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


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


WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. non_recursive  : [eval_p1_stop/13]
1. non_recursive  : [eval_p1_20/13]
2. non_recursive  : [eval_p1_19/13]
3. non_recursive  : [eval_p1_bb12_in/13]
4. recursive  : [eval_p1_10/10,eval_p1_11/10,eval_p1_7/10,eval_p1_8/10,eval_p1_bb3_in/10,eval_p1_bb4_in/10,eval_p1_bb5_in/10]
5. recursive  : [eval_p1__critedge_in/15,eval_p1_bb2_in/15,eval_p1_bb3_in_loop_cont/16]
6. recursive  : [eval_p1_14/5,eval_p1_15/5,eval_p1_bb8_in/5,eval_p1_bb9_in/5]
7. recursive  : [eval_p1_bb6_in/8,eval_p1_bb7_in/8,eval_p1_bb8_in_loop_cont/9]
8. non_recursive  : [eval_p1_bb10_in/13]
9. non_recursive  : [exit_location/1]
10. non_recursive  : [eval_p1_bb6_in_loop_cont/14]
11. non_recursive  : [eval_p1__critedge_in_loop_cont/14]
12. non_recursive  : [eval_p1_18/13]
13. non_recursive  : [eval_p1_17/13]
14. non_recursive  : [eval_p1_bb11_in/13]
15. non_recursive  : [eval_p1_bb1_in/13]
16. non_recursive  : [eval_p1_3/13]
17. non_recursive  : [eval_p1_2/13]
18. non_recursive  : [eval_p1_1/13]
19. non_recursive  : [eval_p1_0/13]
20. non_recursive  : [eval_p1_bb0_in/13]
21. non_recursive  : [eval_p1_start/13]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_p1_bb3_in/10
5. SCC is partially evaluated into eval_p1__critedge_in/15
6. SCC is partially evaluated into eval_p1_bb8_in/5
7. SCC is partially evaluated into eval_p1_bb6_in/8
8. SCC is completely evaluated into other SCCs
9. SCC is completely evaluated into other SCCs
10. SCC is partially evaluated into eval_p1_bb6_in_loop_cont/14
11. SCC is partially evaluated into eval_p1__critedge_in_loop_cont/14
12. SCC is completely evaluated into other SCCs
13. SCC is completely evaluated into other SCCs
14. SCC is completely evaluated into other SCCs
15. SCC is partially evaluated into eval_p1_bb1_in/13
16. SCC is partially evaluated into eval_p1_3/13
17. SCC is completely evaluated into other SCCs
18. SCC is completely evaluated into other SCCs
19. SCC is completely evaluated into other SCCs
20. SCC is completely evaluated into other SCCs
21. SCC is partially evaluated into eval_p1_start/13

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

### Specialization of cost equations eval_p1_bb3_in/10 
* CE 15 is refined into CE [26] 
* CE 12 is refined into CE [27] 
* CE 16 is refined into CE [28] 
* CE 14 is refined into CE [29] 
* CE 13 is refined into CE [30] 


### Cost equations --> "Loop" of eval_p1_bb3_in/10 
* CEs [29] --> Loop 26 
* CEs [30] --> Loop 27 
* CEs [26] --> Loop 28 
* CEs [27] --> Loop 29 
* CEs [28] --> Loop 30 

### Ranking functions of CR eval_p1_bb3_in(V__0,V__01,V__1,V_6,V_8,B,C,D,E,F) 
* RF of phase [26,27]: [V__1]

#### Partial ranking functions of CR eval_p1_bb3_in(V__0,V__01,V__1,V_6,V_8,B,C,D,E,F) 
* Partial RF of phase [26,27]:
  - RF of loop [26:1,27:1]:
    V__1


### Specialization of cost equations eval_p1__critedge_in/15 
* CE 6 is refined into CE [31,32] 
* CE 9 is refined into CE [33] 
* CE 8 is refined into CE [34] 
* CE 7 is refined into CE [35,36,37,38] 


### Cost equations --> "Loop" of eval_p1__critedge_in/15 
* CEs [38] --> Loop 31 
* CEs [37] --> Loop 32 
* CEs [36] --> Loop 33 
* CEs [35] --> Loop 34 
* CEs [31] --> Loop 35 
* CEs [32] --> Loop 36 
* CEs [33] --> Loop 37 
* CEs [34] --> Loop 38 

### Ranking functions of CR eval_p1__critedge_in(V__0,V__01,V__1,V__2,V_3,V_6,V_8,B,C,D,E,F,G,H,I) 
* RF of phase [32,33,34]: [V__0]

#### Partial ranking functions of CR eval_p1__critedge_in(V__0,V__01,V__1,V__2,V_3,V_6,V_8,B,C,D,E,F,G,H,I) 
* Partial RF of phase [32,33,34]:
  - RF of loop [32:1,33:1,34:1]:
    V__0


### Specialization of cost equations eval_p1_bb8_in/5 
* CE 25 is refined into CE [39] 
* CE 24 is refined into CE [40] 
* CE 23 is refined into CE [41] 


### Cost equations --> "Loop" of eval_p1_bb8_in/5 
* CEs [41] --> Loop 39 
* CEs [39] --> Loop 40 
* CEs [40] --> Loop 41 

### Ranking functions of CR eval_p1_bb8_in(V__2,V_i_0,V_z,B,C) 
* RF of phase [39]: [-V_i_0+V_z]

#### Partial ranking functions of CR eval_p1_bb8_in(V__2,V_i_0,V_z,B,C) 
* Partial RF of phase [39]:
  - RF of loop [39:1]:
    -V_i_0+V_z


### Specialization of cost equations eval_p1_bb6_in/8 
* CE 19 is refined into CE [42] 
* CE 17 is refined into CE [43,44] 
* CE 20 is refined into CE [45] 
* CE 18 is refined into CE [46,47] 


### Cost equations --> "Loop" of eval_p1_bb6_in/8 
* CEs [47] --> Loop 42 
* CEs [46] --> Loop 43 
* CEs [42] --> Loop 44 
* CEs [44] --> Loop 45 
* CEs [43] --> Loop 46 
* CEs [45] --> Loop 47 

### Ranking functions of CR eval_p1_bb6_in(V__2,V_10,V_i_0,V_z,B,C,D,E) 
* RF of phase [42]: [V__2]
* RF of phase [43]: [V__2]

#### Partial ranking functions of CR eval_p1_bb6_in(V__2,V_10,V_i_0,V_z,B,C,D,E) 
* Partial RF of phase [42]:
  - RF of loop [42:1]:
    V__2
* Partial RF of phase [43]:
  - RF of loop [43:1]:
    V__2


### Specialization of cost equations eval_p1_bb6_in_loop_cont/14 
* CE 21 is refined into CE [48] 
* CE 22 is refined into CE [49] 


### Cost equations --> "Loop" of eval_p1_bb6_in_loop_cont/14 
* CEs [48] --> Loop 48 
* CEs [49] --> Loop 49 

### Ranking functions of CR eval_p1_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR eval_p1_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 


### Specialization of cost equations eval_p1__critedge_in_loop_cont/14 
* CE 10 is refined into CE [50] 
* CE 11 is refined into CE [51,52,53,54,55,56,57,58,59] 


### Cost equations --> "Loop" of eval_p1__critedge_in_loop_cont/14 
* CEs [50] --> Loop 50 
* CEs [51] --> Loop 51 
* CEs [56] --> Loop 52 
* CEs [55,58] --> Loop 53 
* CEs [54] --> Loop 54 
* CEs [53] --> Loop 55 
* CEs [52,57] --> Loop 56 
* CEs [59] --> Loop 57 

### Ranking functions of CR eval_p1__critedge_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR eval_p1__critedge_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 


### Specialization of cost equations eval_p1_bb1_in/13 
* CE 5 is refined into CE [60,61,62,63,64,65,66,67,68,69] 
* CE 4 is refined into CE [70] 


### Cost equations --> "Loop" of eval_p1_bb1_in/13 
* CEs [69] --> Loop 58 
* CEs [64,65] --> Loop 59 
* CEs [60,63,66,67,68] --> Loop 60 
* CEs [61,62] --> Loop 61 
* CEs [70] --> Loop 62 

### Ranking functions of CR eval_p1_bb1_in(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_p1_bb1_in(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 


### Specialization of cost equations eval_p1_3/13 
* CE 2 is refined into CE [71,72,73,74,75] 
* CE 3 is refined into CE [76] 


### Cost equations --> "Loop" of eval_p1_3/13 
* CEs [75] --> Loop 63 
* CEs [74] --> Loop 64 
* CEs [73] --> Loop 65 
* CEs [72] --> Loop 66 
* CEs [71] --> Loop 67 
* CEs [76] --> Loop 68 

### Ranking functions of CR eval_p1_3(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_p1_3(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 


### Specialization of cost equations eval_p1_start/13 
* CE 1 is refined into CE [77,78,79,80,81,82] 


### Cost equations --> "Loop" of eval_p1_start/13 
* CEs [82] --> Loop 69 
* CEs [81] --> Loop 70 
* CEs [80] --> Loop 71 
* CEs [79] --> Loop 72 
* CEs [78] --> Loop 73 
* CEs [77] --> Loop 74 

### Ranking functions of CR eval_p1_start(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_p1_start(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B) 


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

#### Cost of chains of eval_p1_bb3_in(V__0,V__01,V__1,V_6,V_8,B,C,D,E,F):
* Chain [[26,27],30]: 2*it(26)+0
  Such that:aux(3) =< V__1
it(26) =< aux(3)

  with precondition: [B=3,V__0>=1,V__1>=1,V__01+1>=V__1] 

* Chain [[26,27],29]: 2*it(26)+0
  Such that:aux(1) =< V__1
aux(2) =< V__1-D
it(26) =< aux(1)
it(26) =< aux(2)

  with precondition: [B=4,E=0,C=D,C=F,V__0>=1,C>=1,V__01+1>=V__1,V__1>=C+1] 

* Chain [[26,27],28]: 2*it(26)+0
  Such that:aux(4) =< V__1
it(26) =< aux(4)

  with precondition: [B=4,C=0,D=0,F=0,V__0>=1,V__1>=1,V__01+1>=V__1] 

* Chain [30]: 0
  with precondition: [B=3,V__0>=1,V__01+1>=V__1] 

* Chain [29]: 0
  with precondition: [B=4,E=0,F=V_8,V__1=C,V__1=D,V__0>=1,V__1>=1,V__01+1>=V__1] 

* Chain [28]: 0
  with precondition: [B=4,E=V_6,F=V_8,V__1=C,V__1=D,0>=V__1,V__0>=1,V__01+1>=V__1] 


#### Cost of chains of eval_p1__critedge_in(V__0,V__01,V__1,V__2,V_3,V_6,V_8,B,C,D,E,F,G,H,I):
* Chain [[32,33,34],38]: 2*it(32)+1*it(34)+2*s(11)+2*s(14)+0
  Such that:aux(7) =< V__0+V__01
aux(8) =< V__0+V__01-F
aux(10) =< V__0
it(32) =< aux(10)
it(34) =< aux(10)
s(12) =< aux(7)
it(34) =< aux(8)
s(12) =< aux(8)
s(13) =< it(32)*aux(7)
s(14) =< s(12)
s(11) =< s(13)
s(11) =< s(12)

  with precondition: [B=2,C=0,G=0,D=E,D=F,V__0>=1,V__01>=0,D>=0,V__0+V__01>=D] 

* Chain [[32,33,34],37]: 2*it(32)+1*it(34)+2*s(11)+2*s(14)+0
  Such that:aux(11) =< V__0
aux(12) =< V__0+V__01
it(32) =< aux(11)
it(34) =< aux(11)
it(34) =< aux(12)
s(13) =< it(32)*aux(12)
s(14) =< aux(12)
s(11) =< s(13)
s(11) =< aux(12)

  with precondition: [B=3,V__0>=1,V__01>=0] 

* Chain [[32,33,34],36]: 2*it(32)+1*it(34)+2*s(11)+2*s(14)+0
  Such that:aux(13) =< V__0
aux(14) =< V__0+V__01
it(32) =< aux(13)
it(34) =< aux(13)
it(34) =< aux(14)
s(13) =< it(32)*aux(14)
s(14) =< aux(14)
s(11) =< s(13)
s(11) =< aux(14)

  with precondition: [B=3,V__0>=2,V__01>=0] 

* Chain [[32,33,34],35]: 2*it(32)+1*it(34)+2*s(11)+4*s(14)+0
  Such that:aux(15) =< V__0
aux(16) =< V__0+V__01
s(14) =< aux(16)
it(32) =< aux(15)
it(34) =< aux(15)
it(34) =< aux(16)
s(13) =< it(32)*aux(16)
s(11) =< s(13)
s(11) =< aux(16)

  with precondition: [B=3,V__0>=2,V__01>=0] 

* Chain [37]: 0
  with precondition: [B=3,V__0>=0,V__01>=0] 

* Chain [36]: 0
  with precondition: [B=3,V__0>=1,V__01>=0] 

* Chain [35]: 2*s(17)+0
  Such that:s(16) =< V__01+1
s(17) =< s(16)

  with precondition: [B=3,V__0>=1,V__01>=0] 


#### Cost of chains of eval_p1_bb8_in(V__2,V_i_0,V_z,B,C):
* Chain [[39],41]: 1*it(39)+0
  Such that:it(39) =< -V_i_0+C

  with precondition: [B=2,V_z=C,V__2>=1,V_i_0>=0,V_z>=V_i_0+1] 

* Chain [[39],40]: 1*it(39)+0
  Such that:it(39) =< -V_i_0+V_z

  with precondition: [B=3,V__2>=1,V_i_0>=0,V_z>=V_i_0+1] 

* Chain [41]: 0
  with precondition: [B=2,V_i_0=C,V__2>=1,V_i_0>=0,V_i_0>=V_z] 

* Chain [40]: 0
  with precondition: [B=3,V__2>=1,V_i_0>=0] 


#### Cost of chains of eval_p1_bb6_in(V__2,V_10,V_i_0,V_z,B,C,D,E):
* Chain [[43],47]: 1*it(43)+0
  Such that:it(43) =< V__2

  with precondition: [B=3,0>=V_z,V__2>=1] 

* Chain [[43],46]: 1*it(43)+0
  Such that:it(43) =< V__2

  with precondition: [B=3,0>=V_z,V__2>=2] 

* Chain [[43],44]: 1*it(43)+0
  Such that:it(43) =< V__2

  with precondition: [B=5,C=0,D=0,E=0,0>=V_z,V__2>=1] 

* Chain [[42],47]: 1*it(42)+1*s(43)+0
  Such that:it(42) =< V__2
aux(19) =< V_z
s(43) =< it(42)*aux(19)

  with precondition: [B=3,V__2>=1,V_z>=1] 

* Chain [[42],46]: 1*it(42)+1*s(43)+0
  Such that:it(42) =< V__2
aux(19) =< V_z
s(43) =< it(42)*aux(19)

  with precondition: [B=3,V__2>=2,V_z>=1] 

* Chain [[42],45]: 1*it(42)+1*s(43)+1*s(44)+0
  Such that:it(42) =< V__2
aux(20) =< V_z
s(44) =< aux(20)
s(43) =< it(42)*aux(20)

  with precondition: [B=3,V__2>=2,V_z>=1] 

* Chain [[42],44]: 1*it(42)+1*s(43)+0
  Such that:it(42) =< V__2
aux(19) =< V_z
s(43) =< it(42)*aux(19)

  with precondition: [B=5,C=0,D=0,V_z=E,V__2>=1,V_z>=1] 

* Chain [47]: 0
  with precondition: [B=3] 

* Chain [46]: 0
  with precondition: [B=3,V__2>=1] 

* Chain [45]: 1*s(44)+0
  Such that:s(44) =< V_z

  with precondition: [B=3,V__2>=1,V_z>=1] 

* Chain [44]: 0
  with precondition: [B=5,D=V_10,E=V_i_0,V__2=C,0>=V__2] 


#### Cost of chains of eval_p1_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
* Chain [49]: 0
  with precondition: [A=3,K>=1,L>=1] 

* Chain [48]: 0
  with precondition: [A=5,K>=1,L>=1] 


#### Cost of chains of eval_p1__critedge_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
* Chain [57]: 0
  with precondition: [A=2,0>=E,K>=1,L>=1] 

* Chain [56]: 2*s(56)+0
  Such that:aux(24) =< E
s(56) =< aux(24)

  with precondition: [A=2,0>=M,E>=1,K>=1,L>=1] 

* Chain [55]: 1*s(58)+0
  Such that:s(58) =< E

  with precondition: [A=2,0>=M,E>=2,K>=1,L>=1] 

* Chain [54]: 0
  with precondition: [A=2,E>=1,K>=1,L>=1] 

* Chain [53]: 2*s(59)+1*s(61)+2*s(62)+0
  Such that:aux(25) =< E
aux(26) =< M
s(59) =< aux(25)
s(61) =< aux(26)
s(62) =< s(59)*aux(26)

  with precondition: [A=2,E>=1,K>=1,L>=1,M>=1] 

* Chain [52]: 2*s(68)+1*s(69)+2*s(70)+0
  Such that:s(66) =< E
s(67) =< M
s(68) =< s(66)
s(69) =< s(67)
s(70) =< s(68)*s(67)

  with precondition: [A=2,E>=2,K>=1,L>=1,M>=1] 

* Chain [51]: 0
  with precondition: [A=2,K>=1,L>=1] 

* Chain [50]: 0
  with precondition: [A=3,K>=1,L>=1] 


#### Cost of chains of eval_p1_bb1_in(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B):
* Chain [62]: 0
  with precondition: [0>=V_y,V_x>=1] 

* Chain [61]: 4*s(74)+2*s(75)+7*s(78)+4*s(79)+0
  Such that:aux(29) =< V_x
aux(30) =< V_x+V_y
s(78) =< aux(30)
s(74) =< aux(29)
s(75) =< aux(29)
s(75) =< aux(30)
s(77) =< s(74)*aux(30)
s(79) =< s(77)
s(79) =< aux(30)

  with precondition: [0>=V_z,V_x>=1,V_y>=1] 

* Chain [60]: 8*s(95)+4*s(96)+8*s(99)+8*s(100)+2*s(127)+0
  Such that:s(121) =< V_y+1
aux(34) =< V_x
aux(35) =< V_x+V_y
s(95) =< aux(34)
s(96) =< aux(34)
s(96) =< aux(35)
s(98) =< s(95)*aux(35)
s(99) =< aux(35)
s(100) =< s(98)
s(100) =< aux(35)
s(127) =< s(121)

  with precondition: [V_x>=1,V_y>=1] 

* Chain [59]: 4*s(131)+2*s(132)+8*s(135)+4*s(136)+2*s(140)+4*s(141)+0
  Such that:aux(38) =< V_x
aux(39) =< V_x+V_y
aux(40) =< V_z
s(135) =< aux(39)
s(140) =< aux(40)
s(141) =< s(135)*aux(40)
s(131) =< aux(38)
s(132) =< aux(38)
s(132) =< aux(39)
s(134) =< s(131)*aux(39)
s(136) =< s(134)
s(136) =< aux(39)

  with precondition: [V_x>=1,V_y>=1,V_z>=1] 

* Chain [58]: 6*s(158)+4*s(159)+2*s(160)+4*s(162)+0
  Such that:s(156) =< V_x
s(157) =< V_x+V_y
s(158) =< s(157)
s(159) =< s(156)
s(160) =< s(156)
s(160) =< s(157)
s(161) =< s(159)*s(157)
s(162) =< s(161)
s(162) =< s(157)

  with precondition: [V_x>=2,V_y>=1] 


#### Cost of chains of eval_p1_3(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B):
* Chain [68]: 0
  with precondition: [0>=V_x] 

* Chain [67]: 0
  with precondition: [0>=V_y,V_x>=1] 

* Chain [66]: 7*s(165)+4*s(166)+2*s(167)+4*s(169)+0
  Such that:s(163) =< V_x
s(164) =< V_x+V_y
s(165) =< s(164)
s(166) =< s(163)
s(167) =< s(163)
s(167) =< s(164)
s(168) =< s(166)*s(164)
s(169) =< s(168)
s(169) =< s(164)

  with precondition: [0>=V_z,V_x>=1,V_y>=1] 

* Chain [65]: 8*s(173)+4*s(174)+8*s(176)+8*s(177)+2*s(178)+0
  Such that:s(171) =< V_x
s(172) =< V_x+V_y
s(170) =< V_y+1
s(173) =< s(171)
s(174) =< s(171)
s(174) =< s(172)
s(175) =< s(173)*s(172)
s(176) =< s(172)
s(177) =< s(175)
s(177) =< s(172)
s(178) =< s(170)

  with precondition: [V_x>=1,V_y>=1] 

* Chain [64]: 8*s(182)+2*s(183)+4*s(184)+4*s(185)+2*s(186)+4*s(188)+0
  Such that:s(179) =< V_x
s(180) =< V_x+V_y
s(181) =< V_z
s(182) =< s(180)
s(183) =< s(181)
s(184) =< s(182)*s(181)
s(185) =< s(179)
s(186) =< s(179)
s(186) =< s(180)
s(187) =< s(185)*s(180)
s(188) =< s(187)
s(188) =< s(180)

  with precondition: [V_x>=1,V_y>=1,V_z>=1] 

* Chain [63]: 6*s(191)+4*s(192)+2*s(193)+4*s(195)+0
  Such that:s(189) =< V_x
s(190) =< V_x+V_y
s(191) =< s(190)
s(192) =< s(189)
s(193) =< s(189)
s(193) =< s(190)
s(194) =< s(192)*s(190)
s(195) =< s(194)
s(195) =< s(190)

  with precondition: [V_x>=2,V_y>=1] 


#### Cost of chains of eval_p1_start(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B):
* Chain [74]: 0
  with precondition: [0>=V_x] 

* Chain [73]: 0
  with precondition: [0>=V_y,V_x>=1] 

* Chain [72]: 7*s(198)+4*s(199)+2*s(200)+4*s(202)+0
  Such that:s(196) =< V_x
s(197) =< V_x+V_y
s(198) =< s(197)
s(199) =< s(196)
s(200) =< s(196)
s(200) =< s(197)
s(201) =< s(199)*s(197)
s(202) =< s(201)
s(202) =< s(197)

  with precondition: [0>=V_z,V_x>=1,V_y>=1] 

* Chain [71]: 8*s(206)+4*s(207)+8*s(209)+8*s(210)+2*s(211)+0
  Such that:s(203) =< V_x
s(204) =< V_x+V_y
s(205) =< V_y+1
s(206) =< s(203)
s(207) =< s(203)
s(207) =< s(204)
s(208) =< s(206)*s(204)
s(209) =< s(204)
s(210) =< s(208)
s(210) =< s(204)
s(211) =< s(205)

  with precondition: [V_x>=1,V_y>=1] 

* Chain [70]: 8*s(215)+2*s(216)+4*s(217)+4*s(218)+2*s(219)+4*s(221)+0
  Such that:s(212) =< V_x
s(213) =< V_x+V_y
s(214) =< V_z
s(215) =< s(213)
s(216) =< s(214)
s(217) =< s(215)*s(214)
s(218) =< s(212)
s(219) =< s(212)
s(219) =< s(213)
s(220) =< s(218)*s(213)
s(221) =< s(220)
s(221) =< s(213)

  with precondition: [V_x>=1,V_y>=1,V_z>=1] 

* Chain [69]: 6*s(224)+4*s(225)+2*s(226)+4*s(228)+0
  Such that:s(222) =< V_x
s(223) =< V_x+V_y
s(224) =< s(223)
s(225) =< s(222)
s(226) =< s(222)
s(226) =< s(223)
s(227) =< s(225)*s(223)
s(228) =< s(227)
s(228) =< s(223)

  with precondition: [V_x>=2,V_y>=1] 


Closed-form bounds of eval_p1_start(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B): 
-------------------------------------
* Chain [74] with precondition: [0>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [73] with precondition: [0>=V_y,V_x>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [72] with precondition: [0>=V_z,V_x>=1,V_y>=1] 
    - Upper bound: 17*V_x+11*V_y 
    - Complexity: n 
* Chain [71] with precondition: [V_x>=1,V_y>=1] 
    - Upper bound: 28*V_x+18*V_y+2 
    - Complexity: n 
* Chain [70] with precondition: [V_x>=1,V_y>=1,V_z>=1] 
    - Upper bound: 6*V_x+2*V_z+(V_x+V_y)*(4*V_z)+(12*V_x+12*V_y) 
    - Complexity: n^2 
* Chain [69] with precondition: [V_x>=2,V_y>=1] 
    - Upper bound: 16*V_x+10*V_y 
    - Complexity: n 

### Maximum cost of eval_p1_start(V__0,V__01,V__1,V__2,V_10,V_3,V_6,V_8,V_i_0,V_x,V_y,V_z,B): nat(V_x+V_y)+max([nat(V_z)*4*nat(V_x+V_y)+nat(V_z)*2,nat(V_x+V_y)*4+nat(V_x)*6+nat(V_y+1)*2])+nat(V_x+V_y)+(nat(V_x+V_y)*10+nat(V_x)*6) 
Asymptotic class: n^2 
* Total analysis performed in 1166 ms.