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

#### Computed strongly connected components 
0. recursive  : [f20/19,f32/19,f9/19]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f38/10]
3. non_recursive  : [f9_loop_cont/11]
4. non_recursive  : [f0/10]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f9/19
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f9_loop_cont/11
4. SCC is partially evaluated into f0/10

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

### Specialization of cost equations f9/19 
* CE 44 is refined into CE [47] 
* CE 43 is refined into CE [48] 
* CE 42 is refined into CE [49] 
* CE 2 is refined into CE [50] 
* CE 7 is refined into CE [51] 
* CE 15 is refined into CE [52] 
* CE 19 is refined into CE [53] 
* CE 3 is discarded (unfeasible) 
* CE 8 is discarded (unfeasible) 
* CE 16 is discarded (unfeasible) 
* CE 20 is discarded (unfeasible) 
* CE 27 is refined into CE [54] 
* CE 32 is refined into CE [55] 
* CE 28 is discarded (unfeasible) 
* CE 33 is discarded (unfeasible) 
* CE 11 is refined into CE [56] 
* CE 23 is refined into CE [57] 
* CE 12 is discarded (unfeasible) 
* CE 24 is discarded (unfeasible) 
* CE 37 is refined into CE [58] 
* CE 38 is discarded (unfeasible) 
* CE 4 is refined into CE [59] 
* CE 9 is refined into CE [60] 
* CE 17 is refined into CE [61] 
* CE 21 is refined into CE [62] 
* CE 6 is discarded (unfeasible) 
* CE 36 is discarded (unfeasible) 
* CE 31 is refined into CE [63] 
* CE 5 is discarded (unfeasible) 
* CE 10 is discarded (unfeasible) 
* CE 18 is discarded (unfeasible) 
* CE 22 is discarded (unfeasible) 
* CE 13 is discarded (unfeasible) 
* CE 25 is discarded (unfeasible) 
* CE 14 is discarded (unfeasible) 
* CE 26 is discarded (unfeasible) 
* CE 29 is discarded (unfeasible) 
* CE 34 is discarded (unfeasible) 
* CE 30 is discarded (unfeasible) 
* CE 35 is discarded (unfeasible) 
* CE 39 is refined into CE [64] 
* CE 40 is discarded (unfeasible) 
* CE 41 is refined into CE [65] 


### Cost equations --> "Loop" of f9/19 
* CEs [50] --> Loop 47 
* CEs [51] --> Loop 48 
* CEs [52] --> Loop 49 
* CEs [53] --> Loop 50 
* CEs [54] --> Loop 51 
* CEs [55] --> Loop 52 
* CEs [56] --> Loop 53 
* CEs [57] --> Loop 54 
* CEs [58] --> Loop 55 
* CEs [63] --> Loop 56 
* CEs [65] --> Loop 57 
* CEs [59] --> Loop 58 
* CEs [60] --> Loop 59 
* CEs [61] --> Loop 60 
* CEs [62] --> Loop 61 
* CEs [64] --> Loop 62 
* CEs [47] --> Loop 63 
* CEs [48] --> Loop 64 
* CEs [49] --> Loop 65 

### Ranking functions of CR f9(A,B,C,D,E,F,G,H,I,L,M,N,O,P,Q,R,S,T,U) 

#### Partial ranking functions of CR f9(A,B,C,D,E,F,G,H,I,L,M,N,O,P,Q,R,S,T,U) 
* Partial RF of phase [47,48,49,50,55,57,58,59,60,61,62]:
  - RF of loop [47:1,48:1,49:1,50:1,55:1]:
    F depends on loops [58:1,59:1,60:1,61:1,62:1] 
  - RF of loop [57:1]:
    C depends on loops [58:1,59:1,60:1,61:1,62:1] 
  - RF of loop [58:1,59:1,60:1,61:1,62:1]:
    -A+1
    -B+2
    -C/2+1/2 depends on loops [57:1] 
    -F+1 depends on loops [47:1,48:1,49:1,50:1,55:1] 


### Specialization of cost equations f9_loop_cont/11 
* CE 46 is refined into CE [66] 
* CE 45 is refined into CE [67] 


### Cost equations --> "Loop" of f9_loop_cont/11 
* CEs [66] --> Loop 66 
* CEs [67] --> Loop 67 

### Ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 

#### Partial ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 


### Specialization of cost equations f0/10 
* CE 1 is refined into CE [68,69,70,71,72,73,74,75,76,77,78,79,80] 


### Cost equations --> "Loop" of f0/10 
* CEs [68,69,70,71,72,73,74,75,76,77,78,79,80] --> Loop 68 

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

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


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

#### Cost of chains of f9(A,B,C,D,E,F,G,H,I,L,M,N,O,P,Q,R,S,T,U):
* Chain [[47,48,49,50,55,57,58,59,60,61,62],63]: 5*it(47)+1*it(57)+5*it(58)+0
  Such that:aux(2) =< -6*B+3*C+2*F+4
aux(2) =< -2*B+C+2
aux(1) =< C
aux(31) =< -B+2
it(58) =< aux(31)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+1>=B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],56,64]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< A
aux(32) =< -A+1
aux(33) =< C
aux(2) =< aux(33)
it(58) =< aux(32)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(33)

  with precondition: [L=2,M=1,N=2,O=1,P=1,Q=0,R=0,S=1,T=0,U=1,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+1>=B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],56,63]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< A
aux(34) =< -B+2
aux(35) =< C
aux(2) =< aux(35)
it(58) =< aux(34)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(35)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+1>=B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],54,65]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< B-O
aux(1) =< C
aux(2) =< C-O
aux(36) =< -B+2
aux(37) =< -B+N
it(58) =< aux(36)
it(58) =< aux(37)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=2,P=0,Q=1,U=0,B=A+1,D=E,M+1=N,1>=D,0>=T+1,B>=1,D>=0,R>=0,O>=2*M,M+1>=O,F+2*M>=2*B,C+2*M+2>=2*B+O,B+O>=C+M+1] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],54,63]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< -6*B+3*C+2*F+4
aux(2) =< -2*B+C+2
aux(1) =< C
aux(38) =< -B+2
it(58) =< aux(38)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+2>=2*B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],53,65]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< B-O
aux(1) =< C
aux(2) =< C-O
aux(39) =< -B+2
aux(40) =< -B+N
it(58) =< aux(39)
it(58) =< aux(40)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=2,P=0,Q=1,U=0,B=A+1,D=E,M+1=N,1>=D,B>=1,D>=0,R>=0,T>=1,O>=2*M,M+1>=O,F+2*M>=2*B,C+2*M+2>=2*B+O,B+O>=C+M+1] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],53,63]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< -6*B+3*C+2*F+4
aux(2) =< -2*B+C+2
aux(1) =< C
aux(41) =< -B+2
it(58) =< aux(41)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+2>=2*B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],52,64]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< B-O
aux(1) =< C
aux(2) =< C-O
aux(42) =< -B+2
aux(43) =< -B+N
it(58) =< aux(42)
it(58) =< aux(43)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=2,P=1,Q=0,T=0,B=A+1,D=E,M+1=N,1>=D,0>=U+1,B>=1,D>=0,R>=0,O>=2*M,M+1>=O,F+2*M>=2*B,C+2*M+2>=2*B+O,B+O>=C+M+1] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],52,63]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< -6*B+3*C+2*F+4
aux(2) =< -2*B+C+2
aux(1) =< C
aux(44) =< -B+2
it(58) =< aux(44)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+2>=2*B,B>=C] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],51,64]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< B-O
aux(1) =< C
aux(2) =< C-O
aux(45) =< -B+2
aux(46) =< -B+N
it(58) =< aux(45)
it(58) =< aux(46)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=2,P=1,Q=0,T=0,B=A+1,D=E,M+1=N,1>=D,B>=1,D>=0,R>=0,U>=1,O>=2*M,M+1>=O,F+2*M>=2*B,C+2*M+2>=2*B+O,B+O>=C+M+1] 

* Chain [[47,48,49,50,55,57,58,59,60,61,62],51,63]: 5*it(47)+1*it(57)+5*it(58)+1
  Such that:aux(2) =< -6*B+3*C+2*F+4
aux(2) =< -2*B+C+2
aux(1) =< C
aux(47) =< -B+2
it(58) =< aux(47)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(2)
it(57) =< it(58)*2+it(58)*2+it(58)*2+it(58)*2+it(58)*2+aux(1)

  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,C+2>=2*B,F+2>=2*B,B>=C] 

* Chain [63]: 0
  with precondition: [L=3,B=A+1,2>=B,1>=D,1>=E,B>=1,D>=0,E>=0,C+1>=B,B>=C,C+3>=2*B+E,C+D+2>=2*B] 

* Chain [54,65]: 1
  with precondition: [L=2,P=0,Q=1,U=0,M=A,M+1=B,D=E,R+1=F,M+1=N,C=O,G=S,1>=D,0>=T+1,D>=0,M>=0,R>=0,C>=2*M,M+1>=C] 

* Chain [54,63]: 1
  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,F>=1,C+2>=2*B,B>=C] 

* Chain [53,65]: 1
  with precondition: [L=2,P=0,Q=1,U=0,M=A,M+1=B,D=E,R+1=F,M+1=N,C=O,G=S,1>=D,D>=0,M>=0,R>=0,T>=1,C>=2*M,M+1>=C] 

* Chain [53,63]: 1
  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,F>=1,C+2>=2*B,B>=C] 

* Chain [52,64]: 1
  with precondition: [L=2,P=1,Q=0,T=0,M=A,M+1=B,D=E,R+1=F,M+1=N,C=O,G=S,1>=D,0>=U+1,D>=0,M>=0,R>=0,C>=2*M,M+1>=C] 

* Chain [52,63]: 1
  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,F>=1,C+2>=2*B,B>=C] 

* Chain [51,64]: 1
  with precondition: [L=2,P=1,Q=0,T=0,M=A,M+1=B,D=E,R+1=F,M+1=N,C=O,G=S,1>=D,D>=0,M>=0,R>=0,U>=1,C>=2*M,M+1>=C] 

* Chain [51,63]: 1
  with precondition: [L=3,B=A+1,D=E,1>=D,B>=1,D>=0,F>=1,C+2>=2*B,B>=C] 


#### Cost of chains of f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
* Chain [67]: 0
  with precondition: [A=2] 

* Chain [66]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,L):
* Chain [68]: 1*aux(62)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,L): 
-------------------------------------
* Chain [68] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,L): inf 
Asymptotic class: infinity 
* Total analysis performed in 2978 ms.

