/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [lbl91/9]
1. recursive  : [lbl81/9,lbl91_loop_cont/10]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/5]
4. non_recursive  : [lbl81_loop_cont/6]
5. non_recursive  : [start/5]
6. non_recursive  : [start0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl91/9
1. SCC is partially evaluated into lbl81/9
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl81_loop_cont/6
5. SCC is partially evaluated into start/5
6. SCC is partially evaluated into start0/5

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

### Specialization of cost equations lbl91/9 
* CE 10 is refined into CE [16] 
* CE 8 is refined into CE [17] 
* CE 9 is refined into CE [18] 


### Cost equations --> "Loop" of lbl91/9 
* CEs [18] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I) 
* RF of phase [15]: [A-B-2,-B+D-2]

#### Partial ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    A-B-2
    -B+D-2


### Specialization of cost equations lbl81/9 
* CE 15 is refined into CE [19] 
* CE 13 is refined into CE [20] 
* CE 14 is refined into CE [21] 


### Cost equations --> "Loop" of lbl81/9 
* CEs [21] --> Loop 18 
* CEs [19] --> Loop 19 
* CEs [20] --> Loop 20 

### Ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I) 
* RF of phase [18]: [B-D-2,C-D-2]

#### Partial ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    B-D-2
    C-D-2


### Specialization of cost equations lbl81_loop_cont/6 
* CE 12 is refined into CE [22] 
* CE 11 is refined into CE [23] 


### Cost equations --> "Loop" of lbl81_loop_cont/6 
* CEs [22] --> Loop 21 
* CEs [23] --> Loop 22 

### Ranking functions of CR lbl81_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR lbl81_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations start/5 
* CE 2 is refined into CE [24,25] 
* CE 3 is refined into CE [26,27] 
* CE 7 is refined into CE [28,29,30,31] 
* CE 6 is refined into CE [32] 
* CE 5 is refined into CE [33] 
* CE 4 is refined into CE [34] 


### Cost equations --> "Loop" of start/5 
* CEs [25,27] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [29,31] --> Loop 25 
* CEs [30] --> Loop 26 
* CEs [32] --> Loop 27 
* CEs [33] --> Loop 28 
* CEs [34] --> Loop 29 
* CEs [26] --> Loop 30 
* CEs [28] --> Loop 31 

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

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


### Specialization of cost equations start0/5 
* CE 1 is refined into CE [35,36,37,38,39,40,41,42,43] 


### Cost equations --> "Loop" of start0/5 
* CEs [41] --> Loop 32 
* CEs [40] --> Loop 33 
* CEs [43] --> Loop 34 
* CEs [42] --> Loop 35 
* CEs [39] --> Loop 36 
* CEs [37] --> Loop 37 
* CEs [38] --> Loop 38 
* CEs [35] --> Loop 39 
* CEs [36] --> Loop 40 

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

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


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

#### Cost of chains of lbl91(A,B,C,D,E,F,G,H,I):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< -B+I

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

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

  with precondition: [E=4,A=D,C>=0,A>=B+3,B>=C+1] 

* Chain [17]: 0
  with precondition: [E=2,A=B+2,A=D,A=F,A=G+2,C=H,A=I,C>=0,A>=C+3] 

* Chain [16]: 0
  with precondition: [E=4,D=A,C>=0,D>=B+2,B>=C+1] 


#### Cost of chains of lbl81(A,B,C,D,E,F,G,H,I):
* Chain [[18],20]: 1*it(18)+0
  Such that:it(18) =< -D+I

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

* Chain [[18],19]: 1*it(18)+0
  Such that:it(18) =< B-D

  with precondition: [E=4,B=C,A>=0,D>=A+1,B>=D+3] 

* Chain [20]: 0
  with precondition: [E=2,C=B,C=D+2,A=F,C=G,C=H,C=I+2,A>=0,C>=A+3] 

* Chain [19]: 0
  with precondition: [E=4,C=B,A>=0,D>=A+1,C>=D+2] 


#### Cost of chains of lbl81_loop_cont(A,B,C,D,E,F):
* Chain [22]: 0
  with precondition: [A=2] 

* Chain [21]: 0
  with precondition: [A=4] 


#### Cost of chains of start(A,B,C,D,E):
* Chain [31]: 0
  with precondition: [B=A+3,B=C,B=D+3,B>=3] 

* Chain [30]: 0
  with precondition: [B+3=A,B=C,B+3=D,B>=0] 

* Chain [29]: 0
  with precondition: [D=A,C=B,0>=D+1] 

* Chain [28]: 0
  with precondition: [D=A,C=B,0>=C+1] 

* Chain [27]: 0
  with precondition: [D=A,C=B,C>=0,D>=0,D+2>=C,C+2>=D] 

* Chain [26]: 0
  with precondition: [D=A,C=B,D>=0,C>=D+3] 

* Chain [25]: 2*s(1)+0
  Such that:aux(1) =< C-D
s(1) =< aux(1)

  with precondition: [D=A,C=B,D>=0,C>=D+4] 

* Chain [24]: 0
  with precondition: [D=A,C=B,C>=0,D>=C+3] 

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

  with precondition: [D=A,C=B,C>=0,D>=C+4] 


#### Cost of chains of start0(A,B,C,D,E):
* Chain [40]: 0
  with precondition: [C=A+3,C>=3] 

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

* Chain [38]: 0
  with precondition: [0>=A+1] 

* Chain [37]: 0
  with precondition: [0>=C+1] 

* Chain [36]: 0
  with precondition: [A>=0,C>=0,C+2>=A,A+2>=C] 

* Chain [35]: 0
  with precondition: [A>=0,C>=A+3] 

* Chain [34]: 2*s(6)+0
  Such that:s(5) =< -A+C
s(6) =< s(5)

  with precondition: [A>=0,C>=A+4] 

* Chain [33]: 0
  with precondition: [C>=0,A>=C+3] 

* Chain [32]: 2*s(8)+0
  Such that:s(7) =< A-C
s(8) =< s(7)

  with precondition: [C>=0,A>=C+4] 


Closed-form bounds of start0(A,B,C,D,E): 
-------------------------------------
* Chain [40] with precondition: [C=A+3,C>=3] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [39] with precondition: [A=C+3,A>=3] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [38] with precondition: [0>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [37] with precondition: [0>=C+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [36] with precondition: [A>=0,C>=0,C+2>=A,A+2>=C] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [A>=0,C>=A+3] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [A>=0,C>=A+4] 
    - Upper bound: -2*A+2*C 
    - Complexity: n 
* Chain [33] with precondition: [C>=0,A>=C+3] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [C>=0,A>=C+4] 
    - Upper bound: 2*A-2*C 
    - Complexity: n 

### Maximum cost of start0(A,B,C,D,E): max([nat(-A+C)*2,nat(A-C)*2]) 
Asymptotic class: n 
* Total analysis performed in 343 ms.