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


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MAYBE

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

#### Computed strongly connected components 
0. non_recursive  : [f1/60]
1. recursive  : [f16/43]
2. non_recursive  : [exit_location/1]
3. recursive  : [f14/48]
4. recursive  : [f7/28]
5. non_recursive  : [f7_loop_cont/61]
6. non_recursive  : [f14_loop_cont/61]
7. non_recursive  : [f16_loop_cont/61]
8. non_recursive  : [f0/60]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into f16/43
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f14/48
4. SCC is partially evaluated into f7/28
5. SCC is partially evaluated into f7_loop_cont/61
6. SCC is partially evaluated into f14_loop_cont/61
7. SCC is partially evaluated into f16_loop_cont/61
8. SCC is partially evaluated into f0/60

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

### Specialization of cost equations f16/43 
* CE 8 is refined into CE [24] 
* CE 7 is refined into CE [25] 
* CE 6 is refined into CE [26] 
* CE 5 is refined into CE [27] 
* CE 4 is refined into CE [28] 
* CE 3 is refined into CE [29] 


### Cost equations --> "Loop" of f16/43 
* CEs [29] --> Loop 24 
* CEs [24] --> Loop 25 
* CEs [25] --> Loop 26 
* CEs [26] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [28] --> Loop 29 

### Ranking functions of CR f16(A,B,C,D,E,F,G,H,I,K,L,M,N,O,R,S,T,O1,U1,W1,X1,Y1,Z1,A2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3) 
* RF of phase [24]: [A-B,-B+L]

#### Partial ranking functions of CR f16(A,B,C,D,E,F,G,H,I,K,L,M,N,O,R,S,T,O1,U1,W1,X1,Y1,Z1,A2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3) 
* Partial RF of phase [24]:
  - RF of loop [24:1]:
    A-B
    -B+L


### Specialization of cost equations f14/48 
* CE 15 is refined into CE [30] 
* CE 13 is refined into CE [31] 
* CE 14 is refined into CE [32] 
* CE 12 is refined into CE [33] 
* CE 11 is refined into CE [34] 


### Cost equations --> "Loop" of f14/48 
* CEs [33] --> Loop 30 
* CEs [34] --> Loop 31 
* CEs [30] --> Loop 32 
* CEs [31] --> Loop 33 
* CEs [32] --> Loop 34 

### Ranking functions of CR f14(I,K,L,M,N,O,S,T,U,X,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,W1,B2,E2,F2,G2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3) 
* RF of phase [30,31]: [T+1]

#### Partial ranking functions of CR f14(I,K,L,M,N,O,S,T,U,X,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,W1,B2,E2,F2,G2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3) 
* Partial RF of phase [30,31]:
  - RF of loop [30:1,31:1]:
    T+1


### Specialization of cost equations f7/28 
* CE 21 is refined into CE [35] 
* CE 20 is refined into CE [36] 
* CE 19 is refined into CE [37] 
* CE 18 is refined into CE [38] 


### Cost equations --> "Loop" of f7/28 
* CEs [37] --> Loop 35 
* CEs [38] --> Loop 36 
* CEs [35] --> Loop 37 
* CEs [36] --> Loop 38 

### Ranking functions of CR f7(I,L,U,G1,I1,J1,K1,L1,M1,N1,O1,Q1,R1,S1,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3) 
* RF of phase [35,36]: [Q1+1]

#### Partial ranking functions of CR f7(I,L,U,G1,I1,J1,K1,L1,M1,N1,O1,Q1,R1,S1,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3) 
* Partial RF of phase [35,36]:
  - RF of loop [35:1,36:1]:
    Q1+1


### Specialization of cost equations f7_loop_cont/61 
* CE 23 is refined into CE [39] 
* CE 22 is refined into CE [40] 


### Cost equations --> "Loop" of f7_loop_cont/61 
* CEs [39] --> Loop 39 
* CEs [40] --> Loop 40 

### Ranking functions of CR f7_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 

#### Partial ranking functions of CR f7_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 


### Specialization of cost equations f14_loop_cont/61 
* CE 17 is refined into CE [41,42,43,44] 
* CE 16 is refined into CE [45] 


### Cost equations --> "Loop" of f14_loop_cont/61 
* CEs [44] --> Loop 41 
* CEs [43] --> Loop 42 
* CEs [42] --> Loop 43 
* CEs [41] --> Loop 44 
* CEs [45] --> Loop 45 

### Ranking functions of CR f14_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 

#### Partial ranking functions of CR f14_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 


### Specialization of cost equations f16_loop_cont/61 
* CE 10 is refined into CE [46,47,48,49,50,51,52,53,54,55] 
* CE 9 is refined into CE [56] 


### Cost equations --> "Loop" of f16_loop_cont/61 
* CEs [55] --> Loop 46 
* CEs [54] --> Loop 47 
* CEs [51] --> Loop 48 
* CEs [53] --> Loop 49 
* CEs [52] --> Loop 50 
* CEs [50] --> Loop 51 
* CEs [49] --> Loop 52 
* CEs [48] --> Loop 53 
* CEs [47] --> Loop 54 
* CEs [46] --> Loop 55 
* CEs [56] --> Loop 56 

### Ranking functions of CR f16_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 

#### Partial ranking functions of CR f16_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2) 


### Specialization of cost equations f0/60 
* CE 1 is refined into CE [57] 
* CE 2 is refined into CE [58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139] 


### Cost equations --> "Loop" of f0/60 
* CEs [92,95,132,135] --> Loop 57 
* CEs [97,137] --> Loop 58 
* CEs [96,136] --> Loop 59 
* CEs [87,127] --> Loop 60 
* CEs [86,126] --> Loop 61 
* CEs [82,85,122,125] --> Loop 62 
* CEs [94,134] --> Loop 63 
* CEs [93,133] --> Loop 64 
* CEs [84,124] --> Loop 65 
* CEs [83,123] --> Loop 66 
* CEs [72,75,112,115] --> Loop 67 
* CEs [77,117] --> Loop 68 
* CEs [76,116] --> Loop 69 
* CEs [67,107] --> Loop 70 
* CEs [66,106] --> Loop 71 
* CEs [62,65,102,105] --> Loop 72 
* CEs [74,114] --> Loop 73 
* CEs [73,113] --> Loop 74 
* CEs [64,104] --> Loop 75 
* CEs [63,103] --> Loop 76 
* CEs [91,131] --> Loop 77 
* CEs [90,130] --> Loop 78 
* CEs [80,120] --> Loop 79 
* CEs [81,121] --> Loop 80 
* CEs [89,129] --> Loop 81 
* CEs [88,128] --> Loop 82 
* CEs [78,118] --> Loop 83 
* CEs [79,119] --> Loop 84 
* CEs [71,111] --> Loop 85 
* CEs [70,110] --> Loop 86 
* CEs [60,100] --> Loop 87 
* CEs [61,101] --> Loop 88 
* CEs [69,109] --> Loop 89 
* CEs [68,108] --> Loop 90 
* CEs [58,98] --> Loop 91 
* CEs [59,99] --> Loop 92 
* CEs [57] --> Loop 93 
* CEs [138,139] --> Loop 94 

### Ranking functions of CR f0(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,Z1,A2,B2,C2,D2,E2,F2,G2,F3) 

#### Partial ranking functions of CR f0(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,Z1,A2,B2,C2,D2,E2,F2,G2,F3) 


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

#### Cost of chains of f16(A,B,C,D,E,F,G,H,I,K,L,M,N,O,R,S,T,O1,U1,W1,X1,Y1,Z1,A2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3):
* Chain [[24],29]: 1*it(24)+0
  Such that:it(24) =< A-B

  with precondition: [S=0,F3=5,S3=0,C=E,A=L,R=T,A=M3+1,I=N3,Q3=R3,0>=K+1,0>=W1+1,B>=2,P3>=2,A>=B+1,R>=P3,X3>=P3] 

* Chain [[24],28]: 1*it(24)+0
  Such that:it(24) =< A-B

  with precondition: [S=0,F3=5,S3=0,C=E,A=L,R=T,A=M3+1,I=N3,Q3=R3,0>=K+1,B>=2,W1>=1,P3>=2,A>=B+1,R>=P3,X3>=P3] 

* Chain [[24],27]: 1*it(24)+0
  Such that:it(24) =< A-B

  with precondition: [S=0,F3=5,S3=0,C=E,A=L,R=T,A=M3+1,I=N3,Q3=R3,0>=W1+1,B>=2,K>=1,P3>=2,A>=B+1,R>=P3,X3>=P3] 

* Chain [[24],26]: 1*it(24)+0
  Such that:it(24) =< A-B

  with precondition: [S=0,F3=5,S3=0,C=E,A=L,R=T,A=M3+1,I=N3,Q3=R3,B>=2,K>=1,W1>=1,P3>=2,A>=B+1,R>=P3,X3>=P3] 

* Chain [[24],25]: 1*it(24)+0
  Such that:it(24) =< A-B

  with precondition: [F3=3,C=E,A=L,B>=2,A>=B+1] 

* Chain [29]: 0
  with precondition: [S=0,F3=5,S3=0,A=B,E=C,L3=F,M3=G,N3=H,A=L,R=T,R3=Q3,0>=K+1,0>=W1+1,A>=2,P3>=2,R>=P3,X3>=P3] 

* Chain [28]: 0
  with precondition: [S=0,F3=5,S3=0,A=B,E=C,L3=F,M3=G,N3=H,A=L,R=T,R3=Q3,0>=K+1,A>=2,W1>=1,P3>=2,R>=P3,X3>=P3] 

* Chain [27]: 0
  with precondition: [S=0,F3=5,S3=0,A=B,E=C,L3=F,M3=G,N3=H,A=L,R=T,R3=Q3,0>=W1+1,A>=2,K>=1,P3>=2,R>=P3,X3>=P3] 

* Chain [26]: 0
  with precondition: [S=0,F3=5,S3=0,A=B,E=C,L3=F,M3=G,N3=H,A=L,R=T,R3=Q3,A>=2,K>=1,W1>=1,P3>=2,R>=P3,X3>=P3] 

* Chain [25]: 0
  with precondition: [F3=3,L=A,E=C,B>=2,L>=B] 


#### Cost of chains of f14(I,K,L,M,N,O,S,T,U,X,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,W1,B2,E2,F2,G2,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3,T3,U3,V3,W3,X3,Y3):
* Chain [[30,31],34]: 2*it(30)+0
  Such that:aux(2) =< -S+B2
aux(1) =< -S+B2+M3
it(30) =< aux(1)
it(30) =< aux(2)

  with precondition: [F3=4,T3=0,U3=0,B2=L3+1,I=P3,X=Q3,B2=R3+1,S+T+1=B2+M3,S+T+1=B2+S3,0>=M1+1,S>=0,H3>=2,B2>=S+2,S+T+1>=B2] 

* Chain [[30,31],33]: 2*it(30)+0
  Such that:aux(2) =< -S+B2
aux(1) =< -S+B2+M3
it(30) =< aux(1)
it(30) =< aux(2)

  with precondition: [F3=4,T3=0,U3=0,B2=L3+1,I=P3,X=Q3,B2=R3+1,S+T+1=B2+M3,S+T+1=B2+S3,S>=0,M1>=1,H3>=2,B2>=S+2,S+T+1>=B2] 

* Chain [[30,31],32]: 2*it(30)+0
  Such that:aux(3) =< T+1
it(30) =< aux(3)

  with precondition: [F3=3,S>=0,T>=0] 

* Chain [34]: 0
  with precondition: [K=0,F3=4,T3=0,U3=0,K3=O,O3=B1,P3=C1,Q3=D1,R3=E1,S3=F1,S+1=B2,S=L3,T=M3,0>=M1+1,S>=0,T>=0,H3>=2] 

* Chain [33]: 0
  with precondition: [K=0,F3=4,T3=0,U3=0,K3=O,O3=B1,P3=C1,Q3=D1,R3=E1,S3=F1,S+1=B2,S=L3,T=M3,S>=0,T>=0,M1>=1,H3>=2] 

* Chain [32]: 0
  with precondition: [F3=3] 


#### Cost of chains of f7(I,L,U,G1,I1,J1,K1,L1,M1,N1,O1,Q1,R1,S1,F3,G3,H3,I3,J3,K3,L3,M3,N3,O3,P3,Q3,R3,S3):
* Chain [[35,36],38]: 2*it(35)+0
  Such that:aux(4) =< Q1+1
aux(5) =< Q1-Q3
it(35) =< aux(4)
it(35) =< aux(5)

  with precondition: [G1=0,I1=0,N1=0,F3=2,J1=L1,J1=M1,I=R3,Q3=S3,G3>=2,Q3>=0,Q1>=Q3+1] 

* Chain [[35,36],37]: 2*it(35)+0
  Such that:aux(6) =< Q1+1
it(35) =< aux(6)

  with precondition: [I1=0,F3=3,J1=L1,J1=M1,G1=N1,Q1>=0] 

* Chain [38]: 0
  with precondition: [F3=2,H3=U,G1=I1,L1=J1,L1=M1,G1=N1,R3=R1,S3=S1,Q1=Q3,Q1>=0,G3>=2] 

* Chain [37]: 0
  with precondition: [F3=3,N1=G1,L1=J1,L1=M1] 


#### Cost of chains of f7_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2):
* Chain [40]: 0
  with precondition: [A=2,Z1=J,Z1=F2] 

* Chain [39]: 0
  with precondition: [A=3,Z1=J,Z1=F2] 


#### Cost of chains of f14_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2):
* Chain [45]: 0
  with precondition: [A=3,Z1=J,K1=H1,R1=I1,K1=M1,K1=N1,K1=O1,Z1=F2] 

* Chain [44]: 2*s(3)+0
  Such that:s(2) =< I1
s(1) =< I1+1
s(3) =< s(1)
s(3) =< s(2)

  with precondition: [A=4,H1=0,J1=0,K1=0,M1=0,N1=0,O1=0,Z1=J,R1=I1,Z1=F2,R1>=1] 

* Chain [43]: 2*s(5)+0
  Such that:s(4) =< R1+1
s(5) =< s(4)

  with precondition: [A=4,J1=0,Z1=J,K1=H1,R1=I1,K1=M1,K1=N1,K1=O1,Z1=F2,R1>=0] 

* Chain [42]: 0
  with precondition: [A=4,Z1=J,R1=I1,H1=J1,H1=K1,H1=M1,H1=N1,H1=O1,Z1=F2,R1>=0] 

* Chain [41]: 0
  with precondition: [A=4,Z1=J,K1=H1,R1=I1,K1=M1,K1=N1,K1=O1,Z1=F2] 


#### Cost of chains of f16_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,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2):
* Chain [56]: 0
  with precondition: [A=3,Z1=J,Y=O,U=S] 

* Chain [55]: 2*s(7)+0
  Such that:s(6) =< R1+1
s(7) =< s(6)

  with precondition: [A=5,L=0,Z1=J,Y=O,U=S,C2=T+1,0>=N1+1,U>=0,R1>=0,C2>=1] 

* Chain [54]: 0
  with precondition: [A=5,L=0,Z1=J,Y=O,U=S,C2=T+1,0>=N1+1,U>=0,C2>=1] 

* Chain [53]: 2*s(9)+0
  Such that:s(8) =< R1+1
s(9) =< s(8)

  with precondition: [A=5,L=0,Z1=J,Y=O,U=S,C2=T+1,U>=0,N1>=1,R1>=0,C2>=1] 

* Chain [52]: 0
  with precondition: [A=5,L=0,Z1=J,Y=O,U=S,C2=T+1,U>=0,N1>=1,C2>=1] 

* Chain [51]: 0
  with precondition: [A=5,Z1=J,Y=O,U=S] 

* Chain [50]: 2*s(12)+2*s(14)+0
  Such that:s(10) =< -T+C2
s(11) =< U+1
s(13) =< R1+1
s(14) =< s(13)
s(12) =< s(11)
s(12) =< s(10)

  with precondition: [A=5,Z1=J,Y=O,U=S,0>=N1+1,T>=0,R1>=0,C2>=T+2,T+U+1>=C2] 

* Chain [49]: 2*s(17)+0
  Such that:s(16) =< S+1
s(15) =< -T+C2
s(17) =< s(16)
s(17) =< s(15)

  with precondition: [A=5,Z1=J,Y=O,U=S,0>=N1+1,T>=0,C2>=T+2,T+U+1>=C2] 

* Chain [48]: 2*s(19)+0
  Such that:s(18) =< U+1
s(19) =< s(18)

  with precondition: [A=5,Z1=J,Y=O,U=S,T>=0,U>=0] 

* Chain [47]: 2*s(22)+2*s(24)+0
  Such that:s(20) =< -T+C2
s(21) =< U+1
s(23) =< R1+1
s(24) =< s(23)
s(22) =< s(21)
s(22) =< s(20)

  with precondition: [A=5,Z1=J,Y=O,U=S,T>=0,N1>=1,R1>=0,C2>=T+2,T+U+1>=C2] 

* Chain [46]: 2*s(27)+0
  Such that:s(26) =< S+1
s(25) =< -T+C2
s(27) =< s(26)
s(27) =< s(25)

  with precondition: [A=5,Z1=J,Y=O,U=S,T>=0,N1>=1,C2>=T+2,T+U+1>=C2] 


#### Cost of chains of f0(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,Z1,A2,B2,C2,D2,E2,F2,G2,F3):
* Chain [94]: 1*aux(7)+0
  with precondition: [] 

* Chain [93]: 0
  with precondition: [K=0,M1=0] 

* Chain [92]: 1*aux(8)+0
  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2] 

* Chain [91]: 4*s(31)+1*s(32)+0
  Such that:aux(9) =< Q1+1
s(31) =< aux(9)

  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,Q1>=0] 

* Chain [90]: 4*s(36)+1*s(37)+0
  Such that:aux(10) =< Q1+1
s(36) =< aux(10)

  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,R>=2,Q1>=0,W1>=1] 

* Chain [89]: 1*aux(11)+0
  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,R>=2,W1>=1] 

* Chain [88]: 1*aux(12)+0
  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1] 

* Chain [87]: 4*s(43)+1*s(44)+0
  Such that:aux(13) =< Q1+1
s(43) =< aux(13)

  with precondition: [S=0,B2=1,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,Q1>=0] 

* Chain [86]: 4*s(48)+1*s(49)+0
  Such that:aux(14) =< Q1+1
s(48) =< aux(14)

  with precondition: [S=0,B2=1,R=T,0>=K+1,R>=2,M1>=1,Q1>=0,W1>=1] 

* Chain [85]: 1*aux(15)+0
  with precondition: [S=0,B2=1,R=T,0>=K+1,R>=2,M1>=1,W1>=1] 

* Chain [84]: 1*aux(16)+0
  with precondition: [S=0,B2=1,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2] 

* Chain [83]: 4*s(55)+1*s(56)+0
  Such that:aux(17) =< Q1+1
s(55) =< aux(17)

  with precondition: [S=0,B2=1,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,Q1>=0] 

* Chain [82]: 4*s(60)+1*s(61)+0
  Such that:aux(18) =< Q1+1
s(60) =< aux(18)

  with precondition: [S=0,B2=1,R=T,0>=M1+1,K>=1,R>=2,Q1>=0,W1>=1] 

* Chain [81]: 1*aux(19)+0
  with precondition: [S=0,B2=1,R=T,0>=M1+1,K>=1,R>=2,W1>=1] 

* Chain [80]: 1*aux(20)+0
  with precondition: [S=0,B2=1,R=T,0>=W1+1,K>=1,R>=2,M1>=1] 

* Chain [79]: 4*s(67)+1*s(68)+0
  Such that:aux(21) =< Q1+1
s(67) =< aux(21)

  with precondition: [S=0,B2=1,R=T,0>=W1+1,K>=1,R>=2,M1>=1,Q1>=0] 

* Chain [78]: 4*s(72)+1*s(73)+0
  Such that:aux(22) =< Q1+1
s(72) =< aux(22)

  with precondition: [S=0,B2=1,R=T,K>=1,R>=2,M1>=1,Q1>=0,W1>=1] 

* Chain [77]: 1*aux(23)+0
  with precondition: [S=0,B2=1,R=T,K>=1,R>=2,M1>=1,W1>=1] 

* Chain [76]: 4*s(80)+2*s(81)+1*s(82)+2*s(87)+0
  Such that:s(84) =< R+1
s(78) =< T+1
aux(24) =< Q1+1
aux(25) =< B2
s(80) =< aux(24)
s(87) =< s(84)
s(87) =< aux(25)
s(81) =< s(78)
s(81) =< aux(25)

  with precondition: [S=0,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,Q1>=0,B2>=2,R+1>=B2] 

* Chain [75]: 4*s(90)+1*s(91)+0
  Such that:aux(26) =< T+1
aux(27) =< B2
s(90) =< aux(26)
s(90) =< aux(27)

  with precondition: [S=0,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,B2>=2,R+1>=B2] 

* Chain [74]: 4*s(98)+2*s(99)+1*s(100)+2*s(105)+0
  Such that:s(102) =< R+1
s(96) =< T+1
aux(28) =< Q1+1
aux(29) =< B2
s(98) =< aux(28)
s(105) =< s(102)
s(105) =< aux(29)
s(99) =< s(96)
s(99) =< aux(29)

  with precondition: [S=0,R=T,0>=K+1,0>=M1+1,R>=2,Q1>=0,W1>=1,B2>=2,R+1>=B2] 

* Chain [73]: 4*s(108)+1*s(109)+0
  Such that:aux(30) =< T+1
aux(31) =< B2
s(108) =< aux(30)
s(108) =< aux(31)

  with precondition: [S=0,R=T,0>=K+1,0>=M1+1,R>=2,W1>=1,B2>=2,R+1>=B2] 

* Chain [72]: 4*s(114)+2*s(115)+0
  Such that:aux(32) =< R+1
s(114) =< aux(32)

  with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2] 

* Chain [71]: 4*s(122)+2*s(123)+1*s(124)+2*s(129)+0
  Such that:s(126) =< R+1
s(120) =< T+1
aux(33) =< Q1+1
aux(34) =< B2
s(122) =< aux(33)
s(129) =< s(126)
s(129) =< aux(34)
s(123) =< s(120)
s(123) =< aux(34)

  with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,Q1>=0,B2>=2,R+1>=B2] 

* Chain [70]: 4*s(132)+1*s(133)+0
  Such that:aux(35) =< T+1
aux(36) =< B2
s(132) =< aux(35)
s(132) =< aux(36)

  with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,B2>=2,R+1>=B2] 

* Chain [69]: 4*s(140)+2*s(141)+1*s(142)+2*s(147)+0
  Such that:s(144) =< R+1
s(138) =< T+1
aux(37) =< Q1+1
aux(38) =< B2
s(140) =< aux(37)
s(147) =< s(144)
s(147) =< aux(38)
s(141) =< s(138)
s(141) =< aux(38)

  with precondition: [S=0,R=T,0>=K+1,R>=2,M1>=1,Q1>=0,W1>=1,B2>=2,R+1>=B2] 

* Chain [68]: 4*s(150)+1*s(151)+0
  Such that:aux(39) =< T+1
aux(40) =< B2
s(150) =< aux(39)
s(150) =< aux(40)

  with precondition: [S=0,R=T,0>=K+1,R>=2,M1>=1,W1>=1,B2>=2,R+1>=B2] 

* Chain [67]: 4*s(156)+2*s(157)+0
  Such that:aux(41) =< R+1
s(156) =< aux(41)

  with precondition: [S=0,R=T,0>=K+1,R>=2,W1>=1] 

* Chain [66]: 4*s(164)+2*s(165)+1*s(166)+2*s(171)+0
  Such that:s(168) =< R+1
s(162) =< T+1
aux(42) =< Q1+1
aux(43) =< B2
s(164) =< aux(42)
s(171) =< s(168)
s(171) =< aux(43)
s(165) =< s(162)
s(165) =< aux(43)

  with precondition: [S=0,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,Q1>=0,B2>=2,R+1>=B2] 

* Chain [65]: 4*s(174)+1*s(175)+0
  Such that:aux(44) =< T+1
aux(45) =< B2
s(174) =< aux(44)
s(174) =< aux(45)

  with precondition: [S=0,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,B2>=2,R+1>=B2] 

* Chain [64]: 4*s(182)+2*s(183)+1*s(184)+2*s(189)+0
  Such that:s(186) =< R+1
s(180) =< T+1
aux(46) =< Q1+1
aux(47) =< B2
s(182) =< aux(46)
s(189) =< s(186)
s(189) =< aux(47)
s(183) =< s(180)
s(183) =< aux(47)

  with precondition: [S=0,R=T,0>=M1+1,K>=1,R>=2,Q1>=0,W1>=1,B2>=2,R+1>=B2] 

* Chain [63]: 4*s(192)+1*s(193)+0
  Such that:aux(48) =< T+1
aux(49) =< B2
s(192) =< aux(48)
s(192) =< aux(49)

  with precondition: [S=0,R=T,0>=M1+1,K>=1,R>=2,W1>=1,B2>=2,R+1>=B2] 

* Chain [62]: 4*s(198)+2*s(199)+0
  Such that:aux(50) =< R+1
s(198) =< aux(50)

  with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2] 

* Chain [61]: 4*s(206)+2*s(207)+1*s(208)+2*s(213)+0
  Such that:s(210) =< R+1
s(204) =< T+1
aux(51) =< Q1+1
aux(52) =< B2
s(206) =< aux(51)
s(213) =< s(210)
s(213) =< aux(52)
s(207) =< s(204)
s(207) =< aux(52)

  with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2,M1>=1,Q1>=0,B2>=2,R+1>=B2] 

* Chain [60]: 4*s(216)+1*s(217)+0
  Such that:aux(53) =< T+1
aux(54) =< B2
s(216) =< aux(53)
s(216) =< aux(54)

  with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2,M1>=1,B2>=2,R+1>=B2] 

* Chain [59]: 4*s(224)+2*s(225)+1*s(226)+2*s(231)+0
  Such that:s(228) =< R+1
s(222) =< T+1
aux(55) =< Q1+1
aux(56) =< B2
s(224) =< aux(55)
s(231) =< s(228)
s(231) =< aux(56)
s(225) =< s(222)
s(225) =< aux(56)

  with precondition: [S=0,R=T,K>=1,R>=2,M1>=1,Q1>=0,W1>=1,B2>=2,R+1>=B2] 

* Chain [58]: 4*s(234)+1*s(235)+0
  Such that:aux(57) =< T+1
aux(58) =< B2
s(234) =< aux(57)
s(234) =< aux(58)

  with precondition: [S=0,R=T,K>=1,R>=2,M1>=1,W1>=1,B2>=2,R+1>=B2] 

* Chain [57]: 4*s(240)+2*s(241)+0
  Such that:aux(59) =< R+1
s(240) =< aux(59)

  with precondition: [S=0,R=T,K>=1,R>=2,W1>=1] 


Closed-form bounds of f0(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,Z1,A2,B2,C2,D2,E2,F2,G2,F3): 
-------------------------------------
* Chain [94] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [93] with precondition: [K=0,M1=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [92] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [91] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,Q1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [90] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,R>=2,Q1>=0,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [89] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=M1+1,R>=2,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [88] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [87] with precondition: [S=0,B2=1,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,Q1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [86] with precondition: [S=0,B2=1,R=T,0>=K+1,R>=2,M1>=1,Q1>=0,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [85] with precondition: [S=0,B2=1,R=T,0>=K+1,R>=2,M1>=1,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [84] with precondition: [S=0,B2=1,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [83] with precondition: [S=0,B2=1,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,Q1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [82] with precondition: [S=0,B2=1,R=T,0>=M1+1,K>=1,R>=2,Q1>=0,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [81] with precondition: [S=0,B2=1,R=T,0>=M1+1,K>=1,R>=2,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [80] with precondition: [S=0,B2=1,R=T,0>=W1+1,K>=1,R>=2,M1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [79] with precondition: [S=0,B2=1,R=T,0>=W1+1,K>=1,R>=2,M1>=1,Q1>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [78] with precondition: [S=0,B2=1,R=T,K>=1,R>=2,M1>=1,Q1>=0,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [77] with precondition: [S=0,B2=1,R=T,K>=1,R>=2,M1>=1,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [76] with precondition: [S=0,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,Q1>=0,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [75] with precondition: [S=0,R=T,0>=K+1,0>=M1+1,0>=W1+1,R>=2,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [74] with precondition: [S=0,R=T,0>=K+1,0>=M1+1,R>=2,Q1>=0,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [73] with precondition: [S=0,R=T,0>=K+1,0>=M1+1,R>=2,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [72] with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [71] with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,Q1>=0,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [70] with precondition: [S=0,R=T,0>=K+1,0>=W1+1,R>=2,M1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [69] with precondition: [S=0,R=T,0>=K+1,R>=2,M1>=1,Q1>=0,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [68] with precondition: [S=0,R=T,0>=K+1,R>=2,M1>=1,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [67] with precondition: [S=0,R=T,0>=K+1,R>=2,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [66] with precondition: [S=0,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,Q1>=0,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [65] with precondition: [S=0,R=T,0>=M1+1,0>=W1+1,K>=1,R>=2,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [64] with precondition: [S=0,R=T,0>=M1+1,K>=1,R>=2,Q1>=0,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [63] with precondition: [S=0,R=T,0>=M1+1,K>=1,R>=2,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [62] with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [61] with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2,M1>=1,Q1>=0,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [60] with precondition: [S=0,R=T,0>=W1+1,K>=1,R>=2,M1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [59] with precondition: [S=0,R=T,K>=1,R>=2,M1>=1,Q1>=0,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [58] with precondition: [S=0,R=T,K>=1,R>=2,M1>=1,W1>=1,B2>=2,R+1>=B2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [57] with precondition: [S=0,R=T,K>=1,R>=2,W1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(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,Z1,A2,B2,C2,D2,E2,F2,G2,F3): inf 
Asymptotic class: infinity 
* Total analysis performed in 6757 ms.