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


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [lbl111/25]
1. recursive  : [lbl111_loop_cont/26,lbl121/25]
2. recursive  : [lbl121_loop_cont/26,lbl131/25]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [stop/13]
5. non_recursive  : [lbl131_loop_cont/14]
6. non_recursive  : [start/13]
7. non_recursive  : [start0/13]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl111/25
1. SCC is partially evaluated into lbl121/25
2. SCC is partially evaluated into lbl131/25
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into lbl131_loop_cont/14
6. SCC is partially evaluated into start/13
7. SCC is partially evaluated into start0/13

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

### Specialization of cost equations lbl111/25 
* CE 14 is refined into CE [28] 
* CE 12 is refined into CE [29] 
* CE 13 is refined into CE [30] 


### Cost equations --> "Loop" of lbl111/25 
* CEs [30] --> Loop 24 
* CEs [28] --> Loop 25 
* CEs [29] --> Loop 26 

### Ranking functions of CR lbl111(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) 
* RF of phase [24]: [A-F,-F+L]

#### Partial ranking functions of CR lbl111(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) 
* Partial RF of phase [24]:
  - RF of loop [24:1]:
    A-F
    -F+L


### Specialization of cost equations lbl121/25 
* CE 17 is refined into CE [31] 
* CE 19 is refined into CE [32] 
* CE 18 is refined into CE [33] 


### Cost equations --> "Loop" of lbl121/25 
* CEs [33] --> Loop 27 
* CEs [31] --> Loop 28 
* CEs [32] --> Loop 29 

### Ranking functions of CR lbl121(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) 
* RF of phase [27]: [D-H,E-H]

#### Partial ranking functions of CR lbl121(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) 
* Partial RF of phase [27]:
  - RF of loop [27:1]:
    D-H
    E-H


### Specialization of cost equations lbl131/25 
* CE 25 is refined into CE [34] 
* CE 20 is refined into CE [35,36] 
* CE 21 is refined into CE [37,38,39,40] 
* CE 22 is refined into CE [41,42] 
* CE 27 is refined into CE [43] 
* CE 23 is refined into CE [44,45,46,47] 
* CE 24 is refined into CE [48,49] 
* CE 26 is refined into CE [50] 


### Cost equations --> "Loop" of lbl131/25 
* CEs [49] --> Loop 30 
* CEs [47] --> Loop 31 
* CEs [45] --> Loop 32 
* CEs [48] --> Loop 33 
* CEs [46] --> Loop 34 
* CEs [44] --> Loop 35 
* CEs [50] --> Loop 36 
* CEs [34] --> Loop 37 
* CEs [40] --> Loop 38 
* CEs [36,39] --> Loop 39 
* CEs [35] --> Loop 40 
* CEs [42] --> Loop 41 
* CEs [41] --> Loop 42 
* CEs [38] --> Loop 43 
* CEs [37] --> Loop 44 
* CEs [43] --> Loop 45 

### Ranking functions of CR lbl131(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) 
* RF of phase [30]: [B-J,C-J]
* RF of phase [33]: [B-J,C-J]
* RF of phase [36]: [B-J,C-J]

#### Partial ranking functions of CR lbl131(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) 
* Partial RF of phase [30]:
  - RF of loop [30:1]:
    B-J
    C-J
* Partial RF of phase [33]:
  - RF of loop [33:1]:
    B-J
    C-J
* Partial RF of phase [36]:
  - RF of loop [36:1]:
    B-J
    C-J


### Specialization of cost equations lbl131_loop_cont/14 
* CE 15 is refined into CE [51] 
* CE 16 is refined into CE [52] 


### Cost equations --> "Loop" of lbl131_loop_cont/14 
* CEs [51] --> Loop 46 
* CEs [52] --> Loop 47 

### Ranking functions of CR lbl131_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR lbl131_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 


### Specialization of cost equations start/13 
* CE 2 is refined into CE [53,54] 
* CE 3 is refined into CE [55,56,57,58] 
* CE 5 is refined into CE [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82] 
* CE 8 is refined into CE [83] 
* CE 9 is refined into CE [84] 
* CE 7 is refined into CE [85] 
* CE 11 is refined into CE [86,87,88,89] 
* CE 10 is refined into CE [90] 
* CE 4 is refined into CE [91,92] 
* CE 6 is refined into CE [93,94,95,96,97,98,99,100,101,102,103,104] 


### Cost equations --> "Loop" of start/13 
* CEs [80] --> Loop 48 
* CEs [78,79,82] --> Loop 49 
* CEs [81] --> Loop 50 
* CEs [58,77] --> Loop 51 
* CEs [54,57] --> Loop 52 
* CEs [53] --> Loop 53 
* CEs [83] --> Loop 54 
* CEs [84] --> Loop 55 
* CEs [85] --> Loop 56 
* CEs [72] --> Loop 57 
* CEs [71,73,75] --> Loop 58 
* CEs [76] --> Loop 59 
* CEs [74] --> Loop 60 
* CEs [86,87] --> Loop 61 
* CEs [88] --> Loop 62 
* CEs [89] --> Loop 63 
* CEs [90] --> Loop 64 
* CEs [68] --> Loop 65 
* CEs [66,67,70] --> Loop 66 
* CEs [56,65] --> Loop 67 
* CEs [55] --> Loop 68 
* CEs [69] --> Loop 69 
* CEs [60] --> Loop 70 
* CEs [59,61,63] --> Loop 71 
* CEs [62] --> Loop 72 
* CEs [64] --> Loop 73 
* CEs [102] --> Loop 74 
* CEs [100,101,104] --> Loop 75 
* CEs [92,99] --> Loop 76 
* CEs [91] --> Loop 77 
* CEs [94] --> Loop 78 
* CEs [93,95,97] --> Loop 79 
* CEs [96] --> Loop 80 
* CEs [103] --> Loop 81 
* CEs [98] --> Loop 82 

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

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


### Specialization of cost equations start0/13 
* CE 1 is refined into CE [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 start0/13 
* CEs [139] --> Loop 83 
* CEs [138] --> Loop 84 
* CEs [137] --> Loop 85 
* CEs [136] --> Loop 86 
* CEs [135] --> Loop 87 
* CEs [134] --> Loop 88 
* CEs [132] --> Loop 89 
* CEs [131] --> Loop 90 
* CEs [133] --> Loop 91 
* CEs [130] --> Loop 92 
* CEs [129] --> Loop 93 
* CEs [128] --> Loop 94 
* CEs [127] --> Loop 95 
* CEs [126] --> Loop 96 
* CEs [125] --> Loop 97 
* CEs [124] --> Loop 98 
* CEs [123] --> Loop 99 
* CEs [122] --> Loop 100 
* CEs [121] --> Loop 101 
* CEs [120] --> Loop 102 
* CEs [119] --> Loop 103 
* CEs [118] --> Loop 104 
* CEs [117] --> Loop 105 
* CEs [116] --> Loop 106 
* CEs [115] --> Loop 107 
* CEs [114] --> Loop 108 
* CEs [113] --> Loop 109 
* CEs [112] --> Loop 110 
* CEs [111] --> Loop 111 
* CEs [110] --> Loop 112 
* CEs [109] --> Loop 113 
* CEs [108] --> Loop 114 
* CEs [107] --> Loop 115 
* CEs [106] --> Loop 116 
* CEs [105] --> Loop 117 

### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K,L,M) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K,L,M) 


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

#### Cost of chains of lbl111(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):
* Chain [[24],26]: 1*it(24)+0
  Such that:it(24) =< A-F

  with precondition: [H=1,M=2,U=1,B=C,D=E,A=L,A=N,B=O,B=P,D=Q,D=R,A=S,G=T,I=V,A=W,K=X,A=Y,D>=1,J>=0,A>=F+1,B>=J+1,F>=J+1] 

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

  with precondition: [H=1,M=3,B=C,D=E,A=L,D>=1,J>=0,A>=F+1,B>=J+1,F>=J+1] 

* Chain [26]: 0
  with precondition: [H=1,M=2,U=1,C=B,E=D,A=F,T=G,V=I,X=K,A=L,A=N,C=O,C=P,E=Q,E=R,A=S,A=W,A=Y,E>=1,J>=0,A>=J+1,C>=J+1] 

* Chain [25]: 0
  with precondition: [H=1,M=3,L=A,C=B,E=D,E>=1,J>=0,L>=F,C>=J+1,F>=J+1] 


#### Cost of chains of lbl121(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):
* Chain [[27],29]: 1*it(27)+0
  Such that:it(27) =< D-H

  with precondition: [M=3,B=C,D=E,F=J,A=L,A>=0,H>=1,F>=A,D>=H+1,A+B>=F+1] 

* Chain [[27],28]: 1*it(27)+0
  Such that:it(27) =< D-H

  with precondition: [M=4,B=C,D=E,F=J,A=L,A=N,B=O,B=P,D=Q,D=R,F=S,G=T,D=U,I=V,F+1=W,K=X,A=Y,A>=0,H>=1,F>=A,D>=H+1,A+B>=F+1] 

* Chain [29]: 0
  with precondition: [M=3] 

* Chain [28]: 0
  with precondition: [M=4,B=C,D=E,T=G,D=H,V=I,F=J,X=K,A=L,A=N,B=O,B=P,D=Q,D=R,F=S,D=U,F+1=W,A=Y,A>=0,D>=1,F>=A,A+B>=F+1] 


#### Cost of chains of lbl131(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):
* Chain [[36],45]: 1*it(36)+0
  Such that:it(36) =< B-J

  with precondition: [D=0,E=0,H=0,M=3,B=C,A=L,A>=0,J>=1,B>=J+1] 

* Chain [[36],37]: 1*it(36)+0
  Such that:it(36) =< B-J

  with precondition: [D=0,E=0,H=0,M=5,Q=0,R=0,U=0,B=C,A=L,A=N,B=O,B=P,F=S,G=T,I=V,B=W,K=X,A=Y,A>=0,J>=1,B>=J+1] 

* Chain [[33],45]: 1*it(33)+0
  Such that:it(33) =< B-J

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,A>=0,J>=1,J>=A,B>=J+1] 

* Chain [[33],42]: 1*it(33)+0
  Such that:it(33) =< B-J

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,A>=0,J>=1,J>=A,B>=J+2] 

* Chain [[33],37]: 1*it(33)+0
  Such that:it(33) =< B-J

  with precondition: [D=1,E=1,H=1,M=5,Q=1,R=1,U=1,B=C,A=L,A=N,B=O,B=P,B=S+1,G=T,I=V,B=W,K=X,A=Y,A>=0,J>=1,J>=A,B>=J+1] 

* Chain [[30],45]: 1*it(30)+1*s(3)+0
  Such that:it(30) =< B-J
aux(1) =< E
s(3) =< it(30)*aux(1)

  with precondition: [M=3,B=C,D=E,D=H,A=L,A>=0,D>=2,J>=1,J>=A,B>=J+1] 

* Chain [[30],42]: 1*it(30)+1*s(3)+0
  Such that:it(30) =< B-J
aux(1) =< E
s(3) =< it(30)*aux(1)

  with precondition: [M=3,B=C,D=E,D=H,A=L,A>=0,D>=2,J>=1,J>=A,B>=J+2] 

* Chain [[30],41]: 1*it(30)+1*s(3)+1*s(4)+0
  Such that:it(30) =< B-J
aux(2) =< D
s(4) =< aux(2)
s(3) =< it(30)*aux(2)

  with precondition: [M=3,B=C,D=E,D=H,A=L,A>=0,D>=2,J>=1,J>=A,B>=J+2] 

* Chain [[30],37]: 1*it(30)+1*s(3)+0
  Such that:it(30) =< B-J
aux(1) =< U
s(3) =< it(30)*aux(1)

  with precondition: [M=5,B=C,D=E,D=H,A=L,A=N,B=O,B=P,D=Q,D=R,B=S+1,G=T,D=U,I=V,B=W,K=X,A=Y,A>=0,D>=2,J>=1,J>=A,B>=J+1] 

* Chain [45]: 0
  with precondition: [M=3] 

* Chain [44]: 1
  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=1,B>=A] 

* Chain [43]: 1*s(5)+1
  Such that:s(5) =< H

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A] 

* Chain [42]: 0
  with precondition: [M=3,B=C,D=E,D=H,A=L,A>=0,D>=1,J>=1,J>=A,B>=J+1] 

* Chain [41]: 1*s(4)+0
  Such that:s(4) =< H

  with precondition: [M=3,B=C,D=E,D=H,A=L,A>=0,D>=2,J>=1,J>=A,B>=J+1] 

* Chain [40]: 0
  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=1,J>=1,A>=J+1,B>=J+1] 

* Chain [39]: 2*s(6)+1
  Such that:aux(3) =< A-J
s(6) =< aux(3)

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=1,J>=1,A>=J+2,B>=J+1] 

* Chain [38]: 1*s(8)+1*s(9)+1
  Such that:s(8) =< A-J
s(9) =< H

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,A>=J+2,B>=J+1] 

* Chain [37]: 0
  with precondition: [M=5,B=C,D=E,S=F,T=G,D=H,V=I,X=K,A=L,A=N,B=O,B=P,D=Q,D=R,D=U,J=W,A=Y,B>=1,D>=0,J>=B,A+B>=J] 

* Chain [35,[33],45]: 1*it(33)+2
  Such that:it(33) =< B-L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=J+1,A=L,A>=2,B>=A+2] 

* Chain [35,[33],42]: 1*it(33)+2
  Such that:it(33) =< B-L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=J+1,A=L,A>=2,B>=A+3] 

* Chain [35,[33],37]: 1*it(33)+2
  Such that:it(33) =< -A+B

  with precondition: [D=1,E=1,H=1,M=5,Q=1,R=1,U=1,B=C,A=J+1,A=L,A=N,B=O,B=P,B=S+1,G=T,I=V,B=W,K=X,A=Y,A>=2,B>=A+2] 

* Chain [35,45]: 2
  with precondition: [D=1,E=1,H=1,M=3,B=C,A=J+1,A=L,A>=2,B>=A] 

* Chain [35,42]: 2
  with precondition: [D=1,E=1,H=1,M=3,B=C,A=J+1,A=L,A>=2,B>=A+2] 

* Chain [35,37]: 2
  with precondition: [D=1,E=1,H=1,M=5,Q=1,R=1,U=1,B=C,A=J+1,A=L,A=N,B=O,B=P,A=S,G=T,I=V,A+1=W,K=X,A=Y,A>=2,B>=A,A+1>=B] 

* Chain [34,[33],45]: 1*it(33)+1*s(10)+2
  Such that:it(33) =< B-L
s(10) =< -J+L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,J>=1,B>=A+2,A>=J+2] 

* Chain [34,[33],42]: 1*it(33)+1*s(10)+2
  Such that:it(33) =< B-L
s(10) =< -J+L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,J>=1,B>=A+3,A>=J+2] 

* Chain [34,[33],37]: 1*it(33)+1*s(10)+2
  Such that:it(33) =< -A+S
s(10) =< A-J

  with precondition: [D=1,E=1,H=1,M=5,Q=1,R=1,U=1,B=C,A=L,A=N,B=O,B=P,B=S+1,G=T,I=V,B=W,K=X,A=Y,J>=1,B>=A+2,A>=J+2] 

* Chain [34,45]: 1*s(10)+2
  Such that:s(10) =< -J+L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,J>=1,A>=J+2,B>=J+1] 

* Chain [34,42]: 1*s(10)+2
  Such that:s(10) =< -J+L

  with precondition: [D=1,E=1,H=1,M=3,B=C,A=L,J>=1,B>=A+2,A>=J+2] 

* Chain [34,37]: 1*s(10)+2
  Such that:s(10) =< A-J

  with precondition: [D=1,E=1,H=1,M=5,Q=1,R=1,U=1,B=C,A=L,A=N,B=O,B=P,A=S,G=T,I=V,A+1=W,K=X,A=Y,J>=1,A+1>=B,A>=J+2,B>=J+1] 

* Chain [32,[30],45]: 1*it(30)+1*s(3)+1*s(11)+2
  Such that:it(30) =< B-L
aux(4) =< H
s(11) =< aux(4)
s(3) =< it(30)*aux(4)

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A+2] 

* Chain [32,[30],42]: 1*it(30)+1*s(3)+1*s(11)+2
  Such that:it(30) =< B-L
aux(5) =< H
s(11) =< aux(5)
s(3) =< it(30)*aux(5)

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A+3] 

* Chain [32,[30],41]: 1*it(30)+1*s(3)+2*s(4)+2
  Such that:it(30) =< B-L
aux(6) =< H
s(4) =< aux(6)
s(3) =< it(30)*aux(6)

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A+3] 

* Chain [32,[30],37]: 1*it(30)+1*s(3)+1*s(11)+2
  Such that:it(30) =< -A+S
aux(7) =< U
s(11) =< aux(7)
s(3) =< it(30)*aux(7)

  with precondition: [M=5,B=C,D=E,D=H,A=J+1,A=L,A=N,B=O,B=P,D=Q,D=R,B=S+1,G=T,D=U,I=V,B=W,K=X,A=Y,A>=2,D>=2,B>=A+2] 

* Chain [32,45]: 1*s(11)+2
  Such that:s(11) =< H

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A] 

* Chain [32,42]: 1*s(11)+2
  Such that:s(11) =< H

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A+2] 

* Chain [32,41]: 2*s(4)+2
  Such that:aux(8) =< H
s(4) =< aux(8)

  with precondition: [M=3,B=C,D=E,D=H,A=J+1,A=L,A>=2,D>=2,B>=A+2] 

* Chain [32,37]: 1*s(11)+2
  Such that:s(11) =< U

  with precondition: [M=5,B=C,D=E,D=H,A=J+1,A=L,A=N,B=O,B=P,D=Q,D=R,A=S,G=T,D=U,I=V,A+1=W,K=X,A=Y,A>=2,D>=2,B>=A,A+1>=B] 

* Chain [31,[30],45]: 1*it(30)+1*s(3)+1*s(12)+1*s(13)+2
  Such that:it(30) =< B-L
s(12) =< -J+L
aux(9) =< E
s(13) =< aux(9)
s(3) =< it(30)*aux(9)

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,B>=A+2,A>=J+2] 

* Chain [31,[30],42]: 1*it(30)+1*s(3)+1*s(12)+1*s(13)+2
  Such that:it(30) =< B-L
s(12) =< -J+L
aux(10) =< E
s(13) =< aux(10)
s(3) =< it(30)*aux(10)

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,B>=A+3,A>=J+2] 

* Chain [31,[30],41]: 1*it(30)+1*s(3)+2*s(4)+1*s(12)+2
  Such that:it(30) =< B-L
s(12) =< -J+L
aux(11) =< E
s(4) =< aux(11)
s(3) =< it(30)*aux(11)

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,B>=A+3,A>=J+2] 

* Chain [31,[30],37]: 1*it(30)+1*s(3)+1*s(12)+1*s(13)+2
  Such that:it(30) =< -A+S
s(12) =< A-J
aux(12) =< U
s(13) =< aux(12)
s(3) =< it(30)*aux(12)

  with precondition: [M=5,B=C,D=E,D=H,A=L,A=N,B=O,B=P,D=Q,D=R,B=S+1,G=T,D=U,I=V,B=W,K=X,A=Y,D>=2,J>=1,B>=A+2,A>=J+2] 

* Chain [31,45]: 1*s(12)+1*s(13)+2
  Such that:s(13) =< H
s(12) =< -J+L

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,A>=J+2,B>=J+1] 

* Chain [31,42]: 1*s(12)+1*s(13)+2
  Such that:s(13) =< H
s(12) =< -J+L

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,B>=A+2,A>=J+2] 

* Chain [31,41]: 2*s(4)+1*s(12)+2
  Such that:s(12) =< -J+L
aux(13) =< E
s(4) =< aux(13)

  with precondition: [M=3,B=C,D=E,D=H,A=L,D>=2,J>=1,B>=A+2,A>=J+2] 

* Chain [31,37]: 1*s(12)+1*s(13)+2
  Such that:s(12) =< A-J
s(13) =< U

  with precondition: [M=5,B=C,D=E,D=H,A=L,A=N,B=O,B=P,D=Q,D=R,A=S,G=T,D=U,I=V,A+1=W,K=X,A=Y,D>=2,J>=1,A+1>=B,A>=J+2,B>=J+1] 


#### Cost of chains of lbl131_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
* Chain [47]: 0
  with precondition: [A=3] 

* Chain [46]: 0
  with precondition: [A=5] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [82]: 1
  with precondition: [A=0,B=1,C=1,D=1,E=1,L=0,G=F,I=H,K=J] 

* Chain [81]: 1*s(70)+1
  Such that:s(70) =< D

  with precondition: [A=0,B=1,C=1,L=0,E=D,G=F,I=H,K=J,E>=2] 

* Chain [80]: 1
  with precondition: [A=0,D=1,E=1,L=0,C=B,G=F,I=H,K=J,C>=1] 

* Chain [79]: 2*s(71)+1
  Such that:aux(26) =< B
s(71) =< aux(26)

  with precondition: [A=0,D=1,E=1,L=0,C=B,G=F,I=H,K=J,C>=2] 

* Chain [78]: 1*s(73)+1
  Such that:s(73) =< B

  with precondition: [A=0,D=1,E=1,L=0,C=B,G=F,I=H,K=J,C>=3] 

* Chain [77]: 0
  with precondition: [A=0,L=0,C=B,E=D,G=F,I=H,K=J,C>=1,E>=1] 

* Chain [76]: 2*s(74)+1
  Such that:aux(27) =< D
s(74) =< aux(27)

  with precondition: [A=0,L=0,C=B,E=D,G=F,I=H,K=J,C>=1,E>=2] 

* Chain [75]: 2*s(76)+2*s(77)+2*s(78)+1*s(81)+1*s(85)+1
  Such that:aux(28) =< E
aux(30) =< B
aux(31) =< D
s(78) =< aux(30)
s(76) =< aux(31)
s(77) =< aux(28)
s(81) =< s(78)*aux(28)
s(85) =< s(78)*aux(31)

  with precondition: [A=0,L=0,C=B,E=D,G=F,I=H,K=J,C>=2,E>=2] 

* Chain [74]: 2*s(86)+2*s(90)+2*s(92)+1
  Such that:s(89) =< B
aux(32) =< E
s(86) =< aux(32)
s(90) =< s(89)
s(92) =< s(90)*aux(32)

  with precondition: [A=0,L=0,C=B,E=D,G=F,I=H,K=J,C>=3,E>=2] 

* Chain [73]: 2
  with precondition: [A=1,D=1,E=1,L=1,C=B,G=F,I=H,K=J,2>=C,C>=1] 

* Chain [72]: 2
  with precondition: [A=1,D=1,E=1,L=1,C=B,G=F,I=H,K=J,C>=1] 

* Chain [71]: 2*s(94)+2
  Such that:aux(33) =< B
s(94) =< aux(33)

  with precondition: [A=1,D=1,E=1,L=1,C=B,G=F,I=H,K=J,C>=3] 

* Chain [70]: 1*s(96)+2
  Such that:s(96) =< B

  with precondition: [A=1,D=1,E=1,L=1,C=B,G=F,I=H,K=J,C>=4] 

* Chain [69]: 1*s(97)+2
  Such that:s(97) =< D

  with precondition: [A=1,L=1,C=B,E=D,G=F,I=H,K=J,2>=C,C>=1,E>=2] 

* Chain [68]: 1
  with precondition: [A=1,L=1,C=B,E=D,G=F,I=H,K=J,C>=1,E>=1] 

* Chain [67]: 2*s(98)+2
  Such that:aux(34) =< D
s(98) =< aux(34)

  with precondition: [A=1,L=1,C=B,E=D,G=F,I=H,K=J,C>=1,E>=2] 

* Chain [66]: 2*s(100)+2*s(101)+2*s(102)+1*s(105)+1*s(109)+2
  Such that:aux(35) =< E
aux(37) =< B
aux(38) =< D
s(102) =< aux(37)
s(100) =< aux(38)
s(101) =< aux(35)
s(105) =< s(102)*aux(35)
s(109) =< s(102)*aux(38)

  with precondition: [A=1,L=1,C=B,E=D,G=F,I=H,K=J,C>=3,E>=2] 

* Chain [65]: 2*s(110)+2*s(114)+2*s(116)+2
  Such that:s(113) =< B
aux(39) =< E
s(110) =< aux(39)
s(114) =< s(113)
s(116) =< s(114)*aux(39)

  with precondition: [A=1,L=1,C=B,E=D,G=F,I=H,K=J,C>=4,E>=2] 

* Chain [64]: 0
  with precondition: [B=0,C=0,L=A,E=D,G=F,I=H,K=J,E>=0,L>=0] 

* Chain [63]: 0
  with precondition: [B=1,C=1,D=0,E=0,L=A,G=F,I=H,K=J,L>=0] 

* Chain [62]: 0
  with precondition: [D=0,E=0,L=A,C=B,G=F,I=H,K=J,C>=1,L>=0] 

* Chain [61]: 2*s(118)+0
  Such that:aux(40) =< B
s(118) =< aux(40)

  with precondition: [D=0,E=0,L=A,C=B,G=F,I=H,K=J,C>=2,L>=0] 

* Chain [60]: 1*s(120)+2
  Such that:s(120) =< A

  with precondition: [D=1,E=1,L=A,C=B,G=F,I=H,K=J,C>=1,L>=2] 

* Chain [59]: 1*s(121)+2
  Such that:s(121) =< A

  with precondition: [D=1,E=1,L=A,C=B,G=F,I=H,K=J,C>=1,L>=2,L+1>=C] 

* Chain [58]: 3*s(122)+2*s(123)+2
  Such that:aux(41) =< -A+B
aux(42) =< A
s(123) =< aux(41)
s(122) =< aux(42)

  with precondition: [D=1,E=1,L=A,C=B,G=F,I=H,K=J,L>=2,C>=L+2] 

* Chain [57]: 1*s(127)+1*s(128)+2
  Such that:s(128) =< -A+B
s(127) =< A

  with precondition: [D=1,E=1,L=A,C=B,G=F,I=H,K=J,L>=2,C>=L+3] 

* Chain [56]: 0
  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,0>=L+1] 

* Chain [55]: 0
  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,0>=C+1] 

* Chain [54]: 0
  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,0>=E+1] 

* Chain [53]: 0
  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,C>=1,E>=1,L>=1] 

* Chain [52]: 2*s(129)+1
  Such that:aux(43) =< A
s(129) =< aux(43)

  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,C>=1,E>=1,L>=2] 

* Chain [51]: 2*s(131)+2*s(132)+2
  Such that:aux(44) =< A
aux(45) =< D
s(131) =< aux(44)
s(132) =< aux(45)

  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,C>=1,E>=2,L>=2] 

* Chain [50]: 1*s(135)+1*s(136)+2
  Such that:s(135) =< A
s(136) =< D

  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,C>=1,E>=2,L>=2,L+1>=C] 

* Chain [49]: 1*s(137)+1*s(138)+2*s(139)+3*s(140)+2*s(141)+2*s(144)+2
  Such that:s(137) =< A
s(138) =< D
aux(48) =< B-L
aux(49) =< E
aux(50) =< L
s(141) =< aux(48)
s(139) =< aux(50)
s(140) =< aux(49)
s(144) =< s(141)*aux(49)

  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,E>=2,L>=2,C>=L+2] 

* Chain [48]: 1*s(150)+2*s(151)+2*s(155)+2*s(157)+2
  Such that:s(154) =< B-L
s(150) =< L
aux(51) =< E
s(151) =< aux(51)
s(155) =< s(154)
s(157) =< s(155)*aux(51)

  with precondition: [L=A,C=B,E=D,G=F,I=H,K=J,E>=2,L>=2,C>=L+3] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [117]: 1
  with precondition: [A=0,C=1,E=1] 

* Chain [116]: 1*s(159)+1
  Such that:s(159) =< E

  with precondition: [A=0,C=1,E>=2] 

* Chain [115]: 1
  with precondition: [A=0,E=1,C>=1] 

* Chain [114]: 2*s(161)+1
  Such that:s(160) =< C
s(161) =< s(160)

  with precondition: [A=0,E=1,C>=2] 

* Chain [113]: 1*s(162)+1
  Such that:s(162) =< C

  with precondition: [A=0,E=1,C>=3] 

* Chain [112]: 0
  with precondition: [A=0,C>=1,E>=1] 

* Chain [111]: 2*s(164)+1
  Such that:s(163) =< E
s(164) =< s(163)

  with precondition: [A=0,C>=1,E>=2] 

* Chain [110]: 2*s(168)+4*s(169)+2*s(171)+1
  Such that:s(166) =< C
aux(52) =< E
s(168) =< s(166)
s(169) =< aux(52)
s(171) =< s(168)*aux(52)

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

* Chain [109]: 2*s(175)+2*s(176)+2*s(177)+1
  Such that:s(173) =< C
s(174) =< E
s(175) =< s(174)
s(176) =< s(173)
s(177) =< s(176)*s(174)

  with precondition: [A=0,C>=3,E>=2] 

* Chain [108]: 2
  with precondition: [A=1,E=1,2>=C,C>=1] 

* Chain [107]: 2
  with precondition: [A=1,E=1,C>=1] 

* Chain [106]: 2*s(179)+2
  Such that:s(178) =< C
s(179) =< s(178)

  with precondition: [A=1,E=1,C>=3] 

* Chain [105]: 1*s(180)+2
  Such that:s(180) =< C

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

* Chain [104]: 1*s(181)+2
  Such that:s(181) =< E

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

* Chain [103]: 1
  with precondition: [A=1,C>=1,E>=1] 

* Chain [102]: 2*s(183)+2
  Such that:s(182) =< E
s(183) =< s(182)

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

* Chain [101]: 2*s(187)+4*s(188)+2*s(190)+2
  Such that:s(185) =< C
aux(53) =< E
s(187) =< s(185)
s(188) =< aux(53)
s(190) =< s(187)*aux(53)

  with precondition: [A=1,C>=3,E>=2] 

* Chain [100]: 2*s(194)+2*s(195)+2*s(196)+2
  Such that:s(192) =< C
s(193) =< E
s(194) =< s(193)
s(195) =< s(192)
s(196) =< s(195)*s(193)

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

* Chain [99]: 0
  with precondition: [C=0,A>=0,E>=0] 

* Chain [98]: 0
  with precondition: [C=1,E=0,A>=0] 

* Chain [97]: 0
  with precondition: [E=0,A>=0,C>=1] 

* Chain [96]: 2*s(198)+0
  Such that:s(197) =< C
s(198) =< s(197)

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

* Chain [95]: 1*s(199)+2
  Such that:s(199) =< A

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

* Chain [94]: 1*s(200)+2
  Such that:s(200) =< A

  with precondition: [E=1,A>=2,C>=1,A+1>=C] 

* Chain [93]: 2*s(203)+3*s(204)+2
  Such that:s(201) =< -A+C
s(202) =< A
s(203) =< s(201)
s(204) =< s(202)

  with precondition: [E=1,A>=2,C>=A+2] 

* Chain [92]: 1*s(205)+1*s(206)+2
  Such that:s(205) =< -A+C
s(206) =< A

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

* Chain [91]: 0
  with precondition: [0>=A+1] 

* Chain [90]: 0
  with precondition: [0>=C+1] 

* Chain [89]: 0
  with precondition: [0>=E+1] 

* Chain [88]: 0
  with precondition: [A>=1,C>=1,E>=1] 

* Chain [87]: 2*s(208)+1
  Such that:s(207) =< A
s(208) =< s(207)

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

* Chain [86]: 2*s(211)+2*s(212)+2
  Such that:s(209) =< A
s(210) =< E
s(211) =< s(209)
s(212) =< s(210)

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

* Chain [85]: 1*s(213)+1*s(214)+2
  Such that:s(213) =< A
s(214) =< E

  with precondition: [A>=2,C>=1,E>=2,A+1>=C] 

* Chain [84]: 3*s(215)+4*s(216)+2*s(220)+2*s(223)+2
  Such that:s(217) =< -A+C
aux(54) =< A
aux(55) =< E
s(215) =< aux(54)
s(216) =< aux(55)
s(220) =< s(217)
s(223) =< s(220)*aux(55)

  with precondition: [A>=2,E>=2,C>=A+2] 

* Chain [83]: 1*s(225)+2*s(227)+2*s(228)+2*s(229)+2
  Such that:s(224) =< -A+C
s(225) =< A
s(226) =< E
s(227) =< s(226)
s(228) =< s(224)
s(229) =< s(228)*s(226)

  with precondition: [A>=2,E>=2,C>=A+3] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,K,L,M): 
-------------------------------------
* Chain [117] with precondition: [A=0,C=1,E=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [116] with precondition: [A=0,C=1,E>=2] 
    - Upper bound: E+1 
    - Complexity: n 
* Chain [115] with precondition: [A=0,E=1,C>=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [114] with precondition: [A=0,E=1,C>=2] 
    - Upper bound: 2*C+1 
    - Complexity: n 
* Chain [113] with precondition: [A=0,E=1,C>=3] 
    - Upper bound: C+1 
    - Complexity: n 
* Chain [112] with precondition: [A=0,C>=1,E>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [111] with precondition: [A=0,C>=1,E>=2] 
    - Upper bound: 2*E+1 
    - Complexity: n 
* Chain [110] with precondition: [A=0,C>=2,E>=2] 
    - Upper bound: 2*C+1+2*C*E+4*E 
    - Complexity: n^2 
* Chain [109] with precondition: [A=0,C>=3,E>=2] 
    - Upper bound: 2*C+1+2*C*E+2*E 
    - Complexity: n^2 
* Chain [108] with precondition: [A=1,E=1,2>=C,C>=1] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [107] with precondition: [A=1,E=1,C>=1] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [106] with precondition: [A=1,E=1,C>=3] 
    - Upper bound: 2*C+2 
    - Complexity: n 
* Chain [105] with precondition: [A=1,E=1,C>=4] 
    - Upper bound: C+2 
    - Complexity: n 
* Chain [104] with precondition: [A=1,2>=C,C>=1,E>=2] 
    - Upper bound: E+2 
    - Complexity: n 
* Chain [103] with precondition: [A=1,C>=1,E>=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [102] with precondition: [A=1,C>=1,E>=2] 
    - Upper bound: 2*E+2 
    - Complexity: n 
* Chain [101] with precondition: [A=1,C>=3,E>=2] 
    - Upper bound: 2*C+2+2*C*E+4*E 
    - Complexity: n^2 
* Chain [100] with precondition: [A=1,C>=4,E>=2] 
    - Upper bound: 2*C+2+2*C*E+2*E 
    - Complexity: n^2 
* Chain [99] with precondition: [C=0,A>=0,E>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [98] with precondition: [C=1,E=0,A>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [97] with precondition: [E=0,A>=0,C>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [96] with precondition: [E=0,A>=0,C>=2] 
    - Upper bound: 2*C 
    - Complexity: n 
* Chain [95] with precondition: [E=1,A>=2,C>=1] 
    - Upper bound: A+2 
    - Complexity: n 
* Chain [94] with precondition: [E=1,A>=2,C>=1,A+1>=C] 
    - Upper bound: A+2 
    - Complexity: n 
* Chain [93] with precondition: [E=1,A>=2,C>=A+2] 
    - Upper bound: A+2*C+2 
    - Complexity: n 
* Chain [92] with precondition: [E=1,A>=2,C>=A+3] 
    - Upper bound: C+2 
    - Complexity: n 
* Chain [91] with precondition: [0>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [90] with precondition: [0>=C+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [89] with precondition: [0>=E+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [88] with precondition: [A>=1,C>=1,E>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [87] with precondition: [A>=2,C>=1,E>=1] 
    - Upper bound: 2*A+1 
    - Complexity: n 
* Chain [86] with precondition: [A>=2,C>=1,E>=2] 
    - Upper bound: 2*A+2*E+2 
    - Complexity: n 
* Chain [85] with precondition: [A>=2,C>=1,E>=2,A+1>=C] 
    - Upper bound: A+E+2 
    - Complexity: n 
* Chain [84] with precondition: [A>=2,E>=2,C>=A+2] 
    - Upper bound: 3*A+4*E+2+(-A+C)*(2*E)+(-2*A+2*C) 
    - Complexity: n^2 
* Chain [83] with precondition: [A>=2,E>=2,C>=A+3] 
    - Upper bound: A+2*E+2+(-A+C)*(2*E)+(-2*A+2*C) 
    - Complexity: n^2 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,K,L,M): max([max([max([2,nat(A)+1+max([nat(-A+C)+1,nat(A)+1+nat(-A+C)*2+nat(A)])]),nat(C)+max([2,nat(C)+2])]),nat(E)+1+max([max([1,nat(A)+1]),nat(E)+1+max([nat(A)+max([nat(E)*2*nat(-A+C)+nat(-A+C)*2,nat(E)*2+nat(A)+nat(E)*2*nat(-A+C)+nat(-A+C)*2+nat(A)]),nat(C)*2*nat(E)+nat(C)*2+nat(E)*2])])]) 
Asymptotic class: n^2 
* Total analysis performed in 5788 ms.