/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  : [f6/9]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f19/5]
3. non_recursive  : [f15/5]
4. non_recursive  : [f6_loop_cont/6]
5. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/9
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f15/5
4. SCC is partially evaluated into f6_loop_cont/6
5. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f6/9 
* CE 7 is refined into CE [14] 
* CE 6 is refined into CE [15] 
* CE 5 is refined into CE [16] 
* CE 4 is refined into CE [17] 
* CE 2 is refined into CE [18] 
* CE 3 is refined into CE [19] 


### Cost equations --> "Loop" of f6/9 
* CEs [18] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [15] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I) 
* RF of phase [14,15]: [-B+C]

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I) 
* Partial RF of phase [14,15]:
  - RF of loop [14:1,15:1]:
    -B+C
  - RF of loop [15:1]:
    -A/2+C-1/2


### Specialization of cost equations f15/5 
* CE 13 is refined into CE [20] 
* CE 12 is refined into CE [21] 
* CE 11 is refined into CE [22] 


### Cost equations --> "Loop" of f15/5 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR f15(A,B,C,D,E) 

#### Partial ranking functions of CR f15(A,B,C,D,E) 


### Specialization of cost equations f6_loop_cont/6 
* CE 10 is refined into CE [23] 
* CE 9 is refined into CE [24] 
* CE 8 is refined into CE [25,26,27] 


### Cost equations --> "Loop" of f6_loop_cont/6 
* CEs [23] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [26] --> Loop 26 
* CEs [25] --> Loop 27 

### Ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [28,29,30,31,32,33,34,35,36] 


### Cost equations --> "Loop" of f0/5 
* CEs [31,34] --> Loop 28 
* CEs [30,32,36] --> Loop 29 
* CEs [29] --> Loop 30 
* CEs [33] --> Loop 31 
* CEs [28] --> Loop 32 
* CEs [35] --> Loop 33 

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

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


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

#### Cost of chains of f6(A,B,C,D,E,F,G,H,I):
* Chain [[14,15],19]: 1*it(14)+1*it(15)+0
  Such that:it(15) =< -A/2+F/2
aux(3) =< -B+H
it(14) =< aux(3)
it(15) =< aux(3)

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

* Chain [[14,15],18]: 1*it(14)+1*it(15)+0
  Such that:it(15) =< -A/2+F/2
aux(4) =< -B+H
it(14) =< aux(4)
it(15) =< aux(4)

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

* Chain [[14,15],17]: 1*it(14)+1*it(15)+0
  Such that:it(15) =< -A/2+H/2
aux(5) =< -B+H
it(14) =< aux(5)
it(15) =< aux(5)

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

* Chain [[14,15],16]: 2*it(14)+0
  Such that:aux(6) =< -B+C
it(14) =< aux(6)

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

* Chain [18]: 0
  with precondition: [E=2,I=D,A=F,B=G,C=H,A>=0,2*B>=A,A>=C+1,B>=C] 

* Chain [17]: 0
  with precondition: [E=3,I=1,A=C,A=F,B=G,A=H,A>=0,B>=A] 

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


#### Cost of chains of f15(A,B,C,D,E):
* Chain [22]: 0
  with precondition: [C+1=A] 

* Chain [21]: 0
  with precondition: [C>=A] 

* Chain [20]: 0
  with precondition: [A>=C+2] 


#### Cost of chains of f6_loop_cont(A,B,C,D,E,F):
* Chain [27]: 0
  with precondition: [A=2,D+1=B] 

* Chain [26]: 0
  with precondition: [A=2,D>=B] 

* Chain [25]: 0
  with precondition: [A=2,B>=D+2] 

* Chain [24]: 0
  with precondition: [A=3] 

* Chain [23]: 0
  with precondition: [A=4] 


#### Cost of chains of f0(A,B,C,D,E):
* Chain [33]: 0
  with precondition: [] 

* Chain [32]: 0
  with precondition: [C+1=0] 

* Chain [31]: 0
  with precondition: [C=0] 

* Chain [30]: 0
  with precondition: [0>=C+2] 

* Chain [29]: 1*s(1)+4*s(3)+1*s(4)+0
  Such that:s(4) =< C/2
s(1) =< C/2+1/2
aux(7) =< C
s(3) =< aux(7)
s(1) =< aux(7)
s(4) =< aux(7)

  with precondition: [C>=1] 

* Chain [28]: 3*s(9)+1*s(12)+0
  Such that:s(12) =< C/2
aux(9) =< C
s(9) =< aux(9)
s(12) =< aux(9)

  with precondition: [C>=2] 


Closed-form bounds of f0(A,B,C,D,E): 
-------------------------------------
* Chain [33] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [C+1=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [C=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [0>=C+2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [C>=1] 
    - Upper bound: 5*C+1/2 
    - Complexity: n 
* Chain [28] with precondition: [C>=2] 
    - Upper bound: 7/2*C 
    - Complexity: n 

### Maximum cost of f0(A,B,C,D,E): nat(C)*3+nat(C/2)+(nat(C/2+1/2)+nat(C)) 
Asymptotic class: n 
* Total analysis performed in 285 ms.