/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(1))  

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

#### Computed strongly connected components 
0. recursive  : [f19/9]
1. recursive  : [f16/11,f19_loop_cont/12]
2. non_recursive  : [exit_location/1]
3. recursive  : [f36/9]
4. recursive  : [f33/11,f36_loop_cont/12]
5. recursive  : [f59/5]
6. recursive  : [f55/7,f59_loop_cont/8]
7. recursive  : [f52/7,f55_loop_cont/8]
8. non_recursive  : [f73/11]
9. non_recursive  : [f52_loop_cont/12]
10. non_recursive  : [f33_loop_cont/12]
11. non_recursive  : [f16_loop_cont/12]
12. non_recursive  : [f0/11]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f19/9
1. SCC is partially evaluated into f16/11
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f36/9
4. SCC is partially evaluated into f33/11
5. SCC is partially evaluated into f59/5
6. SCC is partially evaluated into f55/7
7. SCC is partially evaluated into f52/7
8. SCC is completely evaluated into other SCCs
9. SCC is partially evaluated into f52_loop_cont/12
10. SCC is partially evaluated into f33_loop_cont/12
11. SCC is partially evaluated into f16_loop_cont/12
12. SCC is partially evaluated into f0/11

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

### Specialization of cost equations f19/9 
* CE 9 is refined into CE [33] 
* CE 10 is refined into CE [34] 
* CE 8 is refined into CE [35] 


### Cost equations --> "Loop" of f19/9 
* CEs [35] --> Loop 33 
* CEs [33] --> Loop 34 
* CEs [34] --> Loop 35 

### Ranking functions of CR f19(A,B,H,J,L,M,N,O,P) 
* RF of phase [33]: [-B+20]

#### Partial ranking functions of CR f19(A,B,H,J,L,M,N,O,P) 
* Partial RF of phase [33]:
  - RF of loop [33:1]:
    -B+20


### Specialization of cost equations f16/11 
* CE 4 is refined into CE [36] 
* CE 2 is refined into CE [37,38] 
* CE 5 is refined into CE [39] 
* CE 3 is refined into CE [40] 


### Cost equations --> "Loop" of f16/11 
* CEs [40] --> Loop 36 
* CEs [36] --> Loop 37 
* CEs [37,38] --> Loop 38 
* CEs [39] --> Loop 39 

### Ranking functions of CR f16(A,B,C,H,J,L,M,N,O,P,Q) 
* RF of phase [36]: [-A+20]

#### Partial ranking functions of CR f16(A,B,C,H,J,L,M,N,O,P,Q) 
* Partial RF of phase [36]:
  - RF of loop [36:1]:
    -A+20


### Specialization of cost equations f36/9 
* 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 f36/9 
* CEs [43] --> Loop 40 
* CEs [41] --> Loop 41 
* CEs [42] --> Loop 42 

### Ranking functions of CR f36(C,D,H,I,L,M,N,O,P) 
* RF of phase [40]: [-D+20]

#### Partial ranking functions of CR f36(C,D,H,I,L,M,N,O,P) 
* Partial RF of phase [40]:
  - RF of loop [40:1]:
    -D+20


### Specialization of cost equations f33/11 
* CE 13 is refined into CE [44] 
* CE 11 is refined into CE [45,46] 
* CE 14 is refined into CE [47] 
* CE 12 is refined into CE [48] 


### Cost equations --> "Loop" of f33/11 
* CEs [48] --> Loop 43 
* CEs [44] --> Loop 44 
* CEs [45,46] --> Loop 45 
* CEs [47] --> Loop 46 

### Ranking functions of CR f33(C,D,E,H,I,L,M,N,O,P,Q) 
* RF of phase [43]: [-C+20]

#### Partial ranking functions of CR f33(C,D,E,H,I,L,M,N,O,P,Q) 
* Partial RF of phase [43]:
  - RF of loop [43:1]:
    -C+20


### Specialization of cost equations f59/5 
* CE 32 is refined into CE [49] 
* CE 31 is refined into CE [50] 
* CE 30 is refined into CE [51] 


### Cost equations --> "Loop" of f59/5 
* CEs [51] --> Loop 47 
* CEs [49] --> Loop 48 
* CEs [50] --> Loop 49 

### Ranking functions of CR f59(F,G,L,M,N) 
* RF of phase [47]: [-G+20]

#### Partial ranking functions of CR f59(F,G,L,M,N) 
* Partial RF of phase [47]:
  - RF of loop [47:1]:
    -G+20


### Specialization of cost equations f55/7 
* CE 28 is refined into CE [52] 
* CE 26 is refined into CE [53,54] 
* CE 29 is refined into CE [55] 
* CE 27 is refined into CE [56] 


### Cost equations --> "Loop" of f55/7 
* CEs [56] --> Loop 50 
* CEs [52] --> Loop 51 
* CEs [53,54] --> Loop 52 
* CEs [55] --> Loop 53 

### Ranking functions of CR f55(E,F,G,L,M,N,O) 
* RF of phase [50]: [-F+20]

#### Partial ranking functions of CR f55(E,F,G,L,M,N,O) 
* Partial RF of phase [50]:
  - RF of loop [50:1]:
    -F+20


### Specialization of cost equations f52/7 
* CE 22 is refined into CE [57] 
* CE 20 is refined into CE [58,59,60] 
* CE 23 is refined into CE [61] 
* CE 21 is refined into CE [62] 


### Cost equations --> "Loop" of f52/7 
* CEs [62] --> Loop 54 
* CEs [57] --> Loop 55 
* CEs [58,59,60] --> Loop 56 
* CEs [61] --> Loop 57 

### Ranking functions of CR f52(E,F,G,L,M,N,O) 
* RF of phase [54]: [-E+20]

#### Partial ranking functions of CR f52(E,F,G,L,M,N,O) 
* Partial RF of phase [54]:
  - RF of loop [54:1]:
    -E+20


### Specialization of cost equations f52_loop_cont/12 
* CE 24 is refined into CE [63] 
* CE 25 is refined into CE [64] 


### Cost equations --> "Loop" of f52_loop_cont/12 
* CEs [63] --> Loop 58 
* CEs [64] --> Loop 59 

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

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


### Specialization of cost equations f33_loop_cont/12 
* CE 16 is refined into CE [65,66,67,68,69] 
* CE 15 is refined into CE [70] 


### Cost equations --> "Loop" of f33_loop_cont/12 
* CEs [69] --> Loop 60 
* CEs [67] --> Loop 61 
* CEs [66,68] --> Loop 62 
* CEs [65] --> Loop 63 
* CEs [70] --> Loop 64 

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

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


### Specialization of cost equations f16_loop_cont/12 
* CE 7 is refined into CE [71,72,73,74,75,76,77,78,79] 
* CE 6 is refined into CE [80] 


### Cost equations --> "Loop" of f16_loop_cont/12 
* CEs [77,78,79] --> Loop 65 
* CEs [73] --> Loop 66 
* CEs [72,74,75,76] --> Loop 67 
* CEs [71] --> Loop 68 
* CEs [80] --> Loop 69 

### Ranking functions of CR f16_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 

#### Partial ranking functions of CR f16_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 


### Specialization of cost equations f0/11 
* CE 1 is refined into CE [81,82,83,84,85,86] 


### Cost equations --> "Loop" of f0/11 
* CEs [81,82,83,84,85,86] --> Loop 70 

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

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


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

#### Cost of chains of f19(A,B,H,J,L,M,N,O,P):
* Chain [[33],35]: 1*it(33)+0
  Such that:it(33) =< -B+20

  with precondition: [L=3,19>=A,19>=B,B>=0] 

* Chain [[33],34]: 1*it(33)+0
  Such that:it(33) =< -B+20

  with precondition: [L=6,N=20,A+1=M,O=P,19>=A,19>=B,B>=0] 

* Chain [35]: 0
  with precondition: [L=3,19>=A,B>=0] 


#### Cost of chains of f16(A,B,C,H,J,L,M,N,O,P,Q):
* Chain [[36],39]: 1*it(36)+1*s(3)+0
  Such that:aux(4) =< -A+20
it(36) =< aux(4)
s(3) =< aux(4)*20

  with precondition: [L=3,19>=A,A>=0] 

* Chain [[36],38]: 1*it(36)+1*s(3)+20
  Such that:aux(3) =< -A+19
aux(2) =< -A+20
aux(1) =< aux(2)
it(36) =< aux(2)
aux(1) =< aux(3)
it(36) =< aux(3)
s(3) =< aux(1)*20

  with precondition: [L=3,18>=A,A>=0] 

* Chain [[36],37]: 1*it(36)+1*s(3)+0
  Such that:aux(5) =< -A+20
it(36) =< aux(5)
s(3) =< aux(5)*20

  with precondition: [L=5,M=20,N=20,O=0,P=Q,19>=A] 

* Chain [39]: 0
  with precondition: [L=3,A>=0] 

* Chain [38]: 20
  with precondition: [L=3,19>=A,A>=0] 


#### Cost of chains of f36(C,D,H,I,L,M,N,O,P):
* Chain [[40],42]: 1*it(40)+0
  Such that:it(40) =< -D+20

  with precondition: [L=3,19>=C,19>=D,D>=0] 

* Chain [[40],41]: 1*it(40)+0
  Such that:it(40) =< -D+20

  with precondition: [L=5,N=20,C+1=M,O=P,19>=C,19>=D,D>=0] 

* Chain [42]: 0
  with precondition: [L=3,19>=C,D>=0] 


#### Cost of chains of f33(C,D,E,H,I,L,M,N,O,P,Q):
* Chain [[43],46]: 1*it(43)+1*s(10)+0
  Such that:aux(9) =< -C+20
it(43) =< aux(9)
s(10) =< aux(9)*20

  with precondition: [L=3,19>=C] 

* Chain [[43],45]: 1*it(43)+1*s(10)+20
  Such that:aux(8) =< -C+19
aux(7) =< -C+20
aux(6) =< aux(7)
it(43) =< aux(7)
aux(6) =< aux(8)
it(43) =< aux(8)
s(10) =< aux(6)*20

  with precondition: [L=3,18>=C] 

* Chain [[43],44]: 1*it(43)+1*s(10)+0
  Such that:aux(10) =< -C+20
it(43) =< aux(10)
s(10) =< aux(10)*20

  with precondition: [L=4,M=20,N=20,O=0,P=Q,19>=C] 

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

* Chain [45]: 20
  with precondition: [L=3,19>=C] 

* Chain [44]: 0
  with precondition: [L=4,O=0,N=D,P=H,Q=I,C=M,C>=20] 


#### Cost of chains of f59(F,G,L,M,N):
* Chain [[47],49]: 1*it(47)+0
  Such that:it(47) =< -G+20

  with precondition: [L=2,N=20,F+1=M,19>=F,19>=G,G>=0] 

* Chain [[47],48]: 1*it(47)+0
  Such that:it(47) =< -G+20

  with precondition: [L=3,19>=F,19>=G,G>=0] 

* Chain [48]: 0
  with precondition: [L=3,19>=F,G>=0] 


#### Cost of chains of f55(E,F,G,L,M,N,O):
* Chain [[50],53]: 1*it(50)+1*s(17)+0
  Such that:aux(14) =< -F+20
it(50) =< aux(14)
s(17) =< aux(14)*20

  with precondition: [L=3,19>=E,19>=F,F>=0] 

* Chain [[50],52]: 1*it(50)+1*s(17)+20
  Such that:aux(13) =< -F+19
aux(12) =< -F+20
aux(11) =< aux(12)
it(50) =< aux(12)
aux(11) =< aux(13)
it(50) =< aux(13)
s(17) =< aux(11)*20

  with precondition: [L=3,19>=E,18>=F,F>=0] 

* Chain [[50],51]: 1*it(50)+1*s(17)+0
  Such that:aux(15) =< -F+20
it(50) =< aux(15)
s(17) =< aux(15)*20

  with precondition: [L=4,N=20,O=20,E+1=M,19>=E,19>=F] 

* Chain [53]: 0
  with precondition: [L=3,19>=E,F>=0] 

* Chain [52]: 20
  with precondition: [L=3,19>=E,19>=F,F>=0] 


#### Cost of chains of f52(E,F,G,L,M,N,O):
* Chain [[54],57]: 1*it(54)+1*s(28)+1*s(29)+0
  Such that:aux(19) =< -E+20
it(54) =< aux(19)
s(30) =< aux(19)*20
s(28) =< s(30)
s(29) =< s(30)*20

  with precondition: [L=3,19>=E] 

* Chain [[54],56]: 1*it(54)+1*s(28)+1*s(29)+860
  Such that:aux(18) =< -E+19
aux(17) =< -E+20
aux(16) =< aux(17)
it(54) =< aux(17)
aux(16) =< aux(18)
it(54) =< aux(18)
s(30) =< aux(16)*20
s(28) =< s(30)
s(29) =< s(30)*20

  with precondition: [L=3,18>=E] 

* Chain [[54],55]: 1*it(54)+1*s(28)+1*s(29)+0
  Such that:aux(21) =< -E+20
it(54) =< aux(21)
s(30) =< aux(21)*20
s(28) =< s(30)
s(29) =< s(30)*20

  with precondition: [L=7,M=20,N=20,O=20,19>=E] 

* Chain [57]: 0
  with precondition: [L=3] 

* Chain [56]: 860
  with precondition: [L=3,19>=E] 

* Chain [55]: 0
  with precondition: [L=7,N=F,O=G,E=M,E>=20] 


#### Cost of chains of f52_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [59]: 0
  with precondition: [A=3] 

* Chain [58]: 0
  with precondition: [A=7] 


#### Cost of chains of f33_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [64]: 0
  with precondition: [A=3] 

* Chain [63]: 0
  with precondition: [A=4] 

* Chain [62]: 2*s(45)+2*s(47)+2*s(48)+860
  Such that:aux(22) =< -F+20
s(45) =< aux(22)
s(46) =< aux(22)*20
s(47) =< s(46)
s(48) =< s(46)*20

  with precondition: [A=4,19>=F] 

* Chain [61]: 1*s(57)+1*s(59)+1*s(60)+860
  Such that:s(54) =< -F+19
s(55) =< -F+20
s(56) =< s(55)
s(57) =< s(55)
s(56) =< s(54)
s(57) =< s(54)
s(58) =< s(56)*20
s(59) =< s(58)
s(60) =< s(58)*20

  with precondition: [A=4,18>=F] 

* Chain [60]: 0
  with precondition: [A=4,F>=20] 


#### Cost of chains of f16_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [69]: 0
  with precondition: [A=3] 

* Chain [68]: 0
  with precondition: [A=5] 

* Chain [67]: 4*s(62)+4*s(63)+2*s(71)+2*s(73)+2*s(74)+1*s(81)+1*s(83)+1*s(84)+860
  Such that:s(78) =< 19
aux(23) =< 20
aux(24) =< -D+20
s(80) =< aux(23)
s(81) =< aux(23)
s(80) =< s(78)
s(81) =< s(78)
s(82) =< s(80)*20
s(83) =< s(82)
s(84) =< s(82)*20
s(62) =< aux(24)
s(63) =< aux(24)*20
s(71) =< aux(23)
s(72) =< aux(23)*20
s(73) =< s(72)
s(74) =< s(72)*20

  with precondition: [A=5,19>=D] 

* Chain [66]: 1*s(88)+1*s(89)+20
  Such that:s(85) =< -D+19
s(86) =< -D+20
s(87) =< s(86)
s(88) =< s(86)
s(87) =< s(85)
s(88) =< s(85)
s(89) =< s(87)*20

  with precondition: [A=5,18>=D] 

* Chain [65]: 26120
  with precondition: [A=5,D>=20] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,L):
* Chain [70]: 30320
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,L): 
-------------------------------------
* Chain [70] with precondition: [] 
    - Upper bound: 30320 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,L): 30320 
Asymptotic class: constant 
* Total analysis performed in 733 ms.