/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  
WARNING: Excluded non-linear constraints:[K=C+I*J]
WARNING: Excluded non-linear constraints:[C>=F*G,F*G+F>=C+1,C>=G*H,G*H+H>=C+1]
WARNING: Excluded non-linear constraints:[P>=Q*R,Q*R+Q>=P+1,P>=R*T,R*T+T>=P+1]
WARNING: Excluded non-linear constraints:[V=U*U,W=E+U*U]
WARNING: Excluded non-linear constraints:[V=U*U,W=E+U*U]

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

#### Computed strongly connected components 
0. recursive  : [f9/16]
1. recursive  : [f26/4]
2. recursive  : [f32/20]
3. recursive  : [f55/8]
4. recursive  : [f62/6]
5. recursive  : [f52/12,f55_loop_cont/13,f62_loop_cont/13]
6. recursive  : [f26_loop_cont/37,f32_loop_cont/37,f5/36,f52_loop_cont/37,f9_loop_cont/37]
7. non_recursive  : [exit_location/1]
8. non_recursive  : [f1/19]
9. non_recursive  : [f5_loop_cont/20]
10. non_recursive  : [f2/19]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f9/16
1. SCC is partially evaluated into f26/4
2. SCC is partially evaluated into f32/20
3. SCC is partially evaluated into f55/8
4. SCC is partially evaluated into f62/6
5. SCC is partially evaluated into f52/12
6. SCC is partially evaluated into f5/36
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into f5_loop_cont/20
10. SCC is partially evaluated into f2/19

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

### Specialization of cost equations f9/16 
* CE 16 is refined into CE [38] 
* CE 15 is discarded (unfeasible) 
* CE 17 is refined into CE [39] 
* CE 14 is refined into CE [40] 
* CE 13 is refined into CE [41] 
* CE 12 is refined into CE [42] 


### Cost equations --> "Loop" of f9/16 
* CEs [41] --> Loop 34 
* CEs [42] --> Loop 35 
* CEs [38] --> Loop 36 
* CEs [39] --> Loop 37 
* CEs [40] --> Loop 38 

### Ranking functions of CR f9(A,B,C,D,E,F,G,R,W,X,Y,Z,A1,B1,C1,D1) 
* RF of phase [34,35]: [A-D+1]

#### Partial ranking functions of CR f9(A,B,C,D,E,F,G,R,W,X,Y,Z,A1,B1,C1,D1) 
* Partial RF of phase [34,35]:
  - RF of loop [34:1,35:1]:
    A-D+1


### Specialization of cost equations f26/4 
* CE 19 is refined into CE [43] 
* CE 20 is refined into CE [44] 
* CE 18 is refined into CE [45] 


### Cost equations --> "Loop" of f26/4 
* CEs [45] --> Loop 39 
* CEs [43] --> Loop 40 
* CEs [44] --> Loop 41 

### Ranking functions of CR f26(A,D,W,X) 
* RF of phase [39]: [A-D+1]

#### Partial ranking functions of CR f26(A,D,W,X) 
* Partial RF of phase [39]:
  - RF of loop [39:1]:
    A-D+1


### Specialization of cost equations f32/20 
* CE 26 is refined into CE [46] 
* CE 24 is refined into CE [47] 
* CE 25 is refined into CE [48] 
* CE 23 is refined into CE [49] 
* CE 22 is refined into CE [50] 
* CE 21 is refined into CE [51] 


### Cost equations --> "Loop" of f32/20 
* CEs [49] --> Loop 42 
* CEs [50] --> Loop 43 
* CEs [51] --> Loop 44 
* CEs [46] --> Loop 45 
* CEs [47] --> Loop 46 
* CEs [48] --> Loop 47 

### Ranking functions of CR f32(A,D,H,I,J,M,N,O,P,Q,W,X,Y,Z,A1,B1,C1,D1,E1,F1) 
* RF of phase [42,43,44]: [A-D+1]

#### Partial ranking functions of CR f32(A,D,H,I,J,M,N,O,P,Q,W,X,Y,Z,A1,B1,C1,D1,E1,F1) 
* Partial RF of phase [42,43,44]:
  - RF of loop [42:1,43:1,44:1]:
    A-D+1


### Specialization of cost equations f55/8 
* CE 33 is refined into CE [52] 
* CE 34 is refined into CE [53] 
* CE 32 is refined into CE [54] 


### Cost equations --> "Loop" of f55/8 
* CEs [54] --> Loop 48 
* CEs [52] --> Loop 49 
* CEs [53] --> Loop 50 

### Ranking functions of CR f55(A,D,J,L,W,X,Y,Z) 
* RF of phase [48]: [A-D+1]

#### Partial ranking functions of CR f55(A,D,J,L,W,X,Y,Z) 
* Partial RF of phase [48]:
  - RF of loop [48:1]:
    A-D+1


### Specialization of cost equations f62/6 
* CE 37 is refined into CE [55] 
* CE 36 is refined into CE [56] 
* CE 35 is refined into CE [57] 


### Cost equations --> "Loop" of f62/6 
* CEs [57] --> Loop 51 
* CEs [55] --> Loop 52 
* CEs [56] --> Loop 53 

### Ranking functions of CR f62(A,D,K,W,X,Y) 
* RF of phase [51]: [A-D+1]

#### Partial ranking functions of CR f62(A,D,K,W,X,Y) 
* Partial RF of phase [51]:
  - RF of loop [51:1]:
    A-D+1


### Specialization of cost equations f52/12 
* CE 30 is refined into CE [58] 
* CE 27 is refined into CE [59,60] 
* CE 29 is refined into CE [61,62] 
* CE 31 is refined into CE [63] 
* CE 28 is refined into CE [64,65] 


### Cost equations --> "Loop" of f52/12 
* CEs [64] --> Loop 54 
* CEs [65] --> Loop 55 
* CEs [58] --> Loop 56 
* CEs [59] --> Loop 57 
* CEs [60,62] --> Loop 58 
* CEs [61] --> Loop 59 
* CEs [63] --> Loop 60 

### Ranking functions of CR f52(A,B,D,J,K,L,W,X,Y,Z,A1,B1) 
* RF of phase [54]: [A-K+1,D-K]

#### Partial ranking functions of CR f52(A,B,D,J,K,L,W,X,Y,Z,A1,B1) 
* Partial RF of phase [54]:
  - RF of loop [54:1]:
    A-K+1
    D-K


### Specialization of cost equations f5/36 
* CE 8 is refined into CE [66] 
* CE 2 is refined into CE [67,68] 
* CE 4 is refined into CE [69] 
* CE 5 is refined into CE [70,71,72,73,74,75,76,77] 
* CE 7 is refined into CE [78] 
* CE 9 is refined into CE [79] 
* CE 6 is refined into CE [80,81,82,83] 
* CE 3 is refined into CE [84,85] 


### Cost equations --> "Loop" of f5/36 
* CEs [82] --> Loop 61 
* CEs [80] --> Loop 62 
* CEs [83] --> Loop 63 
* CEs [81] --> Loop 64 
* CEs [85] --> Loop 65 
* CEs [84] --> Loop 66 
* CEs [66] --> Loop 67 
* CEs [72,76] --> Loop 68 
* CEs [71,73,75,77] --> Loop 69 
* CEs [68,69,70,74,78] --> Loop 70 
* CEs [67] --> Loop 71 
* CEs [79] --> Loop 72 

### Ranking functions of CR f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1) 
* RF of phase [65]: [A-B,-B+D-1]

#### Partial ranking functions of CR f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1) 
* Partial RF of phase [65]:
  - RF of loop [65:1]:
    A-B
    -B+D-1


### Specialization of cost equations f5_loop_cont/20 
* CE 10 is refined into CE [86] 
* CE 11 is refined into CE [87] 


### Cost equations --> "Loop" of f5_loop_cont/20 
* CEs [86] --> Loop 73 
* CEs [87] --> Loop 74 

### Ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 

#### Partial ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) 


### Specialization of cost equations f2/19 
* CE 1 is refined into CE [88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113] 


### Cost equations --> "Loop" of f2/19 
* CEs [101] --> Loop 75 
* CEs [100] --> Loop 76 
* CEs [99,104,105] --> Loop 77 
* CEs [98,103] --> Loop 78 
* CEs [97] --> Loop 79 
* CEs [96] --> Loop 80 
* CEs [95] --> Loop 81 
* CEs [94] --> Loop 82 
* CEs [93] --> Loop 83 
* CEs [92,106,107] --> Loop 84 
* CEs [91] --> Loop 85 
* CEs [90] --> Loop 86 
* CEs [89,108] --> Loop 87 
* CEs [113] --> Loop 88 
* CEs [88] --> Loop 89 
* CEs [109,110] --> Loop 90 
* CEs [102] --> Loop 91 
* CEs [111,112] --> Loop 92 

### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W) 

#### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W) 


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

#### Cost of chains of f9(A,B,C,D,E,F,G,R,W,X,Y,Z,A1,B1,C1,D1):
* Chain [[34,35],38]: 2*it(34)+0
  Such that:aux(3) =< -D+Z
it(34) =< aux(3)

  with precondition: [C=0,W=5,Y=0,A1=0,D1=0,B+1=X,A+1=Z,B1=C1,0>=B1,A>=2,A>=B+1,A>=D] 

* Chain [[34,35],37]: 2*it(34)+0
  Such that:aux(4) =< A-D+1
it(34) =< aux(4)

  with precondition: [W=3,A>=2,C>=0,A>=B+1,A>=D] 

* Chain [[34,35],36]: 2*it(34)+0
  Such that:aux(5) =< -D+Z
it(34) =< aux(5)

  with precondition: [W=7,B=X,A+1=Z,B1=C1,R=D1,A>=2,C>=0,Y>=1,A>=B+1,A1>=C,A>=D,Y>=A1,Y>=B1,A+C+Y>=D+A1+1] 

* Chain [38]: 0
  with precondition: [C=0,W=5,Y=0,D1=0,A1=E,B1=F,C1=G,B+1=X,D=Z,A>=2,D>=A+1,A>=B+1] 

* Chain [37]: 0
  with precondition: [W=3,A>=2,C>=0,A>=B+1] 


#### Cost of chains of f26(A,D,W,X):
* Chain [[39],41]: 1*it(39)+0
  Such that:it(39) =< A-D+1

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

* Chain [[39],40]: 1*it(39)+0
  Such that:it(39) =< -D+X

  with precondition: [W=6,A+1=X,A>=2,A>=D] 

* Chain [41]: 0
  with precondition: [W=3,A>=2] 

* Chain [40]: 0
  with precondition: [W=6,D=X,A>=2,D>=A+1] 


#### Cost of chains of f32(A,D,H,I,J,M,N,O,P,Q,W,X,Y,Z,A1,B1,C1,D1,E1,F1):
* Chain [[42,43,44],47]: 3*it(42)+0
  Such that:aux(8) =< -D+X
it(42) =< aux(8)

  with precondition: [W=2,A+1=X,M=B1,N=C1,D1+F1=0,A>=2,A>=D] 

* Chain [[42,43,44],46]: 3*it(42)+0
  Such that:aux(9) =< -D+X
it(42) =< aux(9)

  with precondition: [W=2,A+1=X,C1=D1,P=E1,Q=F1,A>=2,A>=D] 

* Chain [[42,43,44],45]: 3*it(42)+0
  Such that:aux(10) =< A-D+1
it(42) =< aux(10)

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

* Chain [47]: 0
  with precondition: [W=2,Y=H,Z=I,A1=J,B1=M,C1=N,D=X,D1+F1=0,A>=2,D>=A+1] 

* Chain [46]: 0
  with precondition: [W=2,Y=H,Z=I,A1=J,E1=P,F1=Q,D=X,D1=C1,A>=2,D>=A+1] 

* Chain [45]: 0
  with precondition: [W=3,A>=2] 


#### Cost of chains of f55(A,D,J,L,W,X,Y,Z):
* Chain [[48],50]: 1*it(48)+0
  Such that:it(48) =< A-D+1

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

* Chain [[48],49]: 1*it(48)+0
  Such that:it(48) =< -D+X

  with precondition: [W=4,A+1=X,A>=2,A>=D] 

* Chain [50]: 0
  with precondition: [W=3,A>=2] 

* Chain [49]: 0
  with precondition: [W=4,Y=J,D=X,A>=2,D>=A+1] 


#### Cost of chains of f62(A,D,K,W,X,Y):
* Chain [[51],53]: 1*it(51)+0
  Such that:it(51) =< -D+X

  with precondition: [W=2,A+1=X,K+1=Y,A>=2,A>=D,A>=K] 

* Chain [[51],52]: 1*it(51)+0
  Such that:it(51) =< A-D+1

  with precondition: [W=3,A>=2,A>=D,A>=K] 

* Chain [53]: 0
  with precondition: [W=2,D=X,K+1=Y,A>=2,D>=A+1,A>=K] 

* Chain [52]: 0
  with precondition: [W=3,A>=2,A>=K] 


#### Cost of chains of f52(A,B,D,J,K,L,W,X,Y,Z,A1,B1):
* Chain [[54],60]: 1*it(54)+0
  Such that:it(54) =< A-K+1

  with precondition: [W=3,A>=2,D>=A+1,A>=K] 

* Chain [[54],59]: 1*it(54)+0
  Such that:it(54) =< A-K

  with precondition: [W=3,A>=2,D>=A+1,A>=K+1] 

* Chain [[54],57]: 1*it(54)+0
  Such that:it(54) =< A-K

  with precondition: [W=3,A>=2,D>=A+1,A>=K+1] 

* Chain [[54],56]: 1*it(54)+0
  Such that:it(54) =< A-K+1

  with precondition: [W=5,B+1=X,D=Y,J=Z,A+1=A1,A>=2,D>=A+1,A>=K] 

* Chain [60]: 0
  with precondition: [W=3,A>=2] 

* Chain [59]: 0
  with precondition: [W=3,A>=2,D>=A+1,A>=K] 

* Chain [58]: 2*s(1)+0
  Such that:aux(11) =< A-D+1
s(1) =< aux(11)

  with precondition: [W=3,A>=2,A>=D,A>=K] 

* Chain [57]: 0
  with precondition: [W=3,A>=2,A>=K] 

* Chain [56]: 0
  with precondition: [W=5,X=B+1,Y=D,Z=J,B1=L,K=A1,A>=2,K>=A+1] 

* Chain [55,[54],60]: 1*it(54)+1*s(3)+1
  Such that:s(3) =< A-D+1
it(54) =< A-K

  with precondition: [W=3,A>=2,A>=D,A>=K+1] 

* Chain [55,[54],59]: 1*it(54)+1*s(3)+1
  Such that:s(3) =< A-D+1
it(54) =< A-K

  with precondition: [W=3,A>=2,A>=D,A>=K+2] 

* Chain [55,[54],57]: 1*it(54)+1*s(3)+1
  Such that:s(3) =< A-D+1
it(54) =< A-K

  with precondition: [W=3,A>=2,A>=D,A>=K+2] 

* Chain [55,[54],56]: 1*it(54)+1*s(3)+1
  Such that:s(3) =< -D+A1
it(54) =< -K+A1

  with precondition: [W=5,B+1=X,A+1=Y,A+1=A1,A>=2,A>=D,A>=K+1] 

* Chain [55,60]: 1*s(3)+1
  Such that:s(3) =< A-D+1

  with precondition: [W=3,A>=2,A>=D,A>=K] 

* Chain [55,59]: 1*s(3)+1
  Such that:s(3) =< A-D+1

  with precondition: [W=3,A>=2,A>=D,A>=K+1] 

* Chain [55,57]: 1*s(3)+1
  Such that:s(3) =< A-D+1

  with precondition: [W=3,A>=2,A>=D,A>=K+1] 

* Chain [55,56]: 1*s(3)+1
  Such that:s(3) =< A-D+1

  with precondition: [W=5,A=K,B+1=X,A+1=Y,A+1=A1,A>=2,A>=D] 


#### Cost of chains of f5(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1):
* Chain [[65],72]: 1*it(65)+0
  Such that:it(65) =< A-B

  with precondition: [W=3,A>=2,D>=A+1,A>=B+1] 

* Chain [[65],71]: 1*it(65)+0
  Such that:it(65) =< A-B

  with precondition: [W=3,A>=2,D>=A+1,A>=B+2] 

* Chain [[65],67]: 1*it(65)+0
  Such that:it(65) =< A-B

  with precondition: [W=8,Y=0,N1=0,A=X,D=Z,E=A1,F=B1,G=C1,H=D1,I=E1,J=F1,K=G1,L=H1,M=I1,N=J1,O=K1,P=L1,Q=M1,A>=2,D>=A+1,A>=B+1] 

* Chain [72]: 0
  with precondition: [W=3,A>=2] 

* Chain [71]: 0
  with precondition: [W=3,A>=2,A>=B+1] 

* Chain [70]: 10*s(19)+0
  Such that:aux(17) =< A-D+1
s(19) =< aux(17)

  with precondition: [W=3,A>=2,A>=B+1,A>=D] 

* Chain [69]: 8*s(29)+2*s(30)+0
  Such that:aux(18) =< A-D+1
aux(19) =< A-K+1
s(30) =< aux(19)
s(29) =< aux(18)

  with precondition: [W=3,A>=2,A>=B+1,A>=D,A>=K] 

* Chain [68]: 4*s(39)+4*s(41)+0
  Such that:aux(20) =< A-D+1
aux(21) =< A-K
s(41) =< aux(21)
s(39) =< aux(20)

  with precondition: [W=3,A>=2,A>=B+1,A>=D,A>=K+1] 

* Chain [67]: 0
  with precondition: [W=8,Y=C,Z=D,A1=E,B1=F,C1=G,D1=H,E1=I,F1=J,G1=K,H1=L,I1=M,J1=N,K1=O,L1=P,M1=Q,N1=R,B=X,A>=2,B>=A] 

* Chain [66,[65],72]: 1*it(65)+2*s(47)+1
  Such that:it(65) =< A-B
s(46) =< A-D+1
s(47) =< s(46)

  with precondition: [W=3,A>=2,A>=B+2,A>=D] 

* Chain [66,[65],71]: 1*it(65)+2*s(47)+1
  Such that:it(65) =< A-B
s(46) =< A-D+1
s(47) =< s(46)

  with precondition: [W=3,A>=2,A>=B+3,A>=D] 

* Chain [66,[65],67]: 1*it(65)+2*s(47)+1
  Such that:it(65) =< -B+X
s(46) =< -D+X+1
s(47) =< s(46)

  with precondition: [W=8,Y=0,A1=0,N1=0,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,M=I1,N=J1,O=K1,P=L1,Q=M1,0>=B1,A>=2,A>=B+2,A>=D] 

* Chain [66,72]: 2*s(47)+1
  Such that:s(46) =< A-D+1
s(47) =< s(46)

  with precondition: [W=3,A>=2,A>=B+1,A>=D] 

* Chain [66,71]: 2*s(47)+1
  Such that:s(46) =< A-D+1
s(47) =< s(46)

  with precondition: [W=3,A>=2,A>=B+2,A>=D] 

* Chain [66,67]: 2*s(47)+1
  Such that:s(46) =< A-D+1
s(47) =< s(46)

  with precondition: [W=8,Y=0,A1=0,N1=0,A=B+1,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,M=I1,N=J1,O=K1,P=L1,Q=M1,0>=B1,A>=2,A>=D] 

* Chain [64,[65],72]: 1*it(65)+2*s(49)+1*s(50)+1
  Such that:it(65) =< A-B
s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=3,A>=2,A>=B+2,A>=D,A>=K] 

* Chain [64,[65],71]: 1*it(65)+2*s(49)+1*s(50)+1
  Such that:it(65) =< A-B
s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=3,A>=2,A>=B+3,A>=D,A>=K] 

* Chain [64,[65],67]: 1*it(65)+2*s(49)+1*s(50)+1
  Such that:it(65) =< A-B
s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=8,Y=0,N1=0,Z=A+1,Z=X+1,B1=C1,H=D1,I=E1,J=F1,Z=G1,M=I1,N=J1,K1+M1=0,Z>=3,A1>=0,Z>=B+3,Z>=D+1,Z>=K+1] 

* Chain [64,72]: 2*s(49)+1*s(50)+1
  Such that:s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=3,A>=2,A>=B+1,A>=D,A>=K] 

* Chain [64,71]: 2*s(49)+1*s(50)+1
  Such that:s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=3,A>=2,A>=B+2,A>=D,A>=K] 

* Chain [64,67]: 2*s(49)+1*s(50)+1
  Such that:s(48) =< A-D+1
s(50) =< A-K+1
s(49) =< s(48)

  with precondition: [W=8,Z=A+1,Z=B+2,Z=X+1,B1=C1,H=D1,I=E1,J=F1,Z=G1,M=I1,N=J1,R=N1,K1+M1=0,Y>=1,Z>=3,A1>=0,Z>=D+1,Z>=K+1,Y>=A1,Y>=B1,Y+Z>=D+A1+2] 

* Chain [63,[65],72]: 1*it(65)+2*s(52)+1*s(53)+1
  Such that:it(65) =< A-B
s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=3,A>=2,A>=B+2,A>=D,A>=K] 

* Chain [63,[65],71]: 1*it(65)+2*s(52)+1*s(53)+1
  Such that:it(65) =< A-B
s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=3,A>=2,A>=B+3,A>=D,A>=K] 

* Chain [63,[65],67]: 1*it(65)+2*s(52)+1*s(53)+1
  Such that:it(65) =< A-B
s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=8,Y=0,N1=0,Z=A+1,Z=X+1,B1=C1,H=D1,I=E1,J=F1,Z=G1,J1=K1,P=L1,Q=M1,Z>=3,A1>=0,Z>=B+3,Z>=D+1,Z>=K+1] 

* Chain [63,72]: 2*s(52)+1*s(53)+1
  Such that:s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=3,A>=2,A>=B+1,A>=D,A>=K] 

* Chain [63,71]: 2*s(52)+1*s(53)+1
  Such that:s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=3,A>=2,A>=B+2,A>=D,A>=K] 

* Chain [63,67]: 2*s(52)+1*s(53)+1
  Such that:s(51) =< A-D+1
s(53) =< A-K+1
s(52) =< s(51)

  with precondition: [W=8,Z=A+1,Z=B+2,Z=X+1,B1=C1,H=D1,I=E1,J=F1,Z=G1,J1=K1,P=L1,Q=M1,R=N1,Y>=1,Z>=3,A1>=0,Z>=D+1,Z>=K+1,Y>=A1,Y>=B1,Y+Z>=D+A1+2] 

* Chain [62,[65],72]: 1*it(65)+2*s(55)+1
  Such that:it(65) =< A-B
s(54) =< A-D+1
s(55) =< s(54)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+2,A>=D] 

* Chain [62,[65],71]: 1*it(65)+2*s(55)+1
  Such that:it(65) =< A-B
s(54) =< A-D+1
s(55) =< s(54)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+3,A>=D] 

* Chain [62,[65],67]: 1*it(65)+2*s(55)+1
  Such that:it(65) =< -B+X
s(54) =< -D+X+1
s(55) =< s(54)

  with precondition: [W=8,Y=0,N1=0,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,M=I1,N=J1,K1+M1=0,A>=2,A1>=0,K>=A+1,A>=B+2,A>=D] 

* Chain [62,72]: 2*s(55)+1
  Such that:s(54) =< A-D+1
s(55) =< s(54)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+1,A>=D] 

* Chain [62,71]: 2*s(55)+1
  Such that:s(54) =< A-D+1
s(55) =< s(54)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+2,A>=D] 

* Chain [62,67]: 2*s(55)+1
  Such that:s(54) =< -D+X+1
s(55) =< s(54)

  with precondition: [W=8,A=B+1,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,M=I1,N=J1,R=N1,K1+M1=0,A>=2,Y>=1,A1>=0,K>=A+1,A>=D,Y>=A1,Y>=B1,A+Y>=D+A1+1] 

* Chain [61,[65],72]: 1*it(65)+2*s(57)+1
  Such that:it(65) =< A-B
s(56) =< A-D+1
s(57) =< s(56)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+2,A>=D] 

* Chain [61,[65],71]: 1*it(65)+2*s(57)+1
  Such that:it(65) =< A-B
s(56) =< A-D+1
s(57) =< s(56)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+3,A>=D] 

* Chain [61,[65],67]: 1*it(65)+2*s(57)+1
  Such that:it(65) =< -B+X
s(56) =< -D+X+1
s(57) =< s(56)

  with precondition: [W=8,Y=0,N1=0,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,J1=K1,P=L1,Q=M1,A>=2,A1>=0,K>=A+1,A>=B+2,A>=D] 

* Chain [61,72]: 2*s(57)+1
  Such that:s(56) =< A-D+1
s(57) =< s(56)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+1,A>=D] 

* Chain [61,71]: 2*s(57)+1
  Such that:s(56) =< A-D+1
s(57) =< s(56)

  with precondition: [W=3,A>=2,K>=A+1,A>=B+2,A>=D] 

* Chain [61,67]: 2*s(57)+1
  Such that:s(56) =< -D+X+1
s(57) =< s(56)

  with precondition: [W=8,A=B+1,A=X,A+1=Z,B1=C1,H=D1,I=E1,J=F1,K=G1,L=H1,J1=K1,P=L1,Q=M1,R=N1,A>=2,Y>=1,A1>=0,K>=A+1,A>=D,Y>=A1,Y>=B1,A+Y>=D+A1+1] 


#### Cost of chains of f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T):
* Chain [74]: 0
  with precondition: [A=3,B>=2] 

* Chain [73]: 0
  with precondition: [A=8,B>=2] 


#### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W):
* Chain [92]: 4*s(120)+1
  Such that:aux(37) =< B-D+2
s(120) =< aux(37)

  with precondition: [A=B+1,A>=2,K>=A+1,A>=D] 

* Chain [91]: 2*s(124)+1
  Such that:s(123) =< B-D+2
s(124) =< s(123)

  with precondition: [A=B+1,A>=2,A>=D] 

* Chain [90]: 2*s(126)+4*s(127)+1
  Such that:aux(38) =< B-D+2
aux(39) =< B-K+2
s(126) =< aux(39)
s(127) =< aux(38)

  with precondition: [A=B+1,A>=2,A>=D,A>=K] 

* Chain [89]: 0
  with precondition: [A>=2] 

* Chain [88]: 0
  with precondition: [A>=2,B>=A] 

* Chain [87]: 2*s(131)+0
  Such that:aux(40) =< A-B
s(131) =< aux(40)

  with precondition: [A>=2,D>=A+1,A>=B+1] 

* Chain [86]: 1*s(133)+0
  Such that:s(133) =< A-B

  with precondition: [A>=2,D>=A+1,A>=B+2] 

* Chain [85]: 4*s(135)+1
  Such that:s(134) =< A-D+1
s(135) =< s(134)

  with precondition: [A>=2,K>=A+1,A>=B+1,A>=D] 

* Chain [84]: 4*s(138)+12*s(139)+1
  Such that:aux(41) =< A-B
aux(42) =< A-D+1
s(138) =< aux(41)
s(139) =< aux(42)

  with precondition: [A>=2,K>=A+1,A>=B+2,A>=D] 

* Chain [83]: 2*s(148)+4*s(149)+1
  Such that:s(146) =< A-B
s(147) =< A-D+1
s(148) =< s(146)
s(149) =< s(147)

  with precondition: [A>=2,K>=A+1,A>=B+3,A>=D] 

* Chain [82]: 0
  with precondition: [A>=2,A>=B+1] 

* Chain [81]: 12*s(151)+1
  Such that:s(150) =< A-D+1
s(151) =< s(150)

  with precondition: [A>=2,A>=B+1,A>=D] 

* Chain [80]: 4*s(154)+12*s(155)+1
  Such that:s(152) =< A-D+1
s(153) =< A-K+1
s(154) =< s(153)
s(155) =< s(152)

  with precondition: [A>=2,A>=B+1,A>=D,A>=K] 

* Chain [79]: 4*s(158)+4*s(159)+0
  Such that:s(156) =< A-D+1
s(157) =< A-K
s(158) =< s(157)
s(159) =< s(156)

  with precondition: [A>=2,A>=B+1,A>=D,A>=K+1] 

* Chain [78]: 2*s(160)+6*s(162)+1
  Such that:aux(43) =< A-B
aux(44) =< A-D+1
s(160) =< aux(43)
s(162) =< aux(44)

  with precondition: [A>=2,A>=B+2,A>=D] 

* Chain [77]: 4*s(169)+6*s(170)+12*s(171)+1
  Such that:aux(45) =< A-B
aux(46) =< A-D+1
aux(47) =< A-K+1
s(169) =< aux(45)
s(170) =< aux(47)
s(171) =< aux(46)

  with precondition: [A>=2,A>=B+2,A>=D,A>=K] 

* Chain [76]: 1*s(180)+2*s(182)+1
  Such that:s(180) =< A-B
s(181) =< A-D+1
s(182) =< s(181)

  with precondition: [A>=2,A>=B+3,A>=D] 

* Chain [75]: 2*s(186)+2*s(187)+4*s(188)+1
  Such that:s(183) =< A-B
s(184) =< A-D+1
s(185) =< A-K+1
s(186) =< s(183)
s(187) =< s(185)
s(188) =< s(184)

  with precondition: [A>=2,A>=B+3,A>=D,A>=K] 


Closed-form bounds of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W): 
-------------------------------------
* Chain [92] with precondition: [A=B+1,A>=2,K>=A+1,A>=D] 
    - Upper bound: 4*B-4*D+9 
    - Complexity: n 
* Chain [91] with precondition: [A=B+1,A>=2,A>=D] 
    - Upper bound: 2*B-2*D+5 
    - Complexity: n 
* Chain [90] with precondition: [A=B+1,A>=2,A>=D,A>=K] 
    - Upper bound: 6*B-4*D-2*K+13 
    - Complexity: n 
* Chain [89] with precondition: [A>=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [88] with precondition: [A>=2,B>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [87] with precondition: [A>=2,D>=A+1,A>=B+1] 
    - Upper bound: 2*A-2*B 
    - Complexity: n 
* Chain [86] with precondition: [A>=2,D>=A+1,A>=B+2] 
    - Upper bound: A-B 
    - Complexity: n 
* Chain [85] with precondition: [A>=2,K>=A+1,A>=B+1,A>=D] 
    - Upper bound: 4*A-4*D+5 
    - Complexity: n 
* Chain [84] with precondition: [A>=2,K>=A+1,A>=B+2,A>=D] 
    - Upper bound: 16*A-4*B-12*D+13 
    - Complexity: n 
* Chain [83] with precondition: [A>=2,K>=A+1,A>=B+3,A>=D] 
    - Upper bound: 6*A-2*B-4*D+5 
    - Complexity: n 
* Chain [82] with precondition: [A>=2,A>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [81] with precondition: [A>=2,A>=B+1,A>=D] 
    - Upper bound: 12*A-12*D+13 
    - Complexity: n 
* Chain [80] with precondition: [A>=2,A>=B+1,A>=D,A>=K] 
    - Upper bound: 16*A-12*D-4*K+17 
    - Complexity: n 
* Chain [79] with precondition: [A>=2,A>=B+1,A>=D,A>=K+1] 
    - Upper bound: 8*A-4*D-4*K+4 
    - Complexity: n 
* Chain [78] with precondition: [A>=2,A>=B+2,A>=D] 
    - Upper bound: 8*A-2*B-6*D+7 
    - Complexity: n 
* Chain [77] with precondition: [A>=2,A>=B+2,A>=D,A>=K] 
    - Upper bound: 22*A-4*B-12*D-6*K+19 
    - Complexity: n 
* Chain [76] with precondition: [A>=2,A>=B+3,A>=D] 
    - Upper bound: 3*A-B-2*D+3 
    - Complexity: n 
* Chain [75] with precondition: [A>=2,A>=B+3,A>=D,A>=K] 
    - Upper bound: 8*A-2*B-4*D-2*K+7 
    - Complexity: n 

### Maximum cost of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,W): max([max([nat(A-B)*2,nat(B-K+2)*2+nat(B-D+2)*2+(nat(B-D+2)*2+1)]),nat(A-D+1)*2+max([nat(A-B)+1,nat(A-D+1)*2+max([max([max([1,nat(A-K)*4]),nat(A-B)*2+1+nat(A-K+1)*2]),nat(A-D+1)*2+1+max([nat(A-B)*2,nat(A-D+1)*6+max([nat(A-B)*4,nat(A-B)*4+nat(A-K+1)*2+nat(A-K+1)*4])])])])]) 
Asymptotic class: n 
* Total analysis performed in 3934 ms.