost equations --> "Loop" of f23_loop_cont/9 
* CEs [48] --> Loop 44 
* CEs [49] --> Loop 45 

### Ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f12_loop_cont/9 
* CE 7 is refined into CE [50,51,52,53,54,55,56] 
* CE 6 is refined into CE [57] 


### Cost equations --> "Loop" of f12_loop_cont/9 
* CEs [55,56] --> Loop 46 
* CEs [52] --> Loop 47 
* CEs [51,53,54] --> Loop 48 
* CEs [50] --> Loop 49 
* CEs [57] --> Loop 50 

### Ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [58,59,60,61,62,63] 


### Cost equations --> "Loop" of f0/8 
* CEs [58,59,60,61,62,63] --> Loop 51 

### 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 f15(A,D,E,J,K,L):
* Chain [[25],27]: 1*it(25)+0
  Such that:it(25) =< -E+2

  with precondition: [A=2,J=3,1>=D,1>=E,E>=0] 

* Chain [[25],26]: 1*it(25)+0
  Such that:it(25) =< -E+2

  with precondition: [A=2,J=5,L=2,D+1=K,1>=D,1>=E,E>=0] 

* Chain [27]: 0
  with precondition: [A=2,J=3,1>=D,E>=0] 


#### Cost of chains of f12(A,D,E,J,K,L):
* Chain [[28],31]: 1*it(28)+1*s(3)+0
  Such that:aux(4) =< -D+2
it(28) =< aux(4)
s(3) =< aux(4)*2

  with precondition: [A=2,J=3,1>=D,D>=0] 

* Chain [[28],30]: 1*it(28)+1*s(3)+2
  Such that:aux(3) =< 1
aux(2) =< 2
aux(1) =< aux(2)
it(28) =< aux(2)
aux(1) =< aux(3)
it(28) =< aux(3)
s(3) =< aux(1)*2

  with precondition: [A=2,D=0,J=3] 

* Chain [[28],29]: 1*it(28)+1*s(3)+0
  Such that:aux(5) =< -D+2
it(28) =< aux(5)
s(3) =< aux(5)*2

  with precondition: [A=2,J=4,K=0,L=2,1>=D,D>=0] 

* Chain [31]: 0
  with precondition: [A=2,J=3,D>=0] 

* Chain [30]: 2
  with precondition: [A=2,J=3,1>=D,D>=0] 


#### Cost of chains of f30(A,E,F,J,K,L):
* Chain [[32],34]: 1*it(32)+0
  Such that:it(32) =< -F+2

  with precondition: [A=2,J=2,L=2,E+1=K,1>=E,1>=F,F>=0] 

* Chain [[32],33]: 1*it(32)+0
  Such that:it(32) =< -F+2

  with precondition: [A=2,J=3,1>=E,1>=F,F>=0] 

* Chain [33]: 0
  with precondition: [A=2,J=3,1>=E,F>=0] 


#### Cost of chains of f26(A,D,E,F,J,K,L,M):
* Chain [[35],38]: 1*it(35)+1*s(10)+0
  Such that:aux(9) =< -E+2
it(35) =< aux(9)
s(10) =< aux(9)*2

  with precondition: [A=2,J=3,1>=D,1>=E,E>=0] 

* Chain [[35],37]: 1*it(35)+1*s(10)+2
  Such that:aux(8) =< 1
aux(7) =< 2
aux(6) =< aux(7)
it(35) =< aux(7)
aux(6) =< aux(8)
it(35) =< aux(8)
s(10) =< aux(6)*2

  with precondition: [A=2,E=0,J=3,1>=D] 

* Chain [[35],36]: 1*it(35)+1*s(10)+0
  Such that:aux(10) =< -E+2
it(35) =< aux(10)
s(10) =< aux(10)*2

  with precondition: [A=2,J=4,L=2,M=2,D+1=K,1>=D,1>=E,E>=0] 

* Chain [38]: 0
  with precondition: [A=2,J=3,1>=D,E>=0] 

* Chain [37]: 2
  with precondition: [A=2,J=3,1>=D,1>=E,E>=0] 


#### Cost of chains of f23(A,D,E,F,G,J,K,L,M,N):
* Chain [[39],43]: 1*it(39)+1*s(21)+1*s(22)+0
  Such that:aux(14) =< -D+2
it(39) =< aux(14)
s(23) =< aux(14)*2
s(21) =< s(23)
s(22) =< s(23)*2

  with precondition: [A=2,J=3,1>=D] 

* Chain [[39],42]: 1*it(39)+1*s(21)+1*s(22)+14
  Such that:aux(13) =< -D+1
aux(12) =< -D+2
aux(11) =< aux(12)
it(39) =< aux(12)
aux(11) =< aux(13)
it(39) =< aux(13)
s(23) =< aux(11)*2
s(21) =< s(23)
s(22) =< s(23)*2

  with precondition: [A=2,J=3,0>=D] 

* Chain [[39],41]: 1*it(39)+1*s(21)+1*s(22)+0
  Such that:aux(16) =< -D+2
it(39) =< aux(16)
s(23) =< aux(16)*2
s(21) =< s(23)
s(22) =< s(23)*2

  with precondition: [A=2,J=6,K=2,L=2,M=2,N=0,1>=D] 

* Chain [[39],40]: 1*it(39)+1*s(21)+1*s(22)+0
  Such that:aux(17) =< -D+2
it(39) =< aux(17)
s(23) =< aux(17)*2
s(21) =< s(23)
s(22) =< s(23)*2

  with precondition: [A=2,J=6,K=2,L=2,M=2,N=1,1>=D] 

* Chain [43]: 0
  with precondition: [A=2,J=3] 

* Chain [42]: 14
  with precondition: [A=2,J=3,1>=D] 

* Chain [41]: 0
  with precondition: [A=2,J=6,N=0,L=E,M=F,D=K,D>=2] 

* Chain [40]: 0
  with precondition: [A=2,J=6,N=1,L=E,M=F,D=K,D>=2] 


#### Cost of chains of f23_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [45]: 0
  with precondition: [A=3,B=2] 

* Chain [44]: 0
  with precondition: [A=6,B=2] 


#### Cost of chains of f12_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [50]: 0
  with precondition: [A=3,B=2] 

* Chain [49]: 0
  with precondition: [A=4,B=2] 

* Chain [48]: 3*s(38)+3*s(40)+3*s(41)+14
  Such that:aux(18) =< -E+2
s(38) =< aux(18)
s(39) =< aux(18)*2
s(40) =< s(39)
s(41) =< s(39)*2

  with precondition: [A=4,B=2,1>=E] 

* Chain [47]: 1*s(55)+1*s(57)+1*s(58)+14
  Such that:s(52) =< -E+1
s(53) =< -E+2
s(54) =< s(53)
s(55) =< s(53)
s(54) =< s(52)
s(55) =< s(52)
s(56) =< s(54)*2
s(57) =< s(56)
s(58) =< s(56)*2

  with precondition: [A=4,B=2,0>=E] 

* Chain [46]: 0
  with precondition: [A=4,B=2,E>=2] 


#### Cost of chains of f0(A,B,C,D,E,F,G,J):
* Chain [51]: 100
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,J): 
-------------------------------------
* Chain [51] with precondition: [] 
    - Upper bound: 100 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,J): 100 
Asymptotic class: constant 
* Total analysis performed in 349 ms.

