/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_start_bb3_in/6,eval_start_bb4_in/6]
1. recursive  : [eval_start_bb1_in/9,eval_start_bb2_in/9,eval_start_bb3_in_loop_cont/10]
2. non_recursive  : [eval_start_stop/7]
3. non_recursive  : [eval_start_bb5_in/7]
4. non_recursive  : [exit_location/1]
5. non_recursive  : [eval_start_bb1_in_loop_cont/8]
6. non_recursive  : [eval_start_5/7]
7. non_recursive  : [eval_start_4/7]
8. non_recursive  : [eval_start_3/7]
9. non_recursive  : [eval_start_2/7]
10. non_recursive  : [eval_start_1/7]
11. non_recursive  : [eval_start_0/7]
12. non_recursive  : [eval_start_bb0_in/7]
13. non_recursive  : [eval_start_start/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_start_bb3_in/6
1. SCC is partially evaluated into eval_start_bb1_in/9
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/8
6. SCC is partially evaluated into eval_start_5/7
7. SCC is completely evaluated into other SCCs
8. SCC is completely evaluated into other SCCs
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 partially evaluated into eval_start_start/7

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

### Specialization of cost equations eval_start_bb3_in/6 
* CE 11 is refined into CE [12] 
* CE 10 is refined into CE [13] 
* CE 9 is refined into CE [14] 


### Cost equations --> "Loop" of eval_start_bb3_in/6 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_start_bb3_in(V__0,V__01,V__1,B,C,D) 
* RF of phase [12]: [V__1/100-99/100]

#### Partial ranking functions of CR eval_start_bb3_in(V__0,V__01,V__1,B,C,D) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V__1/100-99/100


### Specialization of cost equations eval_start_bb1_in/9 
* CE 5 is refined into CE [15] 
* CE 3 is refined into CE [16,17] 
* CE 6 is refined into CE [18] 
* CE 4 is refined into CE [19,20] 


### Cost equations --> "Loop" of eval_start_bb1_in/9 
* CEs [20] --> Loop 15 
* CEs [19] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [18] --> Loop 20 

### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,V_1,B,C,D,E,F) 
* RF of phase [15]: [-V__0]
* RF of phase [16]: [-V__0,-V__01/1000-9/10]

#### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,V_1,B,C,D,E,F) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -V__0
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    -V__0
    -V__01/1000-9/10


### Specialization of cost equations eval_start_bb1_in_loop_cont/8 
* CE 7 is refined into CE [21] 
* CE 8 is refined into CE [22] 


### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/8 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations eval_start_5/7 
* CE 2 is refined into CE [23,24,25,26,27,28,29,30,31,32,33,34] 


### Cost equations --> "Loop" of eval_start_5/7 
* CEs [34] --> Loop 23 
* CEs [30] --> Loop 24 
* CEs [29] --> Loop 25 
* CEs [28,32] --> Loop 26 
* CEs [27] --> Loop 27 
* CEs [33] --> Loop 28 
* CEs [26,31] --> Loop 29 
* CEs [25] --> Loop 30 
* CEs [24] --> Loop 31 
* CEs [23] --> Loop 32 

### Ranking functions of CR eval_start_5(V__0,V__01,V__1,V_1,V_n,V_y,B) 

#### Partial ranking functions of CR eval_start_5(V__0,V__01,V__1,V_1,V_n,V_y,B) 


### Specialization of cost equations eval_start_start/7 
* CE 1 is refined into CE [35,36,37,38,39,40,41,42,43,44] 


### Cost equations --> "Loop" of eval_start_start/7 
* CEs [44] --> Loop 33 
* CEs [43] --> Loop 34 
* CEs [42] --> Loop 35 
* CEs [41] --> Loop 36 
* CEs [40] --> Loop 37 
* CEs [39] --> Loop 38 
* CEs [38] --> Loop 39 
* CEs [37] --> Loop 40 
* CEs [36] --> Loop 41 
* CEs [35] --> Loop 42 

### Ranking functions of CR eval_start_start(V__0,V__01,V__1,V_1,V_n,V_y,B) 

#### Partial ranking functions of CR eval_start_start(V__0,V__01,V__1,V_1,V_n,V_y,B) 


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

#### Cost of chains of eval_start_bb3_in(V__0,V__01,V__1,B,C,D):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< V__1/100-D/100

  with precondition: [B=2,C=D,0>=V__0+1,99>=C,C>=0,V__01+1000>=V__1,V__1>=C+100] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< V__1/100

  with precondition: [B=3,0>=V__0+1,V__1>=100,V__01+1000>=V__1] 

* Chain [14]: 0
  with precondition: [B=2,V__1=C,V__1=D,0>=V__0+1,99>=V__1,V__01+1000>=V__1] 

* Chain [13]: 0
  with precondition: [B=3,0>=V__0+1,V__01+1000>=V__1] 


#### Cost of chains of eval_start_bb1_in(V__0,V__01,V__1,V_1,B,C,D,E,F):
* Chain [[16],[15],20]: 1*it(15)+1*it(16)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100
it(16) =< -V__01/1000
aux(1) =< -V__0
it(15) =< aux(1)
it(16) =< aux(1)

  with precondition: [B=3,0>=V__0+2,0>=V__01+901,V__01>=1000*V__0+100] 

* Chain [[16],[15],19]: 1*it(15)+1*it(16)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100
it(16) =< -V__01/1000
aux(2) =< -V__0
it(15) =< aux(2)
it(16) =< aux(2)

  with precondition: [B=3,0>=V__0+3,0>=V__01+901,V__01>=1000*V__0+1100] 

* Chain [[16],[15],18]: 1*it(15)+1*it(16)+1*s(3)+1*s(4)+0
  Such that:it(16) =< -V__01/1000
aux(4) =< -1000*V__0+V__01+1702
aux(5) =< -10*V__0+V__01/100
aux(6) =< -V__0
it(15) =< aux(4)
s(4) =< aux(4)
s(4) =< aux(5)
it(15) =< aux(6)
it(16) =< aux(6)
s(3) =< aux(5)

  with precondition: [B=3,0>=V__0+3,0>=V__01+901,V__01>=1000*V__0+1100] 

* Chain [[16],[15],17]: 1*it(15)+1*it(16)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100-E/100
it(16) =< -V__01/1000
aux(7) =< -V__0
it(15) =< aux(7)
it(16) =< aux(7)

  with precondition: [B=4,C=0,F=0,D=E,0>=V__0+2,0>=V__01+901,99>=D,D>=0,V__01>=1000*V__0+D+100] 

* Chain [[16],20]: 1*it(16)+0
  Such that:it(16) =< -V__0
it(16) =< -V__01/1000

  with precondition: [B=3,0>=V__0+1,0>=V__01+901] 

* Chain [[16],19]: 1*it(16)+0
  Such that:it(16) =< -V__0
it(16) =< -V__01/1000

  with precondition: [B=3,0>=V__0+2,0>=V__01+901] 

* Chain [[16],18]: 1*it(16)+1*s(4)+0
  Such that:s(4) =< 1099/100
s(4) =< -10*V__0+V__01/100
it(16) =< -V__0
it(16) =< -V__01/1000

  with precondition: [B=3,0>=V__0+2,0>=V__01+901,V__01>=1000*V__0+100] 

* Chain [[16],17]: 1*it(16)+0
  Such that:it(16) =< -V__0
it(16) =< -V__0-D/1000

  with precondition: [B=4,C=0,F=0,D+1000*V__0=V__01,E+1000*V__0=V__01,0>=V__0+1,1000*V__0+99>=V__01] 

* Chain [[15],20]: 1*it(15)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100
it(15) =< -V__0

  with precondition: [B=3,0>=V__0+1,V__01+900>=0] 

* Chain [[15],19]: 1*it(15)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100
it(15) =< -V__0

  with precondition: [B=3,0>=V__0+2,V__01+900>=0] 

* Chain [[15],18]: 1*it(15)+1*s(3)+1*s(4)+0
  Such that:it(15) =< -V__0
s(4) =< -99/100*V__0+V__01/100+851/50
aux(3) =< -10*V__0+V__01/100
s(3) =< aux(3)
s(4) =< aux(3)

  with precondition: [B=3,0>=V__0+2,V__01+900>=0] 

* Chain [[15],17]: 1*it(15)+1*s(3)+0
  Such that:s(3) =< -10*V__0+V__01/100-D/100
it(15) =< -V__0

  with precondition: [B=4,C=0,F=0,D=E,0>=V__0+1,99>=D,V__01+900>=0,D>=0,V__01+801>=99*V__0+D] 

* Chain [20]: 0
  with precondition: [B=3] 

* Chain [19]: 0
  with precondition: [B=3,0>=V__0+1] 

* Chain [18]: 1*s(4)+0
  Such that:s(4) =< V__01/100+10

  with precondition: [B=3,0>=V__0+1,V__01+900>=0] 

* Chain [17]: 0
  with precondition: [B=4,D=V__01,E=V__1,F=V_1,V__0=C,V__0>=0] 


#### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H):
* Chain [22]: 0
  with precondition: [A=3] 

* Chain [21]: 0
  with precondition: [A=4] 


#### Cost of chains of eval_start_5(V__0,V__01,V__1,V_1,V_n,V_y,B):
* Chain [32]: 0
  with precondition: [] 

* Chain [31]: 0
  with precondition: [0>=V_n+1] 

* Chain [30]: 1*s(31)+0
  Such that:s(31) =< -V_n
s(31) =< -V_y/1000

  with precondition: [0>=V_n+1,0>=V_y+901] 

* Chain [29]: 2*s(32)+2*s(33)+1*s(34)+0
  Such that:s(34) =< V_y/100+10
aux(16) =< -10*V_n+V_y/100
aux(17) =< -V_n
s(32) =< aux(16)
s(33) =< aux(17)

  with precondition: [0>=V_n+1,V_y+900>=0] 

* Chain [28]: 1*s(37)+0
  Such that:s(37) =< -V_n
s(37) =< -V_y/1000

  with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 

* Chain [27]: 1*s(38)+0
  Such that:s(38) =< -V_n
s(38) =< -V_y/1000

  with precondition: [0>=V_n+2,0>=V_y+901] 

* Chain [26]: 1*s(39)+2*s(43)+3*s(44)+2*s(45)+0
  Such that:s(39) =< 1099/100
aux(18) =< -10*V_n+V_y/100
aux(19) =< -V_n
aux(20) =< -V_y/1000
s(43) =< aux(18)
s(44) =< aux(20)
s(39) =< aux(18)
s(44) =< aux(19)
s(45) =< aux(19)

  with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 

* Chain [25]: 1*s(50)+2*s(53)+2*s(54)+0
  Such that:s(51) =< -10*V_n+V_y/100
s(52) =< -V_n
s(50) =< -99/100*V_n+V_y/100+851/50
s(53) =< s(51)
s(54) =< s(52)
s(50) =< s(51)

  with precondition: [0>=V_n+2,V_y+900>=0] 

* Chain [24]: 2*s(59)+2*s(60)+1*s(61)+1*s(62)+1*s(63)+0
  Such that:s(55) =< -1000*V_n+V_y+1702
s(56) =< -10*V_n+V_y/100
s(57) =< -V_n
s(58) =< -V_y/1000
s(59) =< s(56)
s(60) =< s(58)
s(61) =< s(57)
s(60) =< s(57)
s(62) =< s(55)
s(63) =< s(55)
s(63) =< s(56)
s(62) =< s(57)

  with precondition: [0>=V_n+3,0>=V_y+901,V_y>=1000*V_n+1100] 

* Chain [23]: 0
  with precondition: [V_n>=0] 


#### Cost of chains of eval_start_start(V__0,V__01,V__1,V_1,V_n,V_y,B):
* Chain [42]: 0
  with precondition: [] 

* Chain [41]: 0
  with precondition: [0>=V_n+1] 

* Chain [40]: 1*s(64)+0
  Such that:s(64) =< -V_n
s(64) =< -V_y/1000

  with precondition: [0>=V_n+1,0>=V_y+901] 

* Chain [39]: 1*s(65)+2*s(68)+2*s(69)+0
  Such that:s(66) =< -10*V_n+V_y/100
s(67) =< -V_n
s(65) =< V_y/100+10
s(68) =< s(66)
s(69) =< s(67)

  with precondition: [0>=V_n+1,V_y+900>=0] 

* Chain [38]: 1*s(70)+0
  Such that:s(70) =< -V_n
s(70) =< -V_y/1000

  with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 

* Chain [37]: 1*s(71)+0
  Such that:s(71) =< -V_n
s(71) =< -V_y/1000

  with precondition: [0>=V_n+2,0>=V_y+901] 

* Chain [36]: 1*s(72)+2*s(76)+3*s(77)+2*s(78)+0
  Such that:s(72) =< 1099/100
s(73) =< -10*V_n+V_y/100
s(74) =< -V_n
s(75) =< -V_y/1000
s(76) =< s(73)
s(77) =< s(75)
s(72) =< s(73)
s(77) =< s(74)
s(78) =< s(74)

  with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 

* Chain [35]: 1*s(81)+2*s(82)+2*s(83)+0
  Such that:s(79) =< -10*V_n+V_y/100
s(80) =< -V_n
s(81) =< -99/100*V_n+V_y/100+851/50
s(82) =< s(79)
s(83) =< s(80)
s(81) =< s(79)

  with precondition: [0>=V_n+2,V_y+900>=0] 

* Chain [34]: 2*s(88)+2*s(89)+1*s(90)+1*s(91)+1*s(92)+0
  Such that:s(84) =< -1000*V_n+V_y+1702
s(85) =< -10*V_n+V_y/100
s(86) =< -V_n
s(87) =< -V_y/1000
s(88) =< s(85)
s(89) =< s(87)
s(90) =< s(86)
s(89) =< s(86)
s(91) =< s(84)
s(92) =< s(84)
s(92) =< s(85)
s(91) =< s(86)

  with precondition: [0>=V_n+3,0>=V_y+901,V_y>=1000*V_n+1100] 

* Chain [33]: 0
  with precondition: [V_n>=0] 


Closed-form bounds of eval_start_start(V__0,V__01,V__1,V_1,V_n,V_y,B): 
-------------------------------------
* Chain [42] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [41] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [0>=V_n+1,0>=V_y+901] 
    - Upper bound: -V_n 
    - Complexity: n 
* Chain [39] with precondition: [0>=V_n+1,V_y+900>=0] 
    - Upper bound: -22*V_n+3/100*V_y+10 
    - Complexity: n 
* Chain [38] with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 
    - Upper bound: -V_n 
    - Complexity: n 
* Chain [37] with precondition: [0>=V_n+2,0>=V_y+901] 
    - Upper bound: -V_n 
    - Complexity: n 
* Chain [36] with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 
    - Upper bound: -22*V_n+17/1000*V_y+1099/100 
    - Complexity: n 
* Chain [35] with precondition: [0>=V_n+2,V_y+900>=0] 
    - Upper bound: -2299/100*V_n+3/100*V_y+851/50 
    - Complexity: n 
* Chain [34] with precondition: [0>=V_n+3,0>=V_y+901,V_y>=1000*V_n+1100] 
    - Upper bound: -2021*V_n+1009/500*V_y+3404 
    - Complexity: n 
* Chain [33] with precondition: [V_n>=0] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_start_start(V__0,V__01,V__1,V_1,V_n,V_y,B): nat(-10*V_n+V_y/100)*2+max([nat(-V_n)+max([nat(-99/100*V_n+V_y/100+851/50),nat(V_y/100+10),1099/100+nat(-V_y/1000)*3]),nat(-V_y/1000)*2+nat(-1000*V_n+V_y+1702)*2])+nat(-V_n) 
Asymptotic class: n 
* Total analysis performed in 501 ms.