/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [f10/7]
1. non_recursive  : [exit_location/1]
2. recursive  : [f21/8]
3. recursive  : [f18/8,f21_loop_cont/9]
4. recursive  : [f32/4]
5. non_recursive  : [f41/8]
6. non_recursive  : [f32_loop_cont/9]
7. non_recursive  : [f18_loop_cont/9]
8. non_recursive  : [f10_loop_cont/9]
9. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f10/7
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f21/8
3. SCC is partially evaluated into f18/8
4. SCC is partially evaluated into f32/4
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into f32_loop_cont/9
7. SCC is partially evaluated into f18_loop_cont/9
8. SCC is partially evaluated into f10_loop_cont/9
9. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f10/7 
* CE 4 is refined into CE [21] 
* CE 3 is refined into CE [22] 
* CE 2 is refined into CE [23] 


### Cost equations --> "Loop" of f10/7 
* CEs [23] --> Loop 21 
* CEs [21] --> Loop 22 
* CEs [22] --> Loop 23 

### Ranking functions of CR f10(B,C,D,E,I,J,K) 
* RF of phase [21]: [-B+C]

#### Partial ranking functions of CR f10(B,C,D,E,I,J,K) 
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    -B+C


### Specialization of cost equations f21/8 
* CE 15 is refined into CE [24] 
* CE 14 is refined into CE [25] 
* CE 13 is refined into CE [26] 


### Cost equations --> "Loop" of f21/8 
* CEs [26] --> Loop 24 
* CEs [24] --> Loop 25 
* CEs [25] --> Loop 26 

### Ranking functions of CR f21(D,E,F,G,I,J,K,L) 
* RF of phase [24]: [D-E-F-1]

#### Partial ranking functions of CR f21(D,E,F,G,I,J,K,L) 
* Partial RF of phase [24]:
  - RF of loop [24:1]:
    D-E-F-1


### Specialization of cost equations f18/8 
* CE 9 is refined into CE [27] 
* CE 7 is refined into CE [28,29] 
* CE 10 is refined into CE [30] 
* CE 8 is refined into CE [31] 


### Cost equations --> "Loop" of f18/8 
* CEs [31] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [28,29] --> Loop 29 
* CEs [30] --> Loop 30 

### Ranking functions of CR f18(D,E,F,G,I,J,K,L) 
* RF of phase [27]: [D-E-1]

#### Partial ranking functions of CR f18(D,E,F,G,I,J,K,L) 
* Partial RF of phase [27]:
  - RF of loop [27:1]:
    D-E-1


### Specialization of cost equations f32/4 
* CE 17 is refined into CE [32] 
* CE 18 is refined into CE [33] 
* CE 16 is refined into CE [34] 


### Cost equations --> "Loop" of f32/4 
* CEs [34] --> Loop 31 
* CEs [32] --> Loop 32 
* CEs [33] --> Loop 33 

### Ranking functions of CR f32(D,E,I,J) 
* RF of phase [31]: [D-E-1]

#### Partial ranking functions of CR f32(D,E,I,J) 
* Partial RF of phase [31]:
  - RF of loop [31:1]:
    D-E-1


### Specialization of cost equations f32_loop_cont/9 
* CE 19 is refined into CE [35] 
* CE 20 is refined into CE [36] 


### Cost equations --> "Loop" of f32_loop_cont/9 
* CEs [35] --> Loop 34 
* CEs [36] --> Loop 35 

### Ranking functions of CR f32_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f32_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f18_loop_cont/9 
* CE 12 is refined into CE [37,38,39,40] 
* CE 11 is refined into CE [41] 


### Cost equations --> "Loop" of f18_loop_cont/9 
* CEs [38,39] --> Loop 36 
* CEs [40] --> Loop 37 
* CEs [37] --> Loop 38 
* CEs [41] --> Loop 39 

### Ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f10_loop_cont/9 
* CE 5 is refined into CE [42] 
* CE 6 is refined into CE [43,44,45,46,47,48,49,50,51] 


### Cost equations --> "Loop" of f10_loop_cont/9 
* CEs [42] --> Loop 40 
* CEs [45] --> Loop 41 
* CEs [44,46] --> Loop 42 
* CEs [49] --> Loop 43 
* CEs [48] --> Loop 44 
* CEs [51] --> Loop 45 
* CEs [47] --> Loop 46 
* CEs [50] --> Loop 47 
* CEs [43] --> Loop 48 

### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [52,53,54,55,56,57,58,59,60,61,62] 


### Cost equations --> "Loop" of f0/8 
* CEs [60] --> Loop 49 
* CEs [57,59] --> Loop 50 
* CEs [55,62] --> Loop 51 
* CEs [52,53,54] --> Loop 52 
* CEs [56,58] --> Loop 53 
* CEs [61] --> Loop 54 

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

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


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

#### Cost of chains of f10(B,C,D,E,I,J,K):
* Chain [[21],23]: 1*it(21)+0
  Such that:it(21) =< -B+C

  with precondition: [I=2,K=0,C=J,B>=0,C>=B+1] 

* Chain [[21],22]: 1*it(21)+0
  Such that:it(21) =< -B+C

  with precondition: [I=3,B>=0,C>=B+1] 

* Chain [23]: 0
  with precondition: [I=2,K=0,B=J,B>=0,B>=C] 

* Chain [22]: 0
  with precondition: [I=3,B>=0] 


#### Cost of chains of f21(D,E,F,G,I,J,K,L):
* Chain [[24],26]: 1*it(24)+0
  Such that:it(24) =< D-F-J

  with precondition: [I=2,E+1=J,D=E+K+1,F>=0,D>=E+F+2] 

* Chain [[24],25]: 1*it(24)+0
  Such that:it(24) =< D-E-F

  with precondition: [I=3,F>=0,D>=E+F+2] 

* Chain [25]: 0
  with precondition: [I=3,F>=0,D>=E+2] 


#### Cost of chains of f18(D,E,F,G,I,J,K,L):
* Chain [[27],30]: 1*it(27)+1*s(3)+0
  Such that:aux(3) =< D-E
it(27) =< aux(3)
s(3) =< it(27)*aux(3)

  with precondition: [I=3,D>=E+2] 

* Chain [[27],29]: 2*it(27)+1*s(3)+0
  Such that:aux(4) =< D-E
it(27) =< aux(4)
s(3) =< it(27)*aux(4)

  with precondition: [I=3,D>=E+3] 

* Chain [[27],28]: 1*it(27)+1*s(3)+0
  Such that:aux(5) =< D-E
it(27) =< aux(5)
s(3) =< it(27)*aux(5)

  with precondition: [I=5,J=0,K=1,D>=E+2] 

* Chain [30]: 0
  with precondition: [I=3] 

* Chain [29]: 1*s(4)+0
  Such that:s(4) =< D-E

  with precondition: [I=3,D>=E+2] 

* Chain [28]: 0
  with precondition: [I=5,J=0,K=F,L=G,E+1>=D] 


#### Cost of chains of f32(D,E,I,J):
* Chain [[31],33]: 1*it(31)+0
  Such that:it(31) =< D-E

  with precondition: [I=3,D>=E+2] 

* Chain [[31],32]: 1*it(31)+0
  Such that:it(31) =< D-E

  with precondition: [I=4,D=J+1,D>=E+2] 

* Chain [33]: 0
  with precondition: [I=3] 

* Chain [32]: 0
  with precondition: [I=4,E=J,E+1>=D] 


#### Cost of chains of f32_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [35]: 0
  with precondition: [A=3,E=D] 

* Chain [34]: 0
  with precondition: [A=4,E=D] 


#### Cost of chains of f18_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [39]: 0
  with precondition: [A=3,E=D] 

* Chain [38]: 0
  with precondition: [A=5,E=D] 

* Chain [37]: 0
  with precondition: [A=5,E=D,F+1>=E] 

* Chain [36]: 2*s(9)+0
  Such that:aux(7) =< D-F
s(9) =< aux(7)

  with precondition: [A=5,E=D,E>=F+2] 


#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [48]: 0
  with precondition: [A=2,E=D] 

* Chain [47]: 0
  with precondition: [A=2,E=D,1>=E,F+1>=E] 

* Chain [46]: 1*s(12)+1*s(13)+0
  Such that:s(11) =< D-F
s(12) =< s(11)
s(13) =< s(12)*s(11)

  with precondition: [A=2,E=D,1>=E,E>=F+2] 

* Chain [45]: 2*s(15)+0
  Such that:s(14) =< D
s(15) =< s(14)

  with precondition: [A=2,E=D,E>=2,F+1>=E] 

* Chain [44]: 1*s(17)+1*s(18)+2*s(20)+0
  Such that:s(19) =< D
s(16) =< D-F
s(20) =< s(19)
s(17) =< s(16)
s(18) =< s(17)*s(16)

  with precondition: [A=2,E=D,E>=2,E>=F+2] 

* Chain [43]: 0
  with precondition: [A=2,E=D,F+1>=E] 

* Chain [42]: 3*s(22)+2*s(23)+0
  Such that:aux(8) =< D-F
s(22) =< aux(8)
s(23) =< s(22)*aux(8)

  with precondition: [A=2,E=D,E>=F+2] 

* Chain [41]: 2*s(28)+1*s(29)+0
  Such that:s(27) =< D-F
s(28) =< s(27)
s(29) =< s(28)*s(27)

  with precondition: [A=2,E=D,E>=F+3] 

* Chain [40]: 0
  with precondition: [A=3,E=D] 


#### Cost of chains of f0(A,B,C,D,E,F,G,I):
* Chain [54]: 0
  with precondition: [] 

* Chain [53]: 2
  with precondition: [C=1] 

* Chain [52]: 0
  with precondition: [0>=C] 

* Chain [51]: 2*s(32)+0
  Such that:aux(10) =< C
s(32) =< aux(10)

  with precondition: [C>=1] 

* Chain [50]: 8*s(34)+3*s(39)+0
  Such that:aux(13) =< C
s(34) =< aux(13)
s(39) =< s(34)*aux(13)

  with precondition: [C>=2] 

* Chain [49]: 3*s(44)+1*s(47)+0
  Such that:aux(14) =< C
s(44) =< aux(14)
s(47) =< s(44)*aux(14)

  with precondition: [C>=3] 


Closed-form bounds of f0(A,B,C,D,E,F,G,I): 
-------------------------------------
* Chain [54] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [53] with precondition: [C=1] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [52] with precondition: [0>=C] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [51] with precondition: [C>=1] 
    - Upper bound: 2*C 
    - Complexity: n 
* Chain [50] with precondition: [C>=2] 
    - Upper bound: 3*C*C+8*C 
    - Complexity: n^2 
* Chain [49] with precondition: [C>=3] 
    - Upper bound: 3*C+C*C 
    - Complexity: n^2 

### Maximum cost of f0(A,B,C,D,E,F,G,I): max([2,nat(C)*2*nat(C)+nat(C)*5+(nat(C)*nat(C)+nat(C))+nat(C)*2]) 
Asymptotic class: n^2 
* Total analysis performed in 457 ms.