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

#### Computed strongly connected components 
0. non_recursive  : [f0/50]
1. recursive  : [f15/58]
2. non_recursive  : [exit_location/1]
3. recursive  : [f13/64]
4. recursive  : [f10/25]
5. non_recursive  : [f10_loop_cont/51]
6. non_recursive  : [f13_loop_cont/51]
7. non_recursive  : [f15_loop_cont/51]
8. non_recursive  : [f17/50]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into f15/58
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f13/64
4. SCC is partially evaluated into f10/25
5. SCC is partially evaluated into f10_loop_cont/51
6. SCC is partially evaluated into f13_loop_cont/51
7. SCC is partially evaluated into f15_loop_cont/51
8. SCC is partially evaluated into f17/50

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

### Specialization of cost equations f15/58 
* CE 11 is refined into CE [30] 
* CE 7 is refined into CE [31] 
* CE 10 is refined into CE [32] 
* CE 6 is refined into CE [33] 
* CE 9 is refined into CE [34] 
* CE 5 is refined into CE [35] 
* CE 8 is refined into CE [36] 
* CE 4 is refined into CE [37] 
* CE 12 is refined into CE [38] 
* CE 3 is refined into CE [39] 


### Cost equations --> "Loop" of f15/58 
* CEs [39] --> Loop 29 
* CEs [30] --> Loop 30 
* CEs [31] --> Loop 31 
* CEs [32] --> Loop 32 
* CEs [33] --> Loop 33 
* CEs [34] --> Loop 34 
* CEs [35] --> Loop 35 
* CEs [36] --> Loop 36 
* CEs [37] --> Loop 37 
* CEs [38] --> Loop 38 

### Ranking functions of CR f15(A,B,C,D,E,F,G,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,Z,N1,P1,Q1,R1,S1,T1,U1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4) 
* RF of phase [29]: [A-B,-B+J]

#### Partial ranking functions of CR f15(A,B,C,D,E,F,G,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,Z,N1,P1,Q1,R1,S1,T1,U1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4) 
* Partial RF of phase [29]:
  - RF of loop [29:1]:
    A-B
    -B+J


### Specialization of cost equations f13/64 
* CE 21 is refined into CE [40] 
* CE 19 is refined into CE [41] 
* CE 20 is refined into CE [42] 
* CE 18 is refined into CE [43] 
* CE 17 is refined into CE [44] 
* CE 16 is refined into CE [45] 
* CE 15 is refined into CE [46] 


### Cost equations --> "Loop" of f13/64 
* CEs [43] --> Loop 39 
* CEs [44] --> Loop 40 
* CEs [45] --> Loop 41 
* CEs [46] --> Loop 42 
* CEs [40] --> Loop 43 
* CEs [41] --> Loop 44 
* CEs [42] --> Loop 45 

### Ranking functions of CR f13(H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,R1,V1,W1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4,H4,I4,J4) 
* RF of phase [39,40,41,42]: [I+1]

#### Partial ranking functions of CR f13(H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,R1,V1,W1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4,H4,I4,J4) 
* Partial RF of phase [39,40,41,42]:
  - RF of loop [39:1,40:1,41:1,42:1]:
    I+1


### Specialization of cost equations f10/25 
* CE 27 is refined into CE [47] 
* CE 26 is refined into CE [48] 
* CE 25 is refined into CE [49] 
* CE 24 is refined into CE [50] 


### Cost equations --> "Loop" of f10/25 
* CEs [49] --> Loop 46 
* CEs [50] --> Loop 47 
* CEs [47] --> Loop 48 
* CEs [48] --> Loop 49 

### Ranking functions of CR f10(J,K,L,X,D1,F1,G1,H1,I1,J1,K1,L1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3) 
* RF of phase [46,47]: [K1+1]

#### Partial ranking functions of CR f10(J,K,L,X,D1,F1,G1,H1,I1,J1,K1,L1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3) 
* Partial RF of phase [46,47]:
  - RF of loop [46:1,47:1]:
    K1+1


### Specialization of cost equations f10_loop_cont/51 
* CE 29 is refined into CE [51] 
* CE 28 is refined into CE [52] 


### Cost equations --> "Loop" of f10_loop_cont/51 
* CEs [51] --> Loop 50 
* CEs [52] --> Loop 51 

### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 

#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 


### Specialization of cost equations f13_loop_cont/51 
* CE 23 is refined into CE [53,54,55,56] 
* CE 22 is refined into CE [57] 


### Cost equations --> "Loop" of f13_loop_cont/51 
* CEs [56] --> Loop 52 
* CEs [55] --> Loop 53 
* CEs [54] --> Loop 54 
* CEs [53] --> Loop 55 
* CEs [57] --> Loop 56 

### Ranking functions of CR f13_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 

#### Partial ranking functions of CR f13_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 


### Specialization of cost equations f15_loop_cont/51 
* CE 14 is refined into CE [58,59,60,61,62,63,64,65,66,67] 
* CE 13 is refined into CE [68] 


### Cost equations --> "Loop" of f15_loop_cont/51 
* CEs [67] --> Loop 57 
* CEs [58,60] --> Loop 58 
* CEs [59,61] --> Loop 59 
* CEs [64] --> Loop 60 
* CEs [65] --> Loop 61 
* CEs [62] --> Loop 62 
* CEs [63] --> Loop 63 
* CEs [66] --> Loop 64 
* CEs [68] --> Loop 65 

### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 

#### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1) 


### Specialization of cost equations f17/50 
* CE 1 is refined into CE [69] 
* CE 2 is refined into CE [70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103] 


### Cost equations --> "Loop" of f17/50 
* CEs [72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102] --> Loop 66 
* CEs [73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103] --> Loop 67 
* CEs [69,70,71] --> Loop 68 

### Ranking functions of CR f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,E3) 

#### Partial ranking functions of CR f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,E3) 


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

#### Cost of chains of f15(A,B,C,D,E,F,G,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,Z,N1,P1,Q1,R1,S1,T1,U1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4):
* Chain [[29],38]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=3,C=E,A=J,B>=2,A>=B+1] 

* Chain [[29],37]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=O3+1,0>=A4+1,0>=G4+1,B>=2,P1>=0,M3>=2,E4>=2,A>=B+1] 

* Chain [[29],36]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=O3+1,0>=A4+1,B>=2,P1>=0,M3>=2,E4>=2,G4>=1,A>=B+1] 

* Chain [[29],35]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=A4+1,0>=G4+1,B>=2,P1>=0,M3>=2,O3>=1,E4>=2,A>=B+1] 

* Chain [[29],34]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=A4+1,B>=2,P1>=0,M3>=2,O3>=1,E4>=2,G4>=1,A>=B+1] 

* Chain [[29],33]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=O3+1,0>=G4+1,B>=2,P1>=0,M3>=2,A4>=1,E4>=2,A>=B+1] 

* Chain [[29],32]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=O3+1,B>=2,P1>=0,M3>=2,A4>=1,E4>=2,G4>=1,A>=B+1] 

* Chain [[29],31]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,0>=G4+1,B>=2,P1>=0,M3>=2,O3>=1,A4>=1,E4>=2,A>=B+1] 

* Chain [[29],30]: 1*it(29)+0
  Such that:it(29) =< A-B

  with precondition: [E3=5,S3=0,Z3=0,C=E,A=J,A=L3+1,O3=P3,B>=2,P1>=0,M3>=2,O3>=1,A4>=1,E4>=2,G4>=1,A>=B+1] 

* Chain [38]: 0
  with precondition: [E3=3,J=A,E=C,B>=2,J>=B] 

* Chain [37]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=E+1,0>=O3+1,0>=G4+1,A>=2,P1>=0,M3>=2,E4>=2] 

* Chain [36]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=E+1,0>=O3+1,A>=2,P1>=0,M3>=2,E4>=2,G4>=1] 

* Chain [35]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=E+1,0>=G4+1,A>=2,P1>=0,M3>=2,O3>=1,E4>=2] 

* Chain [34]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=E+1,A>=2,P1>=0,M3>=2,O3>=1,E4>=2,G4>=1] 

* Chain [33]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=O3+1,0>=G4+1,A>=2,E>=1,P1>=0,M3>=2,E4>=2] 

* Chain [32]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=O3+1,A>=2,E>=1,P1>=0,M3>=2,E4>=2,G4>=1] 

* Chain [31]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,0>=G4+1,A>=2,E>=1,P1>=0,M3>=2,O3>=1,E4>=2] 

* Chain [30]: 0
  with precondition: [E3=5,S3=0,Z3=0,A=B,E=C,K3=F,L3=G,A=J,O3=P3,E=A4,A>=2,E>=1,P1>=0,M3>=2,O3>=1,E4>=2,G4>=1] 


#### Cost of chains of f13(H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,R1,V1,W1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3,Z3,A4,B4,C4,D4,E4,F4,G4,H4,I4,J4):
* Chain [[39,40,41,42],45]: 4*it(39)+0
  Such that:aux(2) =< -H+Z3
aux(1) =< I+1
it(39) =< aux(1)
it(39) =< aux(2)

  with precondition: [Z=0,E3=4,W3=0,C4=0,E4=0,G3=A4,J3=B4,J3=D4,J3=F4,J3=G4,G3+Z3=H+I,0>=J3+1,H>=0,G3>=0,H3>=2,I>=G3+1] 

* Chain [[39,40,41,42],44]: 4*it(39)+0
  Such that:aux(2) =< -H+Z3
aux(1) =< I+1
it(39) =< aux(1)
it(39) =< aux(2)

  with precondition: [Z=0,E3=4,W3=0,C4=0,E4=0,G3=A4,J3=B4,J3=D4,J3=F4,J3=G4,G3+Z3=H+I,H>=0,G3>=0,H3>=2,J3>=1,I>=G3+1] 

* Chain [[39,40,41,42],43]: 4*it(39)+0
  Such that:aux(3) =< I+1
it(39) =< aux(3)

  with precondition: [E3=3,H>=0,I>=0] 

* Chain [45]: 0
  with precondition: [Z=0,E3=4,C4=0,E4=0,V3=X,W3=Y,Y3=A1,Z3=B1,A4=C1,I=G3,L=J3,L=B4,L=D4,L=F4,L=G4,0>=L+1,H>=0,I>=0,H3>=2] 

* Chain [44]: 0
  with precondition: [Z=0,E3=4,C4=0,E4=0,V3=X,W3=Y,Y3=A1,Z3=B1,A4=C1,I=G3,L=J3,L=B4,L=D4,L=F4,L=G4,H>=0,I>=0,L>=1,H3>=2] 

* Chain [43]: 0
  with precondition: [E3=3] 


#### Cost of chains of f10(J,K,L,X,D1,F1,G1,H1,I1,J1,K1,L1,E3,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3):
* Chain [[46,47],49]: 2*it(46)+0
  Such that:aux(4) =< K1+1
aux(5) =< K1-P3
it(46) =< aux(4)
it(46) =< aux(5)

  with precondition: [D1=0,F1=0,E3=2,P3=Q3,F3>=2,P3>=0,K1>=P3+1] 

* Chain [[46,47],48]: 2*it(46)+0
  Such that:aux(6) =< K1+1
it(46) =< aux(6)

  with precondition: [F1=0,E3=3,K1>=0] 

* Chain [49]: 0
  with precondition: [E3=2,H3=L,I3=X,F1=D1,Q3=L1,K1=P3,K1>=0,F3>=2] 

* Chain [48]: 0
  with precondition: [E3=3] 


#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1):
* Chain [51]: 0
  with precondition: [A=2] 

* Chain [50]: 0
  with precondition: [A=3] 


#### Cost of chains of f13_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1):
* Chain [56]: 0
  with precondition: [A=3,L1=F1] 

* Chain [55]: 2*s(3)+0
  Such that:s(2) =< F1
s(1) =< F1+1
s(3) =< s(1)
s(3) =< s(2)

  with precondition: [A=4,E1=0,G1=0,L1=F1,L1>=1] 

* Chain [54]: 2*s(5)+0
  Such that:s(4) =< L1+1
s(5) =< s(4)

  with precondition: [A=4,G1=0,L1=F1,L1>=0] 

* Chain [53]: 0
  with precondition: [A=4,G1=E1,L1=F1,L1>=0] 

* Chain [52]: 0
  with precondition: [A=4,L1=F1] 


#### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1):
* Chain [65]: 0
  with precondition: [A=3] 

* Chain [64]: 0
  with precondition: [A=5] 

* Chain [63]: 0
  with precondition: [A=5,A1=0,0>=M+1,I>=0,J>=0] 

* Chain [62]: 2*s(7)+0
  Such that:s(6) =< L1+1
s(7) =< s(6)

  with precondition: [A=5,A1=0,0>=M+1,I>=0,J>=0,L1>=0] 

* Chain [61]: 0
  with precondition: [A=5,A1=0,I>=0,J>=0,M>=1] 

* Chain [60]: 2*s(9)+0
  Such that:s(8) =< L1+1
s(9) =< s(8)

  with precondition: [A=5,A1=0,I>=0,J>=0,M>=1,L1>=0] 

* Chain [59]: 8*s(12)+0
  Such that:aux(7) =< J
aux(8) =< J+1
s(12) =< aux(8)
s(12) =< aux(7)

  with precondition: [A=5,A1=0,I>=0,J>=1] 

* Chain [58]: 8*s(18)+4*s(20)+0
  Such that:aux(9) =< J
aux(10) =< J+1
aux(11) =< L1+1
s(20) =< aux(11)
s(18) =< aux(10)
s(18) =< aux(9)

  with precondition: [A=5,A1=0,I>=0,J>=1,L1>=0] 

* Chain [57]: 4*s(27)+0
  Such that:s(26) =< J+1
s(27) =< s(26)

  with precondition: [A=5,I>=0,J>=0] 


#### Cost of chains of f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,E3):
* Chain [68]: 1*aux(12)+0
  with precondition: [] 

* Chain [67]: 64*s(30)+8*s(45)+0
  Such that:aux(13) =< I+1
s(30) =< aux(13)

  with precondition: [H>=0,I>=0,P1>=0] 

* Chain [66]: 1*aux(14)+0
  with precondition: [P1>=0] 


Closed-form bounds of f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,E3): 
-------------------------------------
* Chain [68] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [67] with precondition: [H>=0,I>=0,P1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [66] with precondition: [P1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f17(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,E3): inf 
Asymptotic class: infinity 
* Total analysis performed in 2508 ms.

