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


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [cut/9]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [stop/9]
3. non_recursive  : [cut_loop_cont/10]
4. non_recursive  : [start/9]
5. non_recursive  : [start0/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into cut/9
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into cut_loop_cont/10
4. SCC is partially evaluated into start/9
5. SCC is partially evaluated into start0/9

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

### Specialization of cost equations cut/9 
* CE 13 is refined into CE [16] 
* CE 11 is refined into CE [17] 
* CE 7 is refined into CE [18] 
* CE 9 is refined into CE [19] 
* CE 12 is refined into CE [20] 
* CE 10 is refined into CE [21] 
* CE 6 is refined into CE [22] 
* CE 8 is refined into CE [23] 


### Cost equations --> "Loop" of cut/9 
* CEs [21] --> Loop 15 
* CEs [22] --> Loop 16 
* CEs [23] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [18] --> Loop 20 
* CEs [19] --> Loop 21 
* CEs [20] --> Loop 22 

### Ranking functions of CR cut(A,B,D,E,G,I,J,K,L) 
* RF of phase [15,16,17]: [G-1]

#### Partial ranking functions of CR cut(A,B,D,E,G,I,J,K,L) 
* Partial RF of phase [15,16,17]:
  - RF of loop [15:1]:
    A-E-1 depends on loops [16:1,17:1] 
    D-E-1 depends on loops [16:1,17:1] 
  - RF of loop [15:1,16:1,17:1]:
    G-1
  - RF of loop [16:1]:
    E-1 depends on loops [15:1] 


### Specialization of cost equations cut_loop_cont/10 
* CE 15 is refined into CE [24] 
* CE 14 is refined into CE [25] 


### Cost equations --> "Loop" of cut_loop_cont/10 
* CEs [24] --> Loop 23 
* CEs [25] --> Loop 24 

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

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


### Specialization of cost equations start/9 
* CE 4 is refined into CE [26,27,28,29,30,31,32] 
* CE 5 is refined into CE [33,34,35,36,37,38,39,40] 
* CE 2 is refined into CE [41] 
* CE 3 is refined into CE [42] 


### Cost equations --> "Loop" of start/9 
* CEs [30] --> Loop 25 
* CEs [28,29,32,35,36,37,38,40] --> Loop 26 
* CEs [31,39] --> Loop 27 
* CEs [41] --> Loop 28 
* CEs [26,27,33,34] --> Loop 29 
* CEs [42] --> Loop 30 

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

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


### Specialization of cost equations start0/9 
* CE 1 is refined into CE [43,44,45,46,47,48] 


### Cost equations --> "Loop" of start0/9 
* CEs [48] --> Loop 31 
* CEs [47] --> Loop 32 
* CEs [46] --> Loop 33 
* CEs [45] --> Loop 34 
* CEs [44] --> Loop 35 
* CEs [43] --> Loop 36 

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

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


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

#### Cost of chains of cut(A,B,D,E,G,I,J,K,L):
* Chain [[15,16,17],22]: 3*it(15)+0
  Such that:aux(8) =< -E+J
aux(7) =< -E+J+1
it(15) =< aux(7)
it(15) =< aux(8)

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

* Chain [[15,16,17],21]: 3*it(15)+0
  Such that:aux(9) =< G
it(15) =< aux(9)

  with precondition: [I=2,K=0,L=0,A=D,E>=0,G>=2,G>=E,A>=G+1,A>=E+G] 

* Chain [[15,16,17],20]: 3*it(15)+0
  Such that:aux(10) =< G
it(15) =< aux(10)

  with precondition: [I=2,L=0,A=D,E>=0,G>=2,K>=1,A>=G+1,A>=E+G,G+K>=E,E+G>=K+2] 

* Chain [[15,16,17],19]: 3*it(15)+0
  Such that:aux(11) =< G
it(15) =< aux(11)

  with precondition: [I=2,L=0,A=D,J+1=K,E>=0,G>=2,J>=0,A>=G+1,A>=E+G,G+J>=E+1,E+G>=J+1,2*A>=E+G+J+3] 

* Chain [[15,16,17],18]: 3*it(15)+0
  Such that:aux(12) =< G
it(15) =< aux(12)

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

* Chain [22]: 0
  with precondition: [G=1,I=2,K=0,L=0,A=D,A=E+1,A=J+1,A>=2] 

* Chain [21]: 0
  with precondition: [G=1,I=2,K=0,L=0,D=A,J=B,1>=E,D>=2,E>=0] 

* Chain [19]: 0
  with precondition: [G=1,I=2,L=0,D=A,E=J,E+1=K,E>=0,D>=E+2] 

* Chain [18]: 0
  with precondition: [I=3,D=A,E>=0,G>=1,D>=G+1,D>=E+G] 


#### Cost of chains of cut_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [24]: 0
  with precondition: [A=2,E=B,E>=2] 

* Chain [23]: 0
  with precondition: [A=3,E=B,E>=2] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I):
* Chain [30]: 0
  with precondition: [A=1,D=1,C=B,F=E,H=G] 

* Chain [29]: 0
  with precondition: [A=2,D=2,C=B,F=E,H=G] 

* Chain [28]: 0
  with precondition: [D=A,C=B,F=E,H=G,0>=D] 

* Chain [27]: 0
  with precondition: [D=A,C=B,F=E,H=G,D>=2] 

* Chain [26]: 21*s(2)+3*s(9)+0
  Such that:aux(13) =< D
aux(14) =< A
s(2) =< aux(14)
s(9) =< aux(13)

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

* Chain [25]: 3*s(19)+0
  Such that:s(18) =< A
s(19) =< s(18)

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


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I):
* Chain [36]: 0
  with precondition: [A=1] 

* Chain [35]: 0
  with precondition: [A=2] 

* Chain [34]: 0
  with precondition: [0>=A] 

* Chain [33]: 0
  with precondition: [A>=2] 

* Chain [32]: 24*s(22)+0
  Such that:aux(15) =< A
s(22) =< aux(15)

  with precondition: [A>=3] 

* Chain [31]: 3*s(25)+0
  Such that:s(24) =< A
s(25) =< s(24)

  with precondition: [A>=4] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 
-------------------------------------
* Chain [36] with precondition: [A=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [A=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [A>=2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [A>=3] 
    - Upper bound: 24*A 
    - Complexity: n 
* Chain [31] with precondition: [A>=4] 
    - Upper bound: 3*A 
    - Complexity: n 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(A)*24 
Asymptotic class: n 
* Total analysis performed in 552 ms.