/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  : [lbl101/13]
1. recursive  : [lbl101_loop_cont/14,lbl121/13]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/7]
4. non_recursive  : [lbl121_loop_cont/8]
5. non_recursive  : [start/7]
6. non_recursive  : [start0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl101/13
1. SCC is partially evaluated into lbl121/13
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl121_loop_cont/8
5. SCC is partially evaluated into start/7
6. SCC is partially evaluated into start0/7

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

### Specialization of cost equations lbl101/13 
* CE 8 is refined into CE [16] 
* CE 7 is refined into CE [17] 
* CE 6 is refined into CE [18] 


### Cost equations --> "Loop" of lbl101/13 
* CEs [18] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M) 
* RF of phase [15]: [A-B,-B+D,-B+F]

#### Partial ranking functions of CR lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    A-B
    -B+D
    -B+F


### Specialization of cost equations lbl121/13 
* CE 11 is refined into CE [19,20] 
* CE 15 is refined into CE [21] 
* CE 13 is refined into CE [22] 
* CE 12 is refined into CE [23,24] 
* CE 14 is refined into CE [25] 


### Cost equations --> "Loop" of lbl121/13 
* CEs [24] --> Loop 18 
* CEs [25] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [19] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [22] --> Loop 24 

### Ranking functions of CR lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M) 
* RF of phase [18]: [D-2]
* RF of phase [19]: [D+1]

#### Partial ranking functions of CR lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    D-2
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    D+1


### Specialization of cost equations lbl121_loop_cont/8 
* CE 9 is refined into CE [26] 
* CE 10 is refined into CE [27] 


### Cost equations --> "Loop" of lbl121_loop_cont/8 
* CEs [26] --> Loop 25 
* CEs [27] --> Loop 26 

### Ranking functions of CR lbl121_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR lbl121_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations start/7 
* CE 2 is refined into CE [28,29] 
* CE 3 is refined into CE [30,31,32,33,34,35,36,37,38,39] 
* CE 4 is refined into CE [40] 
* CE 5 is refined into CE [41,42,43,44] 


### Cost equations --> "Loop" of start/7 
* CEs [38] --> Loop 27 
* CEs [37,39] --> Loop 28 
* CEs [29,35,36] --> Loop 29 
* CEs [28] --> Loop 30 
* CEs [40] --> Loop 31 
* CEs [42] --> Loop 32 
* CEs [33,34] --> Loop 33 
* CEs [30,31,32] --> Loop 34 
* CEs [43,44] --> Loop 35 
* CEs [41] --> Loop 36 

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

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


### Specialization of cost equations start0/7 
* CE 1 is refined into CE [45,46,47,48,49,50,51,52,53,54] 


### Cost equations --> "Loop" of start0/7 
* CEs [54] --> Loop 37 
* CEs [53] --> Loop 38 
* CEs [52] --> Loop 39 
* CEs [51] --> Loop 40 
* CEs [50] --> Loop 41 
* CEs [49] --> Loop 42 
* CEs [48] --> Loop 43 
* CEs [47] --> Loop 44 
* CEs [46] --> Loop 45 
* CEs [45] --> Loop 46 

### Ranking functions of CR start0(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 


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

#### Cost of chains of lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< -B+K+1

  with precondition: [G=2,A=F,A=H,C=J,D=K+1,E=L,A=M,B>=2,I>=2*B,A>=D,I>=D,2*D>=I+2] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< -B+D

  with precondition: [G=3,A=F,B>=2,D>=B+1,A>=D] 

* Chain [17]: 0
  with precondition: [G=2,F=A,J=C,L=E,F=H,B=I,D=K+1,F=M,2*D>=B+2,B>=D,F>=D] 

* Chain [16]: 0
  with precondition: [G=3,F=A,B>=2,2*D>=B+2,F>=D] 


#### Cost of chains of lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M):
* Chain [[19],24]: 1*it(19)+0
  Such that:it(19) =< D+1

  with precondition: [G=4,I=1,K+1=0,A=F,A=H,C=J,E=L,A=M,1>=D,D>=0,A>=D+1,B>=D+1] 

* Chain [[19],23]: 1*it(19)+0
  Such that:it(19) =< D+1

  with precondition: [G=3,A=F,1>=D,D>=0,A>=D+1,B>=D+1] 

* Chain [[18],23]: 1*it(18)+1*s(3)+0
  Such that:aux(1) =< F
aux(3) =< D
it(18) =< aux(3)
aux(1) =< aux(3)
s(3) =< it(18)*aux(1)

  with precondition: [G=3,A=F,D>=3,A>=D+1,B>=D+1] 

* Chain [[18],22]: 1*it(18)+1*s(3)+0
  Such that:aux(1) =< F
aux(4) =< D
it(18) =< aux(4)
aux(1) =< aux(4)
s(3) =< it(18)*aux(1)

  with precondition: [G=3,A=F,D>=3,A>=D+1,B>=D+1] 

* Chain [[18],21]: 2*it(18)+1*s(3)+0
  Such that:aux(1) =< F
aux(5) =< D
it(18) =< aux(5)
aux(1) =< aux(5)
s(3) =< it(18)*aux(1)

  with precondition: [G=3,A=F,D>=4,A>=D+1,B>=D+1] 

* Chain [[18],20,[19],24]: 1*it(18)+1*it(19)+1*s(3)+1
  Such that:it(19) =< 2
aux(1) =< H
aux(6) =< D
it(18) =< aux(6)
aux(1) =< aux(6)
s(3) =< it(18)*aux(1)

  with precondition: [G=4,I=1,K+1=0,A=F,A=H,C=J,E=L,A=M,D>=3,A>=D+1,B>=D+1] 

* Chain [[18],20,[19],23]: 1*it(18)+1*it(19)+1*s(3)+1
  Such that:it(19) =< 2
aux(1) =< F
aux(7) =< D
it(18) =< aux(7)
aux(1) =< aux(7)
s(3) =< it(18)*aux(1)

  with precondition: [G=3,A=F,D>=3,A>=D+1,B>=D+1] 

* Chain [[18],20,23]: 1*it(18)+1*s(3)+1
  Such that:aux(1) =< F
aux(8) =< D
it(18) =< aux(8)
aux(1) =< aux(8)
s(3) =< it(18)*aux(1)

  with precondition: [G=3,A=F,D>=3,A>=D+1,B>=D+1] 

* Chain [24]: 0
  with precondition: [D+1=0,G=4,K+1=0,J=C,L=E,A=F,A=H,B=I,A=M,A>=0,B>=1] 

* Chain [23]: 0
  with precondition: [G=3] 

* Chain [22]: 0
  with precondition: [G=3,A=F,D>=2,A>=D+1,B>=D+1] 

* Chain [21]: 1*s(4)+0
  Such that:s(4) =< D

  with precondition: [G=3,A=F,D>=3,A>=D+1,B>=D+1] 

* Chain [20,[19],24]: 1*it(19)+1
  Such that:it(19) =< 2

  with precondition: [D=2,G=4,I=1,K+1=0,A=F,A=H,C=J,E=L,A=M,A>=3,B>=3] 

* Chain [20,[19],23]: 1*it(19)+1
  Such that:it(19) =< 2

  with precondition: [D=2,G=3,A=F,A>=3,B>=3] 

* Chain [20,23]: 1
  with precondition: [D=2,G=3,A=F,A>=3,B>=3] 


#### Cost of chains of lbl121_loop_cont(A,B,C,D,E,F,G,H):
* Chain [26]: 0
  with precondition: [A=3] 

* Chain [25]: 0
  with precondition: [A=4] 


#### Cost of chains of start(A,B,C,D,E,F,G):
* Chain [36]: 0
  with precondition: [A=0,F=0,C=B,E=D] 

* Chain [35]: 2
  with precondition: [A=1,F=1,C=B,E=D] 

* Chain [34]: 5
  with precondition: [A=2,F=2,C=B,E=D] 

* Chain [33]: 8
  with precondition: [A=3,F=3,C=B,E=D] 

* Chain [32]: 0
  with precondition: [F=A,C=B,E=D,1>=F,F>=0] 

* Chain [31]: 0
  with precondition: [F=A,C=B,E=D,0>=F+1] 

* Chain [30]: 0
  with precondition: [F=A,C=B,E=D,F>=2] 

* Chain [29]: 3*s(31)+1
  Such that:aux(14) =< F
s(31) =< aux(14)

  with precondition: [F=A,C=B,E=D,F>=3] 

* Chain [28]: 8*s(34)+2*s(35)+5*s(40)+2
  Such that:aux(17) =< 2
aux(18) =< F
s(35) =< aux(17)
s(34) =< aux(18)
s(40) =< s(34)*aux(18)

  with precondition: [F=A,C=B,E=D,F>=4] 

* Chain [27]: 3*s(47)+1*s(51)+1
  Such that:aux(19) =< F
s(47) =< aux(19)
s(51) =< s(47)*aux(19)

  with precondition: [F=A,C=B,E=D,F>=5] 


#### Cost of chains of start0(A,B,C,D,E,F,G):
* Chain [46]: 0
  with precondition: [A=0] 

* Chain [45]: 2
  with precondition: [A=1] 

* Chain [44]: 5
  with precondition: [A=2] 

* Chain [43]: 8
  with precondition: [A=3] 

* Chain [42]: 0
  with precondition: [1>=A,A>=0] 

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

* Chain [40]: 0
  with precondition: [A>=2] 

* Chain [39]: 3*s(53)+1
  Such that:s(52) =< A
s(53) =< s(52)

  with precondition: [A>=3] 

* Chain [38]: 2*s(56)+8*s(57)+5*s(58)+2
  Such that:s(54) =< 2
s(55) =< A
s(56) =< s(54)
s(57) =< s(55)
s(58) =< s(57)*s(55)

  with precondition: [A>=4] 

* Chain [37]: 3*s(60)+1*s(61)+1
  Such that:s(59) =< A
s(60) =< s(59)
s(61) =< s(60)*s(59)

  with precondition: [A>=5] 


Closed-form bounds of start0(A,B,C,D,E,F,G): 
-------------------------------------
* Chain [46] with precondition: [A=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [45] with precondition: [A=1] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [44] with precondition: [A=2] 
    - Upper bound: 5 
    - Complexity: constant 
* Chain [43] with precondition: [A=3] 
    - Upper bound: 8 
    - Complexity: constant 
* Chain [42] with precondition: [1>=A,A>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [41] with precondition: [0>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [A>=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [A>=3] 
    - Upper bound: 3*A+1 
    - Complexity: n 
* Chain [38] with precondition: [A>=4] 
    - Upper bound: 8*A+6+5*A*A 
    - Complexity: n^2 
* Chain [37] with precondition: [A>=5] 
    - Upper bound: 3*A+1+A*A 
    - Complexity: n^2 

### Maximum cost of start0(A,B,C,D,E,F,G): max([8,nat(A)*5+5+nat(A)*4*nat(A)+nat(A)*nat(A)+(nat(A)*3+1)]) 
Asymptotic class: n^2 
* Total analysis performed in 816 ms.