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


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WORST_CASE(?,O(1))  

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

#### Computed strongly connected components 
0. recursive  : [f15/5]
1. non_recursive  : [exit_location/1]
2. recursive  : [f25/5]
3. recursive  : [f33/5]
4. recursive  : [f42/5]
5. recursive  : [f52/5]
6. recursive  : [f60/3]
7. non_recursive  : [f69/8]
8. non_recursive  : [f60_loop_cont/9]
9. non_recursive  : [f52_loop_cont/9]
10. non_recursive  : [f42_loop_cont/9]
11. non_recursive  : [f33_loop_cont/9]
12. non_recursive  : [f25_loop_cont/9]
13. non_recursive  : [f15_loop_cont/9]
14. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f15/5
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f25/5
3. SCC is partially evaluated into f33/5
4. SCC is partially evaluated into f42/5
5. SCC is partially evaluated into f52/5
6. SCC is partially evaluated into f60/3
7. SCC is completely evaluated into other SCCs
8. SCC is partially evaluated into f60_loop_cont/9
9. SCC is partially evaluated into f52_loop_cont/9
10. SCC is partially evaluated into f42_loop_cont/9
11. SCC is partially evaluated into f33_loop_cont/9
12. SCC is partially evaluated into f25_loop_cont/9
13. SCC is partially evaluated into f15_loop_cont/9
14. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f15/5 
* CE 3 is refined into CE [32] 
* CE 4 is refined into CE [33] 
* CE 2 is refined into CE [34] 


### Cost equations --> "Loop" of f15/5 
* CEs [34] --> Loop 32 
* CEs [32] --> Loop 33 
* CEs [33] --> Loop 34 

### Ranking functions of CR f15(D,E,J,K,L) 
* RF of phase [32]: [-D+50]

#### Partial ranking functions of CR f15(D,E,J,K,L) 
* Partial RF of phase [32]:
  - RF of loop [32:1]:
    -D+50


### Specialization of cost equations f25/5 
* CE 8 is refined into CE [35] 
* CE 9 is refined into CE [36] 
* CE 7 is refined into CE [37] 


### Cost equations --> "Loop" of f25/5 
* CEs [37] --> Loop 35 
* CEs [35] --> Loop 36 
* CEs [36] --> Loop 37 

### Ranking functions of CR f25(A,E,J,K,L) 
* RF of phase [35]: [-E+50]

#### Partial ranking functions of CR f25(A,E,J,K,L) 
* Partial RF of phase [35]:
  - RF of loop [35:1]:
    -E+50


### Specialization of cost equations f33/5 
* CE 13 is refined into CE [38] 
* CE 14 is refined into CE [39] 
* CE 12 is refined into CE [40] 


### Cost equations --> "Loop" of f33/5 
* CEs [40] --> Loop 38 
* CEs [38] --> Loop 39 
* CEs [39] --> Loop 40 

### Ranking functions of CR f33(A,F,J,K,L) 
* RF of phase [38]: [-A+50]

#### Partial ranking functions of CR f33(A,F,J,K,L) 
* Partial RF of phase [38]:
  - RF of loop [38:1]:
    -A+50


### Specialization of cost equations f42/5 
* CE 18 is refined into CE [41] 
* CE 19 is refined into CE [42] 
* CE 17 is refined into CE [43] 


### Cost equations --> "Loop" of f42/5 
* CEs [43] --> Loop 41 
* CEs [41] --> Loop 42 
* CEs [42] --> Loop 43 

### Ranking functions of CR f42(F,G,J,K,L) 
* RF of phase [41]: [-F+50]

#### Partial ranking functions of CR f42(F,G,J,K,L) 
* Partial RF of phase [41]:
  - RF of loop [41:1]:
    -F+50


### Specialization of cost equations f52/5 
* CE 23 is refined into CE [44] 
* CE 24 is refined into CE [45] 
* CE 22 is refined into CE [46] 


### Cost equations --> "Loop" of f52/5 
* CEs [46] --> Loop 44 
* CEs [44] --> Loop 45 
* CEs [45] --> Loop 46 

### Ranking functions of CR f52(A,G,J,K,L) 
* RF of phase [44]: [-G+50]

#### Partial ranking functions of CR f52(A,G,J,K,L) 
* Partial RF of phase [44]:
  - RF of loop [44:1]:
    -G+50


### Specialization of cost equations f60/3 
* CE 29 is refined into CE [47] 
* CE 28 is refined into CE [48] 
* CE 27 is refined into CE [49] 


### Cost equations --> "Loop" of f60/3 
* CEs [49] --> Loop 47 
* CEs [47] --> Loop 48 
* CEs [48] --> Loop 49 

### Ranking functions of CR f60(A,J,K) 
* RF of phase [47]: [-A+50]

#### Partial ranking functions of CR f60(A,J,K) 
* Partial RF of phase [47]:
  - RF of loop [47:1]:
    -A+50


### Specialization of cost equations f60_loop_cont/9 
* CE 31 is refined into CE [50] 
* CE 30 is refined into CE [51] 


### Cost equations --> "Loop" of f60_loop_cont/9 
* CEs [50] --> Loop 50 
* CEs [51] --> Loop 51 

### Ranking functions of CR f60_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f60_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f52_loop_cont/9 
* CE 26 is refined into CE [52,53,54,55] 
* CE 25 is refined into CE [56] 


### Cost equations --> "Loop" of f52_loop_cont/9 
* CEs [53] --> Loop 52 
* CEs [52,55] --> Loop 53 
* CEs [54] --> Loop 54 
* CEs [56] --> Loop 55 

### Ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f42_loop_cont/9 
* CE 21 is refined into CE [57,58,59,60,61,62] 
* CE 20 is refined into CE [63] 


### Cost equations --> "Loop" of f42_loop_cont/9 
* CEs [61,62] --> Loop 56 
* CEs [58,59,60] --> Loop 57 
* CEs [57] --> Loop 58 
* CEs [63] --> Loop 59 

### Ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f33_loop_cont/9 
* CE 16 is refined into CE [64,65,66,67,68,69] 
* CE 15 is refined into CE [70] 


### Cost equations --> "Loop" of f33_loop_cont/9 
* CEs [68,69] --> Loop 60 
* CEs [65,66,67] --> Loop 61 
* CEs [64] --> Loop 62 
* CEs [70] --> Loop 63 

### Ranking functions of CR f33_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f33_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f25_loop_cont/9 
* CE 11 is refined into CE [71,72,73,74,75,76] 
* CE 10 is refined into CE [77] 


### Cost equations --> "Loop" of f25_loop_cont/9 
* CEs [75,76] --> Loop 64 
* CEs [72,73,74] --> Loop 65 
* CEs [71] --> Loop 66 
* CEs [77] --> Loop 67 

### Ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f15_loop_cont/9 
* CE 6 is refined into CE [78,79,80,81,82,83] 
* CE 5 is refined into CE [84] 


### Cost equations --> "Loop" of f15_loop_cont/9 
* CEs [82,83] --> Loop 68 
* CEs [79,80,81] --> Loop 69 
* CEs [78] --> Loop 70 
* CEs [84] --> Loop 71 

### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [85,86,87,88] 


### Cost equations --> "Loop" of f0/8 
* CEs [85,86,87,88] --> Loop 72 

### Ranking functions of CR f0(A,B,C,D,E,F,G,J) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,J) 


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

#### Cost of chains of f15(D,E,J,K,L):
* Chain [[32],34]: 1*it(32)+0
  Such that:it(32) =< -D+50

  with precondition: [J=3,49>=D,D>=0] 

* Chain [[32],33]: 1*it(32)+0
  Such that:it(32) =< -D+50

  with precondition: [J=8,K=50,L=0,49>=D,D>=0] 

* Chain [34]: 0
  with precondition: [J=3,D>=0] 


#### Cost of chains of f25(A,E,J,K,L):
* Chain [[35],37]: 1*it(35)+0
  Such that:it(35) =< -E+50

  with precondition: [A=0,J=3,49>=E] 

* Chain [[35],36]: 1*it(35)+0
  Such that:it(35) =< -E+50

  with precondition: [A=0,J=7,K=0,L=50,49>=E] 

* Chain [37]: 0
  with precondition: [A=0,J=3] 

* Chain [36]: 0
  with precondition: [A=0,J=7,K=0,E=L,E>=50] 


#### Cost of chains of f33(A,F,J,K,L):
* Chain [[38],40]: 1*it(38)+0
  Such that:it(38) =< -A+50

  with precondition: [J=3,49>=A] 

* Chain [[38],39]: 1*it(38)+0
  Such that:it(38) =< -A+50

  with precondition: [J=6,K=50,L=0,49>=A] 

* Chain [40]: 0
  with precondition: [J=3] 

* Chain [39]: 0
  with precondition: [J=6,L=0,A=K,A>=50] 


#### Cost of chains of f42(F,G,J,K,L):
* Chain [[41],43]: 1*it(41)+0
  Such that:it(41) =< -F+50

  with precondition: [J=3,49>=F] 

* Chain [[41],42]: 1*it(41)+0
  Such that:it(41) =< -F+50

  with precondition: [J=5,K=50,L=0,49>=F] 

* Chain [43]: 0
  with precondition: [J=3] 

* Chain [42]: 0
  with precondition: [J=5,L=0,F=K,F>=50] 


#### Cost of chains of f52(A,G,J,K,L):
* Chain [[44],46]: 1*it(44)+0
  Such that:it(44) =< -G+50

  with precondition: [J=3,49>=G] 

* Chain [[44],45]: 1*it(44)+0
  Such that:it(44) =< -G+50

  with precondition: [J=4,K=0,L=50,49>=G] 

* Chain [46]: 0
  with precondition: [J=3] 

* Chain [45]: 0
  with precondition: [J=4,K=0,G=L,G>=50] 


#### Cost of chains of f60(A,J,K):
* Chain [[47],49]: 1*it(47)+0
  Such that:it(47) =< -A+50

  with precondition: [J=2,K=50,49>=A] 

* Chain [[47],48]: 1*it(47)+0
  Such that:it(47) =< -A+50

  with precondition: [J=3,49>=A] 

* Chain [49]: 0
  with precondition: [J=2,A=K,A>=50] 

* Chain [48]: 0
  with precondition: [J=3] 


#### Cost of chains of f60_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [51]: 0
  with precondition: [A=2] 

* Chain [50]: 0
  with precondition: [A=3] 


#### Cost of chains of f52_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [55]: 0
  with precondition: [A=3] 

* Chain [54]: 0
  with precondition: [A=4] 

* Chain [53]: 2*s(1)+0
  Such that:aux(1) =< -B+50
s(1) =< aux(1)

  with precondition: [A=4,49>=B] 

* Chain [52]: 0
  with precondition: [A=4,B>=50] 


#### Cost of chains of f42_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [59]: 0
  with precondition: [A=3] 

* Chain [58]: 0
  with precondition: [A=5] 

* Chain [57]: 3*s(3)+2*s(7)+0
  Such that:s(6) =< 50
aux(2) =< -H+50
s(3) =< aux(2)
s(7) =< s(6)

  with precondition: [A=5,49>=H] 

* Chain [56]: 100
  with precondition: [A=5,H>=50] 


#### Cost of chains of f33_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [63]: 0
  with precondition: [A=3] 

* Chain [62]: 0
  with precondition: [A=6] 

* Chain [61]: 3*s(10)+5*s(15)+0
  Such that:aux(3) =< 50
aux(4) =< -G+50
s(10) =< aux(4)
s(15) =< aux(3)

  with precondition: [A=6,49>=G] 

* Chain [60]: 250
  with precondition: [A=6,G>=50] 


#### Cost of chains of f25_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [67]: 0
  with precondition: [A=3] 

* Chain [66]: 0
  with precondition: [A=7] 

* Chain [65]: 3*s(21)+8*s(26)+0
  Such that:aux(6) =< 50
aux(7) =< -B+50
s(21) =< aux(7)
s(26) =< aux(6)

  with precondition: [A=7,49>=B] 

* Chain [64]: 400
  with precondition: [A=7,B>=50] 


#### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [71]: 0
  with precondition: [A=3,B=0] 

* Chain [70]: 0
  with precondition: [A=8,B=0] 

* Chain [69]: 3*s(32)+11*s(37)+0
  Such that:aux(9) =< 50
aux(10) =< -F+50
s(32) =< aux(10)
s(37) =< aux(9)

  with precondition: [A=8,B=0,49>=F] 

* Chain [68]: 550
  with precondition: [A=8,B=0,F>=50] 


#### Cost of chains of f0(A,B,C,D,E,F,G,J):
* Chain [72]: 850
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,J): 
-------------------------------------
* Chain [72] with precondition: [] 
    - Upper bound: 850 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,J): 850 
Asymptotic class: constant 
* Total analysis performed in 427 ms.