/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^4))  

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

#### Computed strongly connected components 
0. recursive  : [eval_abc_bb4_in/5,eval_abc_bb5_in/5]
1. recursive  : [eval_abc_bb3_in/8,eval_abc_bb4_in_loop_cont/9]
2. recursive  : [eval_abc_12/13,eval_abc_13/13,eval_abc_bb2_in/13,eval_abc_bb3_in_loop_cont/14,eval_abc_bb6_in/13]
3. recursive  : [eval_abc_15/16,eval_abc_16/16,eval_abc_bb1_in/16,eval_abc_bb2_in_loop_cont/17,eval_abc_bb7_in/16]
4. non_recursive  : [eval_abc_stop/9]
5. non_recursive  : [eval_abc_bb8_in/9]
6. non_recursive  : [exit_location/1]
7. non_recursive  : [eval_abc_bb1_in_loop_cont/10]
8. non_recursive  : [eval_abc_6/9]
9. non_recursive  : [eval_abc_5/9]
10. non_recursive  : [eval_abc_4/9]
11. non_recursive  : [eval_abc_3/9]
12. non_recursive  : [eval_abc_2/9]
13. non_recursive  : [eval_abc_1/9]
14. non_recursive  : [eval_abc_0/9]
15. non_recursive  : [eval_abc_bb0_in/9]
16. non_recursive  : [eval_abc_start/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_abc_bb4_in/5
1. SCC is partially evaluated into eval_abc_bb3_in/8
2. SCC is partially evaluated into eval_abc_bb2_in/13
3. SCC is partially evaluated into eval_abc_bb1_in/16
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is completely evaluated into other SCCs
7. SCC is partially evaluated into eval_abc_bb1_in_loop_cont/10
8. SCC is partially evaluated into eval_abc_6/9
9. SCC is completely evaluated into other SCCs
10. SCC is completely evaluated into other SCCs
11. SCC is completely evaluated into other SCCs
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 completely evaluated into other SCCs
16. SCC is partially evaluated into eval_abc_start/9

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

### Specialization of cost equations eval_abc_bb4_in/5 
* CE 19 is refined into CE [20] 
* CE 18 is refined into CE [21] 
* CE 17 is refined into CE [22] 


### Cost equations --> "Loop" of eval_abc_bb4_in/5 
* CEs [22] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [21] --> Loop 22 

### Ranking functions of CR eval_abc_bb4_in(V_2,V_i_0_sink,V_l_0,B,C) 
* RF of phase [20]: [V_2-V_l_0+1,V_i_0_sink-V_l_0+2]

#### Partial ranking functions of CR eval_abc_bb4_in(V_2,V_i_0_sink,V_l_0,B,C) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    V_2-V_l_0+1
    V_i_0_sink-V_l_0+2


### Specialization of cost equations eval_abc_bb3_in/8 
* CE 15 is refined into CE [23] 
* CE 13 is refined into CE [24,25] 
* CE 16 is refined into CE [26] 
* CE 14 is refined into CE [27] 


### Cost equations --> "Loop" of eval_abc_bb3_in/8 
* CEs [27] --> Loop 23 
* CEs [23] --> Loop 24 
* CEs [24,25] --> Loop 25 
* CEs [26] --> Loop 26 

### Ranking functions of CR eval_abc_bb3_in(V_2,V_i_0_sink,V_l_0,V_m,B,C,D,E) 
* RF of phase [23]: [-V_i_0_sink+V_m]

#### Partial ranking functions of CR eval_abc_bb3_in(V_2,V_i_0_sink,V_l_0,V_m,B,C,D,E) 
* Partial RF of phase [23]:
  - RF of loop [23:1]:
    -V_i_0_sink+V_m


### Specialization of cost equations eval_abc_bb2_in/13 
* CE 11 is refined into CE [28] 
* CE 9 is refined into CE [29,30,31] 
* CE 12 is refined into CE [32] 
* CE 10 is refined into CE [33,34] 


### Cost equations --> "Loop" of eval_abc_bb2_in/13 
* CEs [34] --> Loop 27 
* CEs [33] --> Loop 28 
* CEs [28] --> Loop 29 
* CEs [31] --> Loop 30 
* CEs [30] --> Loop 31 
* CEs [29] --> Loop 32 
* CEs [32] --> Loop 33 

### Ranking functions of CR eval_abc_bb2_in(V_2,V_6,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G) 
* RF of phase [27]: [V_i_0-V_j_0+1,-V_j_0+V_m]
* RF of phase [28]: [V_i_0-V_j_0+1,-V_j_0+V_m+1]

#### Partial ranking functions of CR eval_abc_bb2_in(V_2,V_6,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G) 
* Partial RF of phase [27]:
  - RF of loop [27:1]:
    V_i_0-V_j_0+1
    -V_j_0+V_m
* Partial RF of phase [28]:
  - RF of loop [28:1]:
    V_i_0-V_j_0+1
    -V_j_0+V_m+1


### Specialization of cost equations eval_abc_bb1_in/16 
* CE 5 is refined into CE [35] 
* CE 3 is refined into CE [36,37,38,39,40,41,42,43] 
* CE 6 is refined into CE [44] 
* CE 4 is refined into CE [45,46] 


### Cost equations --> "Loop" of eval_abc_bb1_in/16 
* CEs [45] --> Loop 34 
* CEs [46] --> Loop 35 
* CEs [35] --> Loop 36 
* CEs [43] --> Loop 37 
* CEs [41] --> Loop 38 
* CEs [42] --> Loop 39 
* CEs [40] --> Loop 40 
* CEs [38,39] --> Loop 41 
* CEs [44] --> Loop 42 
* CEs [37] --> Loop 43 
* CEs [36] --> Loop 44 

### Ranking functions of CR eval_abc_bb1_in(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G,H,I) 
* RF of phase [35]: [-V_i_0+V_m]

#### Partial ranking functions of CR eval_abc_bb1_in(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G,H,I) 
* Partial RF of phase [35]:
  - RF of loop [35:1]:
    -V_i_0+V_m


### Specialization of cost equations eval_abc_bb1_in_loop_cont/10 
* CE 7 is refined into CE [47] 
* CE 8 is refined into CE [48] 


### Cost equations --> "Loop" of eval_abc_bb1_in_loop_cont/10 
* CEs [47] --> Loop 45 
* CEs [48] --> Loop 46 

### Ranking functions of CR eval_abc_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR eval_abc_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations eval_abc_6/9 
* CE 2 is refined into CE [49,50,51,52,53,54,55,56,57] 


### Cost equations --> "Loop" of eval_abc_6/9 
* CEs [54] --> Loop 47 
* CEs [53] --> Loop 48 
* CEs [52,57] --> Loop 49 
* CEs [51] --> Loop 50 
* CEs [55] --> Loop 51 
* CEs [49,56] --> Loop 52 
* CEs [50] --> Loop 53 

### Ranking functions of CR eval_abc_6(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B) 

#### Partial ranking functions of CR eval_abc_6(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B) 


### Specialization of cost equations eval_abc_start/9 
* CE 1 is refined into CE [58,59,60,61,62,63,64] 


### Cost equations --> "Loop" of eval_abc_start/9 
* CEs [64] --> Loop 54 
* CEs [63] --> Loop 55 
* CEs [62] --> Loop 56 
* CEs [61] --> Loop 57 
* CEs [60] --> Loop 58 
* CEs [59] --> Loop 59 
* CEs [58] --> Loop 60 

### Ranking functions of CR eval_abc_start(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B) 

#### Partial ranking functions of CR eval_abc_start(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B) 


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

#### Cost of chains of eval_abc_bb4_in(V_2,V_i_0_sink,V_l_0,B,C):
* Chain [[20],22]: 1*it(20)+0
  Such that:it(20) =< -V_l_0+C

  with precondition: [B=2,V_2=V_i_0_sink+1,V_2+1=C,V_2>=2,V_l_0>=1,V_2>=V_l_0] 

* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< V_2-V_l_0+1

  with precondition: [B=3,V_2=V_i_0_sink+1,V_2>=2,V_l_0>=1,V_2>=V_l_0] 

* Chain [21]: 0
  with precondition: [B=3,V_i_0_sink+1=V_2,V_i_0_sink>=1,V_l_0>=1] 


#### Cost of chains of eval_abc_bb3_in(V_2,V_i_0_sink,V_l_0,V_m,B,C,D,E):
* Chain [[23],26]: 1*it(23)+1*s(3)+0
  Such that:it(23) =< -V_i_0_sink+V_m
aux(1) =< V_m
s(3) =< it(23)*aux(1)

  with precondition: [B=3,V_i_0_sink>=1,V_m>=V_i_0_sink+1] 

* Chain [[23],25]: 1*it(23)+1*s(3)+1*s(4)+0
  Such that:it(23) =< -V_i_0_sink+V_m
aux(2) =< V_m
s(4) =< aux(2)
s(3) =< it(23)*aux(2)

  with precondition: [B=3,V_i_0_sink>=1,V_m>=V_i_0_sink+2] 

* Chain [[23],24]: 1*it(23)+1*s(3)+0
  Such that:it(23) =< -V_i_0_sink+C
aux(1) =< C
s(3) =< it(23)*aux(1)

  with precondition: [B=4,V_m+1=C,V_m=D,V_m+1=E,V_i_0_sink>=1,V_m>=V_i_0_sink+1] 

* Chain [26]: 0
  with precondition: [B=3,V_i_0_sink>=1,V_m>=V_i_0_sink] 

* Chain [25]: 1*s(4)+0
  Such that:s(4) =< V_i_0_sink+1

  with precondition: [B=3,V_i_0_sink>=1,V_m>=V_i_0_sink+1] 

* Chain [24]: 0
  with precondition: [B=4,V_m=V_i_0_sink,E=V_l_0,V_m+1=C,V_m=D,V_m>=1] 


#### Cost of chains of eval_abc_bb2_in(V_2,V_6,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G):
* Chain [[28],33]: 1*it(28)+0
  Such that:it(28) =< -V_j_0+V_m+1

  with precondition: [B=3,V_i_0=V_m,V_j_0>=1,V_i_0>=V_j_0] 

* Chain [[28],32]: 1*it(28)+0
  Such that:it(28) =< -V_j_0+V_m

  with precondition: [B=3,V_i_0=V_m,V_j_0>=1,V_i_0>=V_j_0+1] 

* Chain [[28],29]: 1*it(28)+0
  Such that:it(28) =< -V_j_0+C

  with precondition: [B=5,V_i_0=V_m,V_i_0+1=C,V_i_0+1=D,V_i_0=E,V_i_0+1=F,V_l_0=G,V_j_0>=1,V_i_0>=V_j_0] 

* Chain [[27],33]: 1*it(27)+1*s(15)+1*s(16)+0
  Such that:aux(3) =< -V_i_0+V_m+1
it(27) =< V_i_0-V_j_0+1
s(12) =< V_m+1
s(15) =< it(27)*aux(3)
s(16) =< s(15)*s(12)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+1,V_i_0>=V_j_0] 

* Chain [[27],32]: 1*it(27)+1*s(15)+1*s(16)+0
  Such that:aux(3) =< -V_i_0+V_m+1
it(27) =< V_i_0-V_j_0
s(12) =< V_m+1
s(15) =< it(27)*aux(3)
s(16) =< s(15)*s(12)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+1,V_i_0>=V_j_0+1] 

* Chain [[27],31]: 1*it(27)+1*s(15)+1*s(16)+1*s(17)+1*s(18)+1*s(20)+0
  Such that:s(17) =< -V_i_0+V_m
aux(3) =< -V_i_0+V_m+1
s(18) =< V_i_0+1
it(27) =< V_i_0-V_j_0
s(19) =< V_m
s(12) =< V_m+1
s(20) =< s(17)*s(19)
s(15) =< it(27)*aux(3)
s(16) =< s(15)*s(12)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+1,V_i_0>=V_j_0+1] 

* Chain [[27],30]: 1*it(27)+1*s(15)+1*s(16)+1*s(21)+1*s(23)+1*s(24)+0
  Such that:s(21) =< -V_i_0+V_m
aux(3) =< -V_i_0+V_m+1
it(27) =< V_i_0-V_j_0
s(22) =< V_m
s(12) =< V_m+1
s(23) =< s(22)
s(24) =< s(21)*s(22)
s(15) =< it(27)*aux(3)
s(16) =< s(15)*s(12)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+2,V_i_0>=V_j_0+1] 

* Chain [[27],29]: 1*it(27)+1*s(15)+1*s(16)+0
  Such that:it(27) =< -V_j_0+D
s(12) =< C
aux(3) =< C-D+1
s(15) =< it(27)*aux(3)
s(16) =< s(15)*s(12)

  with precondition: [B=5,V_m+1=C,V_i_0+1=D,V_m=E,V_i_0+1=F,V_m+1=G,V_j_0>=1,V_m>=V_i_0+1,V_i_0>=V_j_0] 

* Chain [33]: 0
  with precondition: [B=3,V_i_0>=1,V_j_0>=1,V_m>=V_i_0] 

* Chain [32]: 0
  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0,V_i_0>=V_j_0] 

* Chain [31]: 1*s(17)+1*s(18)+1*s(20)+0
  Such that:s(17) =< -V_i_0+V_m
s(18) =< V_i_0+1
s(19) =< V_m
s(20) =< s(17)*s(19)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+1,V_i_0>=V_j_0] 

* Chain [30]: 1*s(21)+1*s(23)+1*s(24)+0
  Such that:s(21) =< -V_i_0+V_m
s(22) =< V_m
s(23) =< s(22)
s(24) =< s(21)*s(22)

  with precondition: [B=3,V_j_0>=1,V_m>=V_i_0+2,V_i_0>=V_j_0] 


#### Cost of chains of eval_abc_bb1_in(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B,C,D,E,F,G,H,I):
* Chain [[35],44]: 1*it(35)+1*s(48)+1*s(59)+1*s(60)+1*s(61)+0
  Such that:it(35) =< -V_i_0+V_m
aux(9) =< V_m
s(48) =< aux(9)
aux(7) =< aux(9)
aux(7) =< aux(9)
s(54) =< aux(9)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(9)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [[35],43]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(62)+0
  Such that:it(35) =< -V_i_0+V_m
aux(10) =< V_m
s(62) =< aux(10)
aux(7) =< aux(10)
aux(7) =< aux(10)
s(54) =< aux(10)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(10)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [[35],42]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+0
  Such that:it(35) =< -V_i_0+V_m
aux(8) =< V_m
aux(7) =< aux(8)
aux(7) =< aux(8)
s(54) =< aux(8)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(8)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [[35],41]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+0
  Such that:it(35) =< -V_i_0+V_m
aux(8) =< V_m
aux(7) =< aux(8)
aux(7) =< aux(8)
s(54) =< aux(8)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(8)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [[35],40]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(63)+1*s(65)+1*s(66)+1*s(69)+1*s(70)+1*s(71)+0
  Such that:it(35) =< -V_i_0+V_m+1
aux(11) =< -V_i_0+V_m
aux(12) =< V_m
aux(13) =< V_m+1
aux(14) =< V_m+2
it(35) =< aux(11)
s(63) =< aux(11)
s(66) =< aux(12)
s(63) =< aux(13)
s(64) =< aux(13)
s(65) =< aux(13)
s(66) =< aux(13)
s(64) =< aux(14)
s(65) =< aux(14)
s(69) =< s(63)*aux(12)
s(70) =< s(66)*s(64)
s(71) =< s(70)*aux(13)
aux(7) =< aux(12)
aux(7) =< aux(12)
s(54) =< aux(12)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(12)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+2] 

* Chain [[35],39]: 2*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(74)+1*s(75)+0
  Such that:aux(15) =< -V_i_0+V_m
aux(16) =< V_m
it(35) =< aux(15)
s(74) =< aux(16)
s(75) =< it(35)*aux(16)
aux(7) =< aux(16)
aux(7) =< aux(16)
s(54) =< aux(16)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(16)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+3] 

* Chain [[35],38]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(76)+1*s(77)+2*s(82)+1*s(83)+2*s(84)+2*s(85)+0
  Such that:it(35) =< -V_i_0+V_m
aux(17) =< -V_i_0+V_m+1
aux(18) =< V_m
aux(19) =< V_m+1
aux(20) =< V_m+2
it(35) =< aux(17)
s(79) =< aux(17)
s(76) =< aux(18)
s(80) =< aux(18)
s(76) =< aux(19)
s(77) =< aux(19)
s(80) =< aux(19)
s(77) =< aux(20)
s(79) =< aux(20)
s(82) =< s(80)
s(83) =< s(76)*aux(18)
s(84) =< s(82)*s(79)
s(85) =< s(84)*aux(19)
aux(7) =< aux(18)
aux(7) =< aux(18)
s(54) =< aux(18)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(18)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+2] 

* Chain [[35],37]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(86)+1*s(88)+1*s(91)+1*s(92)+1*s(93)+1*s(94)+0
  Such that:aux(21) =< -V_i_0+V_m
aux(22) =< -V_i_0+V_m+1
aux(23) =< V_m
aux(24) =< V_m+1
it(35) =< aux(21)
s(86) =< aux(21)
it(35) =< aux(22)
s(87) =< aux(22)
s(86) =< aux(23)
s(88) =< aux(23)
s(87) =< aux(24)
s(88) =< aux(24)
s(91) =< aux(23)
s(92) =< s(86)*aux(23)
s(93) =< s(88)*s(87)
s(94) =< s(93)*aux(24)
aux(7) =< aux(23)
aux(7) =< aux(23)
s(54) =< aux(23)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(23)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+3] 

* Chain [[35],34,42]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(95)+1
  Such that:it(35) =< -V_i_0+V_m
aux(8) =< V_m
s(95) =< V_m+1
aux(7) =< aux(8)
aux(7) =< aux(8)
s(54) =< aux(8)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(8)
s(61) =< s(60)*s(54)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [[35],34,36]: 1*it(35)+1*s(59)+1*s(60)+1*s(61)+1*s(95)+1
  Such that:it(35) =< -V_i_0+C
aux(25) =< C
s(95) =< aux(25)
aux(7) =< aux(25)
aux(7) =< aux(25)
s(54) =< aux(25)+1
s(59) =< it(35)*aux(7)
s(60) =< s(59)*aux(25)
s(61) =< s(60)*s(54)

  with precondition: [B=6,V_m+1=C,V_m+1=D,V_m+1=E,V_m+1=F,V_m=G,V_m+1=H,V_m+1=I,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [44]: 1*s(48)+0
  Such that:s(48) =< V_i_0

  with precondition: [B=3,V_i_0=V_m,V_i_0>=1] 

* Chain [42]: 0
  with precondition: [B=3,V_i_0>=1] 

* Chain [41]: 0
  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0] 

* Chain [40]: 1*s(63)+1*s(65)+1*s(66)+1*s(69)+1*s(70)+1*s(71)+0
  Such that:s(63) =< -V_i_0+V_m
s(64) =< -V_i_0+V_m+1
s(66) =< V_i_0
s(65) =< V_i_0+1
s(67) =< V_m
s(68) =< V_m+1
s(69) =< s(63)*s(67)
s(70) =< s(66)*s(64)
s(71) =< s(70)*s(68)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 

* Chain [39]: 1*s(72)+1*s(74)+1*s(75)+0
  Such that:s(72) =< -V_i_0+V_m
s(73) =< V_m
s(74) =< s(73)
s(75) =< s(72)*s(73)

  with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+2] 

* Chain [36]: 0
  with precondition: [B=6,C=V_2,D=V_6,E=V_7,G=V_i_0_sink,H=V_j_0,I=V_l_0,V_i_0=F,V_i_0>=1,V_i_0>=V_m+1] 

* Chain [34,42]: 1*s(95)+1
  Such that:s(95) =< V_m+1

  with precondition: [B=3,V_i_0=V_m,V_i_0>=1] 

* Chain [34,36]: 1*s(95)+1
  Such that:s(95) =< C

  with precondition: [B=6,V_i_0=V_m,V_i_0+1=C,V_i_0+1=D,V_i_0+1=E,V_i_0+1=F,V_i_0=G,V_i_0+1=H,V_l_0=I,V_i_0>=1] 


#### Cost of chains of eval_abc_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [46]: 0
  with precondition: [A=3] 

* Chain [45]: 0
  with precondition: [A=6] 


#### Cost of chains of eval_abc_6(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B):
* Chain [53]: 0
  with precondition: [] 

* Chain [52]: 6
  with precondition: [V_m=1] 

* Chain [51]: 0
  with precondition: [0>=V_m] 

* Chain [50]: 0
  with precondition: [V_m>=1] 

* Chain [49]: 1*s(215)+1*s(216)+9*s(220)+2*s(221)+1*s(222)+1*s(223)+1*s(224)+5*s(227)+5*s(228)+5*s(229)+1*s(236)+1*s(237)+1*s(238)+1
  Such that:s(215) =< 1
s(216) =< 2
aux(38) =< V_m
aux(39) =< V_m+1
s(220) =< aux(38)
s(221) =< aux(39)
s(222) =< s(220)*aux(38)
s(223) =< s(215)*aux(38)
s(224) =< s(223)*aux(39)
s(225) =< aux(38)
s(225) =< aux(38)
s(226) =< aux(38)+1
s(227) =< s(220)*s(225)
s(228) =< s(227)*aux(38)
s(229) =< s(228)*s(226)
s(234) =< aux(39)
s(234) =< aux(39)
s(235) =< aux(39)+1
s(236) =< s(220)*s(234)
s(237) =< s(236)*aux(39)
s(238) =< s(237)*s(235)

  with precondition: [V_m>=2] 

* Chain [48]: 4*s(244)+1*s(247)+3*s(249)+2*s(251)+2*s(252)+2*s(253)+2*s(254)+2*s(255)+2*s(258)+2*s(259)+2*s(260)+1*s(264)+1*s(265)+0
  Such that:s(242) =< V_m+1
s(243) =< V_m+2
aux(40) =< V_m
s(244) =< aux(40)
s(247) =< s(244)*aux(40)
s(248) =< aux(40)
s(249) =< aux(40)
s(250) =< aux(40)
s(249) =< s(242)
s(251) =< s(242)
s(250) =< s(242)
s(251) =< s(243)
s(248) =< s(243)
s(252) =< s(250)
s(253) =< s(249)*aux(40)
s(254) =< s(252)*s(248)
s(255) =< s(254)*s(242)
s(256) =< aux(40)
s(256) =< aux(40)
s(257) =< aux(40)+1
s(258) =< s(244)*s(256)
s(259) =< s(258)*aux(40)
s(260) =< s(259)*s(257)
s(262) =< s(242)
s(262) =< s(243)
s(264) =< s(249)*s(262)
s(265) =< s(264)*s(242)

  with precondition: [V_m>=3] 

* Chain [47]: 6*s(270)+1*s(273)+2*s(275)+1*s(276)+1*s(277)+2*s(280)+2*s(281)+2*s(282)+0
  Such that:s(267) =< V_m+1
aux(41) =< V_m
s(270) =< aux(41)
s(272) =< aux(41)
s(273) =< aux(41)
s(272) =< s(267)
s(273) =< s(267)
s(275) =< s(270)*aux(41)
s(276) =< s(273)*s(272)
s(277) =< s(276)*s(267)
s(278) =< aux(41)
s(278) =< aux(41)
s(279) =< aux(41)+1
s(280) =< s(270)*s(278)
s(281) =< s(280)*aux(41)
s(282) =< s(281)*s(279)

  with precondition: [V_m>=4] 


#### Cost of chains of eval_abc_start(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B):
* Chain [60]: 0
  with precondition: [] 

* Chain [59]: 6
  with precondition: [V_m=1] 

* Chain [58]: 0
  with precondition: [0>=V_m] 

* Chain [57]: 0
  with precondition: [V_m>=1] 

* Chain [56]: 1*s(288)+1*s(289)+9*s(292)+2*s(293)+1*s(294)+1*s(295)+1*s(296)+5*s(299)+5*s(300)+5*s(301)+1*s(304)+1*s(305)+1*s(306)+1
  Such that:s(288) =< 1
s(289) =< 2
s(290) =< V_m
s(291) =< V_m+1
s(292) =< s(290)
s(293) =< s(291)
s(294) =< s(292)*s(290)
s(295) =< s(288)*s(290)
s(296) =< s(295)*s(291)
s(297) =< s(290)
s(297) =< s(290)
s(298) =< s(290)+1
s(299) =< s(292)*s(297)
s(300) =< s(299)*s(290)
s(301) =< s(300)*s(298)
s(302) =< s(291)
s(302) =< s(291)
s(303) =< s(291)+1
s(304) =< s(292)*s(302)
s(305) =< s(304)*s(291)
s(306) =< s(305)*s(303)

  with precondition: [V_m>=2] 

* Chain [55]: 4*s(310)+1*s(311)+3*s(313)+2*s(315)+2*s(316)+2*s(317)+2*s(318)+2*s(319)+2*s(322)+2*s(323)+2*s(324)+1*s(326)+1*s(327)+0
  Such that:s(309) =< V_m
s(307) =< V_m+1
s(308) =< V_m+2
s(310) =< s(309)
s(311) =< s(310)*s(309)
s(312) =< s(309)
s(313) =< s(309)
s(314) =< s(309)
s(313) =< s(307)
s(315) =< s(307)
s(314) =< s(307)
s(315) =< s(308)
s(312) =< s(308)
s(316) =< s(314)
s(317) =< s(313)*s(309)
s(318) =< s(316)*s(312)
s(319) =< s(318)*s(307)
s(320) =< s(309)
s(320) =< s(309)
s(321) =< s(309)+1
s(322) =< s(310)*s(320)
s(323) =< s(322)*s(309)
s(324) =< s(323)*s(321)
s(325) =< s(307)
s(325) =< s(308)
s(326) =< s(313)*s(325)
s(327) =< s(326)*s(307)

  with precondition: [V_m>=3] 

* Chain [54]: 6*s(330)+1*s(332)+2*s(333)+1*s(334)+1*s(335)+2*s(338)+2*s(339)+2*s(340)+0
  Such that:s(329) =< V_m
s(328) =< V_m+1
s(330) =< s(329)
s(331) =< s(329)
s(332) =< s(329)
s(331) =< s(328)
s(332) =< s(328)
s(333) =< s(330)*s(329)
s(334) =< s(332)*s(331)
s(335) =< s(334)*s(328)
s(336) =< s(329)
s(336) =< s(329)
s(337) =< s(329)+1
s(338) =< s(330)*s(336)
s(339) =< s(338)*s(329)
s(340) =< s(339)*s(337)

  with precondition: [V_m>=4] 


Closed-form bounds of eval_abc_start(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B): 
-------------------------------------
* Chain [60] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [59] with precondition: [V_m=1] 
    - Upper bound: 6 
    - Complexity: constant 
* Chain [58] with precondition: [0>=V_m] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [57] with precondition: [V_m>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [56] with precondition: [V_m>=2] 
    - Upper bound: 10*V_m+4+6*V_m*V_m+10*V_m*V_m*V_m+5*V_m*V_m*V_m*V_m+(V_m+1)*(2*V_m)+(V_m+1)*((V_m+1)*(2*V_m))+(V_m+1)*((V_m+1)*((V_m+1)*V_m))+(2*V_m+2) 
    - Complexity: n^4 
* Chain [55] with precondition: [V_m>=3] 
    - Upper bound: 7*V_m*V_m+9*V_m+4*V_m*V_m*V_m+2*V_m*V_m*V_m*V_m+(V_m+1)*(2*V_m*V_m)+(V_m+1)*V_m+(V_m+1)*((V_m+1)*V_m)+(2*V_m+2) 
    - Complexity: n^4 
* Chain [54] with precondition: [V_m>=4] 
    - Upper bound: 5*V_m*V_m+7*V_m+4*V_m*V_m*V_m+2*V_m*V_m*V_m*V_m+(V_m+1)*(V_m*V_m) 
    - Complexity: n^4 

### Maximum cost of eval_abc_start(V_2,V_6,V_7,V_i_0,V_i_0_sink,V_j_0,V_l_0,V_m,B): max([6,nat(V_m)*5*nat(V_m)+nat(V_m)*7+nat(V_m)*4*nat(V_m)*nat(V_m)+nat(V_m)*2*nat(V_m)*nat(V_m)*nat(V_m)+max([nat(V_m)*nat(V_m)*nat(V_m+1),nat(V_m)*nat(V_m)+nat(V_m)*2+nat(V_m+1)*nat(V_m)+nat(V_m+1)*nat(V_m)*nat(V_m+1)+nat(V_m+1)*2+max([nat(V_m)*2*nat(V_m)*nat(V_m+1)+nat(V_m)*nat(V_m),nat(V_m)+4+nat(V_m)*6*nat(V_m)*nat(V_m)+nat(V_m)*3*nat(V_m)*nat(V_m)*nat(V_m)+nat(V_m+1)*nat(V_m)+nat(V_m+1)*nat(V_m)*nat(V_m+1)+nat(V_m+1)*nat(V_m)*nat(V_m+1)*nat(V_m+1)])])]) 
Asymptotic class: n^4 
* Total analysis performed in 1251 ms.