/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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


WORST_CASE(?,O(1))  

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

#### Computed strongly connected components 
0. recursive  : [f23/9]
1. recursive  : [f17/13,f23_loop_cont/14]
2. non_recursive  : [exit_location/1]
3. recursive  : [f42/13]
4. recursive  : [f72/9]
5. recursive  : [f66/13,f72_loop_cont/14]
6. recursive  : [f91/15]
7. non_recursive  : [f106/33]
8. non_recursive  : [f91_loop_cont/34]
9. non_recursive  : [f85/33]
10. non_recursive  : [f66_loop_cont/34]
11. non_recursive  : [f56/33]
12. non_recursive  : [f42_loop_cont/34]
13. non_recursive  : [f36/33]
14. non_recursive  : [f17_loop_cont/34]
15. non_recursive  : [f0/33]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f23/9
1. SCC is partially evaluated into f17/13
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f42/13
4. SCC is partially evaluated into f72/9
5. SCC is partially evaluated into f66/13
6. SCC is partially evaluated into f91/15
7. SCC is completely evaluated into other SCCs
8. SCC is partially evaluated into f91_loop_cont/34
9. SCC is partially evaluated into f85/33
10. SCC is partially evaluated into f66_loop_cont/34
11. SCC is partially evaluated into f56/33
12. SCC is partially evaluated into f42_loop_cont/34
13. SCC is partially evaluated into f36/33
14. SCC is partially evaluated into f17_loop_cont/34
15. SCC is partially evaluated into f0/33

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

### Specialization of cost equations f23/9 
* CE 22 is refined into CE [45] 
* CE 21 is refined into CE [46] 
* CE 20 is refined into CE [47] 


### Cost equations --> "Loop" of f23/9 
* CEs [47] --> Loop 45 
* CEs [45] --> Loop 46 
* CEs [46] --> Loop 47 

### Ranking functions of CR f23(H,K,L,F1,I1,J1,K1,L1,M1) 
* RF of phase [45]: [-L+8]

#### Partial ranking functions of CR f23(H,K,L,F1,I1,J1,K1,L1,M1) 
* Partial RF of phase [45]:
  - RF of loop [45:1]:
    -L+8


### Specialization of cost equations f17/13 
* CE 9 is refined into CE [48] 
* CE 7 is refined into CE [49,50] 
* CE 10 is refined into CE [51] 
* CE 8 is refined into CE [52] 


### Cost equations --> "Loop" of f17/13 
* CEs [52] --> Loop 48 
* CEs [48] --> Loop 49 
* CEs [49,50] --> Loop 50 
* CEs [51] --> Loop 51 

### Ranking functions of CR f17(H,I,J,K,L,F1,I1,J1,K1,L1,M1,N1,O1) 
* RF of phase [48]: [-H+256]

#### Partial ranking functions of CR f17(H,I,J,K,L,F1,I1,J1,K1,L1,M1,N1,O1) 
* Partial RF of phase [48]:
  - RF of loop [48:1]:
    -H+256


### Specialization of cost equations f42/13 
* CE 16 is discarded (unfeasible) 
* CE 15 is refined into CE [53] 
* CE 17 is refined into CE [54] 
* CE 14 is refined into CE [55] 
* CE 13 is discarded (unfeasible) 


### Cost equations --> "Loop" of f42/13 
* CEs [55] --> Loop 52 
* CEs [53] --> Loop 53 
* CEs [54] --> Loop 54 

### Ranking functions of CR f42(D,F,G,H,M,O,E1,I1,J1,K1,L1,M1,N1) 
* RF of phase [52]: [-H+41]

#### Partial ranking functions of CR f42(D,F,G,H,M,O,E1,I1,J1,K1,L1,M1,N1) 
* Partial RF of phase [52]:
  - RF of loop [52:1]:
    -H+41


### Specialization of cost equations f72/9 
* CE 43 is refined into CE [56] 
* CE 44 is refined into CE [57] 
* CE 42 is refined into CE [58] 


### Cost equations --> "Loop" of f72/9 
* CEs [58] --> Loop 55 
* CEs [56] --> Loop 56 
* CEs [57] --> Loop 57 

### Ranking functions of CR f72(U,X,Y,D1,I1,J1,K1,L1,M1) 
* RF of phase [55]: [-Y+8]

#### Partial ranking functions of CR f72(U,X,Y,D1,I1,J1,K1,L1,M1) 
* Partial RF of phase [55]:
  - RF of loop [55:1]:
    -Y+8


### Specialization of cost equations f66/13 
* CE 31 is refined into CE [59] 
* CE 29 is refined into CE [60,61] 
* CE 32 is refined into CE [62] 
* CE 30 is refined into CE [63] 


### Cost equations --> "Loop" of f66/13 
* CEs [63] --> Loop 58 
* CEs [59] --> Loop 59 
* CEs [60,61] --> Loop 60 
* CEs [62] --> Loop 61 

### Ranking functions of CR f66(U,V,W,X,Y,D1,I1,J1,K1,L1,M1,N1,O1) 
* RF of phase [58]: [-U+256]

#### Partial ranking functions of CR f66(U,V,W,X,Y,D1,I1,J1,K1,L1,M1,N1,O1) 
* Partial RF of phase [58]:
  - RF of loop [58:1]:
    -U+256


### Specialization of cost equations f91/15 
* CE 38 is discarded (unfeasible) 
* CE 37 is refined into CE [64] 
* CE 39 is refined into CE [65] 
* CE 36 is refined into CE [66] 
* CE 35 is discarded (unfeasible) 


### Cost equations --> "Loop" of f91/15 
* CEs [66] --> Loop 62 
* CEs [64] --> Loop 63 
* CEs [65] --> Loop 64 

### Ranking functions of CR f91(Q,S,T,U,Z,A1,B1,C1,I1,J1,K1,L1,M1,N1,O1) 
* RF of phase [62]: [-U+43]

#### Partial ranking functions of CR f91(Q,S,T,U,Z,A1,B1,C1,I1,J1,K1,L1,M1,N1,O1) 
* Partial RF of phase [62]:
  - RF of loop [62:1]:
    -U+43


### Specialization of cost equations f91_loop_cont/34 
* CE 40 is refined into CE [67] 
* CE 41 is refined into CE [68] 


### Cost equations --> "Loop" of f91_loop_cont/34 
* CEs [67] --> Loop 65 
* CEs [68] --> Loop 66 

### Ranking functions of CR f91_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 

#### Partial ranking functions of CR f91_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 


### Specialization of cost equations f85/33 
* CE 26 is refined into CE [69,70,71] 
* CE 27 is discarded (unfeasible) 
* CE 28 is discarded (unfeasible) 


### Cost equations --> "Loop" of f85/33 
* CEs [69,70,71] --> Loop 67 

### Ranking functions of CR f85(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 

#### Partial ranking functions of CR f85(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 


### Specialization of cost equations f66_loop_cont/34 
* CE 33 is refined into CE [72] 
* CE 34 is refined into CE [73] 


### Cost equations --> "Loop" of f66_loop_cont/34 
* CEs [72] --> Loop 68 
* CEs [73] --> Loop 69 

### Ranking functions of CR f66_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 

#### Partial ranking functions of CR f66_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 


### Specialization of cost equations f56/33 
* CE 24 is refined into CE [74] 
* CE 23 is refined into CE [75] 
* CE 25 is refined into CE [76,77,78,79] 


### Cost equations --> "Loop" of f56/33 
* CEs [74] --> Loop 70 
* CEs [75] --> Loop 71 
* CEs [76,77,78,79] --> Loop 72 

### Ranking functions of CR f56(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 

#### Partial ranking functions of CR f56(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 


### Specialization of cost equations f42_loop_cont/34 
* CE 18 is refined into CE [80,81,82] 
* CE 19 is refined into CE [83] 


### Cost equations --> "Loop" of f42_loop_cont/34 
* CEs [82] --> Loop 73 
* CEs [81] --> Loop 74 
* CEs [80] --> Loop 75 
* CEs [83] --> Loop 76 

### Ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 

#### Partial ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 


### Specialization of cost equations f36/33 
* CE 4 is refined into CE [84,85,86,87,88] 
* CE 5 is discarded (unfeasible) 
* CE 6 is discarded (unfeasible) 


### Cost equations --> "Loop" of f36/33 
* CEs [88] --> Loop 77 
* CEs [87] --> Loop 78 
* CEs [84,85] --> Loop 79 
* CEs [86] --> Loop 80 

### Ranking functions of CR f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 

#### Partial ranking functions of CR f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 


### Specialization of cost equations f17_loop_cont/34 
* CE 11 is refined into CE [89,90] 
* CE 12 is refined into CE [91] 


### Cost equations --> "Loop" of f17_loop_cont/34 
* CEs [89,90] --> Loop 81 
* CEs [91] --> Loop 82 

### Ranking functions of CR f17_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 

#### Partial ranking functions of CR f17_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1) 


### Specialization of cost equations f0/33 
* CE 2 is refined into CE [92,93] 
* CE 1 is refined into CE [94,95] 
* CE 3 is refined into CE [96,97,98,99] 


### Cost equations --> "Loop" of f0/33 
* CEs [92,93] --> Loop 83 
* CEs [94,95] --> Loop 84 
* CEs [96,97,98,99] --> Loop 85 

### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1) 


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

#### Cost of chains of f23(H,K,L,F1,I1,J1,K1,L1,M1):
* Chain [[45],47]: 1*it(45)+0
  Such that:it(45) =< -L+8

  with precondition: [I1=2,L1=8,H+1=J1,K1=M1,255>=H,7>=L,L>=0] 

* Chain [[45],46]: 1*it(45)+0
  Such that:it(45) =< -L+8

  with precondition: [I1=3,255>=H,7>=L,L>=0] 

* Chain [46]: 0
  with precondition: [I1=3,255>=H,L>=0] 


#### Cost of chains of f17(H,I,J,K,L,F1,I1,J1,K1,L1,M1,N1,O1):
* Chain [[48],51]: 1*it(48)+1*s(3)+0
  Such that:aux(4) =< -H+256
it(48) =< aux(4)
s(3) =< aux(4)*8

  with precondition: [I1=3,255>=H,H>=0] 

* Chain [[48],50]: 1*it(48)+1*s(3)+8
  Such that:aux(3) =< -H+255
aux(2) =< -H+256
aux(1) =< aux(2)
it(48) =< aux(2)
aux(1) =< aux(3)
it(48) =< aux(3)
s(3) =< aux(1)*8

  with precondition: [I1=3,254>=H,H>=0] 

* Chain [[48],49]: 1*it(48)+1*s(3)+0
  Such that:aux(5) =< -H+256
it(48) =< aux(5)
s(3) =< aux(5)*8

  with precondition: [I1=5,J1=256,L1=0,N1=8,M1=O1,255>=H] 

* Chain [51]: 0
  with precondition: [I1=3,H>=0] 

* Chain [50]: 8
  with precondition: [I1=3,255>=H,H>=0] 


#### Cost of chains of f42(D,F,G,H,M,O,E1,I1,J1,K1,L1,M1,N1):
* Chain [[52],54]: 1*it(52)+0
  Such that:it(52) =< -H+41

  with precondition: [D=40,F=1,I1=3,40>=H,H>=1] 

* Chain [[52],53]: 1*it(52)+0
  Such that:it(52) =< -H+41

  with precondition: [D=40,F=1,I1=6,K1=41,J1=M1,J1=N1,40>=H,H>=1] 

* Chain [54]: 0
  with precondition: [D=40,F=1,I1=3,H>=1] 


#### Cost of chains of f72(U,X,Y,D1,I1,J1,K1,L1,M1):
* Chain [[55],57]: 1*it(55)+0
  Such that:it(55) =< -Y+8

  with precondition: [I1=3,255>=U,7>=Y,Y>=0] 

* Chain [[55],56]: 1*it(55)+0
  Such that:it(55) =< -Y+8

  with precondition: [I1=4,L1=8,U+1=J1,K1=M1,255>=U,7>=Y,Y>=0] 

* Chain [57]: 0
  with precondition: [I1=3,255>=U,Y>=0] 


#### Cost of chains of f66(U,V,W,X,Y,D1,I1,J1,K1,L1,M1,N1,O1):
* Chain [[58],61]: 1*it(58)+1*s(10)+0
  Such that:aux(9) =< -U+256
it(58) =< aux(9)
s(10) =< aux(9)*8

  with precondition: [I1=3,255>=U,U>=0] 

* Chain [[58],60]: 1*it(58)+1*s(10)+8
  Such that:aux(8) =< -U+255
aux(7) =< -U+256
aux(6) =< aux(7)
it(58) =< aux(7)
aux(6) =< aux(8)
it(58) =< aux(8)
s(10) =< aux(6)*8

  with precondition: [I1=3,254>=U,U>=0] 

* Chain [[58],59]: 1*it(58)+1*s(10)+0
  Such that:aux(10) =< -U+256
it(58) =< aux(10)
s(10) =< aux(10)*8

  with precondition: [I1=7,J1=256,L1=0,N1=8,M1=O1,255>=U] 

* Chain [61]: 0
  with precondition: [I1=3,U>=0] 

* Chain [60]: 8
  with precondition: [I1=3,255>=U,U>=0] 


#### Cost of chains of f91(Q,S,T,U,Z,A1,B1,C1,I1,J1,K1,L1,M1,N1,O1):
* Chain [[62],64]: 1*it(62)+0
  Such that:it(62) =< -U+43

  with precondition: [Q=42,S=1,I1=3,42>=U,U>=1] 

* Chain [[62],63]: 1*it(62)+0
  Such that:it(62) =< -U+43

  with precondition: [Q=42,S=1,I1=8,K1=43,J1=M1,J1=N1,J1=O1,42>=U,U>=1] 

* Chain [64]: 0
  with precondition: [Q=42,S=1,I1=3,U>=1] 


#### Cost of chains of f91_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1):
* Chain [66]: 0
  with precondition: [A=3,C=40,D=0,E=40,F=0,G=1,R=42,S=0,T=1,P=O,P=Q] 

* Chain [65]: 0
  with precondition: [A=8,C=40,D=0,E=40,F=0,G=1,R=42,S=0,T=1,P=O,P=Q] 


#### Cost of chains of f85(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1):
* Chain [67]: 84
  with precondition: [B=40,C=0,D=40,E=0,F=1,Q=42,R=0,S=1,O=N,O=P,O=T] 


#### Cost of chains of f66_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1):
* Chain [69]: 0
  with precondition: [A=3,B=1,C=40,D=0,E=40,F=0,G=1,R=42,S=0,T=1,P=O,P=Q,P=U] 

* Chain [68]: 84
  with precondition: [A=7,B=1,C=40,D=0,E=40,F=0,G=1,R=42,S=0,T=1,P=O,P=Q,P=U] 


#### Cost of chains of f56(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1):
* Chain [72]: 6996
  with precondition: [A=0,B=40,C=0,D=40,E=0,F=1] 

* Chain [71]: 84
  with precondition: [B=40,C=0,D=40,E=0,F=1,0>=A+1] 

* Chain [70]: 84
  with precondition: [B=40,C=0,D=40,E=0,F=1,A>=1] 


#### Cost of chains of f42_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1):
* Chain [76]: 0
  with precondition: [A=3,C=40,D=0,E=40,F=0,G=1] 

* Chain [75]: 6996
  with precondition: [A=6,B=0,C=40,D=0,E=40,F=0,G=1] 

* Chain [74]: 84
  with precondition: [A=6,C=40,D=0,E=40,F=0,G=1,0>=B+1] 

* Chain [73]: 84
  with precondition: [A=6,C=40,D=0,E=40,F=0,G=1,B>=1] 


#### Cost of chains of f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1):
* Chain [80]: 1*s(28)+6996
  Such that:s(28) =< 40

  with precondition: [A=0,B=40,C=0,D=40,E=0,F=1,G=0] 

* Chain [79]: 40
  with precondition: [B=40,C=0,D=40,E=0,F=1,G=0] 

* Chain [78]: 1*s(30)+84
  Such that:s(30) =< 40

  with precondition: [B=40,C=0,D=40,E=0,F=1,G=0,0>=A+1] 

* Chain [77]: 1*s(31)+84
  Such that:s(31) =< 40

  with precondition: [B=40,C=0,D=40,E=0,F=1,G=0,A>=1] 


#### Cost of chains of f17_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1):
* Chain [82]: 0
  with precondition: [A=3,B=1,C=40,D=0,E=40,F=0,G=1,H=0] 

* Chain [81]: 124
  with precondition: [A=5,B=1,C=40,D=0,E=40,F=0,G=1,H=0] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1):
* Chain [85]: 7036
  with precondition: [A=0] 

* Chain [84]: 124
  with precondition: [0>=A+1] 

* Chain [83]: 124
  with precondition: [A>=1] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1): 
-------------------------------------
* Chain [85] with precondition: [A=0] 
    - Upper bound: 7036 
    - Complexity: constant 
* Chain [84] with precondition: [0>=A+1] 
    - Upper bound: 124 
    - Complexity: constant 
* Chain [83] with precondition: [A>=1] 
    - Upper bound: 124 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,I1): 7036 
Asymptotic class: constant 
* Total analysis performed in 1552 ms.