/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  : [f2/5]
1. recursive  : [f2_loop_cont/8,f300/7]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f1/4]
4. non_recursive  : [f300_loop_cont/5]
5. non_recursive  : [f3/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/5
1. SCC is partially evaluated into f300/7
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f300_loop_cont/5
5. SCC is partially evaluated into f3/4

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

### Specialization of cost equations f2/5 
* CE 10 is refined into CE [11] 
* CE 9 is refined into CE [12] 
* CE 8 is refined into CE [13] 


### Cost equations --> "Loop" of f2/5 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR f2(A,B,E,F,G) 
* RF of phase [11]: [A-30]

#### Partial ranking functions of CR f2(A,B,E,F,G) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    A-30


### Specialization of cost equations f300/7 
* CE 4 is refined into CE [14] 
* CE 2 is refined into CE [15,16] 
* CE 5 is refined into CE [17] 
* CE 3 is refined into CE [18,19] 


### Cost equations --> "Loop" of f300/7 
* CEs [19] --> Loop 14 
* CEs [18] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [15] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR f300(A,B,C,E,F,G,H) 
* RF of phase [14]: [B-20]

#### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    B-20


### Specialization of cost equations f300_loop_cont/5 
* CE 6 is refined into CE [20] 
* CE 7 is refined into CE [21] 


### Cost equations --> "Loop" of f300_loop_cont/5 
* CEs [20] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f3/4 
* CE 1 is refined into CE [22,23,24,25,26,27,28,29,30,31,32] 


### Cost equations --> "Loop" of f3/4 
* CEs [29] --> Loop 22 
* CEs [28] --> Loop 23 
* CEs [27,30] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [32] --> Loop 26 
* CEs [25] --> Loop 27 
* CEs [24,31] --> Loop 28 
* CEs [22] --> Loop 29 
* CEs [23] --> Loop 30 

### Ranking functions of CR f3(A,B,C,E) 

#### Partial ranking functions of CR f3(A,B,C,E) 


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

#### Cost of chains of f2(A,B,E,F,G):
* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< A

  with precondition: [E=2,F=30,B=G+1,A>=31,B>=21] 

* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< A

  with precondition: [E=3,A>=31,B>=21] 

* Chain [13]: 0
  with precondition: [E=2,A=F,B=G+1,30>=A,B>=21] 

* Chain [12]: 0
  with precondition: [E=3,B>=21] 


#### Cost of chains of f300(A,B,C,E,F,G,H):
* Chain [[14],19]: 1*it(14)+0
  Such that:it(14) =< B

  with precondition: [E=3,30>=A,B>=21] 

* Chain [[14],17]: 1*it(14)+0
  Such that:it(14) =< B

  with precondition: [E=3,30>=A,B>=22] 

* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< B

  with precondition: [E=4,G=20,A=F,30>=A,B>=21] 

* Chain [19]: 0
  with precondition: [E=3] 

* Chain [18]: 1*s(1)+0
  Such that:s(1) =< A

  with precondition: [E=3,A>=31,B>=21] 

* Chain [17]: 0
  with precondition: [E=3,B>=21] 

* Chain [16]: 0
  with precondition: [E=4,F=A,B=G,20>=B] 

* Chain [15,[14],19]: 1*it(14)+1*s(2)+1
  Such that:s(2) =< A
it(14) =< B

  with precondition: [E=3,A>=31,B>=22] 

* Chain [15,[14],17]: 1*it(14)+1*s(2)+1
  Such that:s(2) =< A
it(14) =< B

  with precondition: [E=3,A>=31,B>=23] 

* Chain [15,[14],16]: 1*it(14)+1*s(2)+1
  Such that:s(2) =< A
it(14) =< B

  with precondition: [E=4,F=30,G=20,A>=31,B>=22] 

* Chain [15,19]: 1*s(2)+1
  Such that:s(2) =< A

  with precondition: [E=3,A>=31,B>=21] 

* Chain [15,17]: 1*s(2)+1
  Such that:s(2) =< A

  with precondition: [E=3,A>=31,B>=22] 

* Chain [15,16]: 1*s(2)+1
  Such that:s(2) =< A

  with precondition: [B=21,E=4,F=30,G=20,A>=31] 


#### Cost of chains of f300_loop_cont(A,B,C,D,E):
* Chain [21]: 0
  with precondition: [A=3] 

* Chain [20]: 0
  with precondition: [A=4] 


#### Cost of chains of f3(A,B,C,E):
* Chain [30]: 0
  with precondition: [] 

* Chain [29]: 1*s(8)+1
  Such that:s(8) =< A

  with precondition: [B=21,A>=31] 

* Chain [28]: 2*s(9)+0
  Such that:aux(3) =< B
s(9) =< aux(3)

  with precondition: [30>=A,B>=21] 

* Chain [27]: 1*s(11)+0
  Such that:s(11) =< B

  with precondition: [30>=A,B>=22] 

* Chain [26]: 0
  with precondition: [20>=B] 

* Chain [25]: 2*s(13)+1
  Such that:s(12) =< A
s(13) =< s(12)

  with precondition: [A>=31,B>=21] 

* Chain [24]: 2*s(14)+3*s(16)+1
  Such that:aux(4) =< A
aux(5) =< B
s(16) =< aux(4)
s(14) =< aux(5)

  with precondition: [A>=31,B>=22] 

* Chain [23]: 1*s(19)+1*s(20)+1
  Such that:s(19) =< A
s(20) =< B

  with precondition: [A>=31,B>=23] 

* Chain [22]: 0
  with precondition: [B>=21] 


Closed-form bounds of f3(A,B,C,E): 
-------------------------------------
* Chain [30] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [B=21,A>=31] 
    - Upper bound: A+1 
    - Complexity: n 
* Chain [28] with precondition: [30>=A,B>=21] 
    - Upper bound: 2*B 
    - Complexity: n 
* Chain [27] with precondition: [30>=A,B>=22] 
    - Upper bound: B 
    - Complexity: n 
* Chain [26] with precondition: [20>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [A>=31,B>=21] 
    - Upper bound: 2*A+1 
    - Complexity: n 
* Chain [24] with precondition: [A>=31,B>=22] 
    - Upper bound: 3*A+2*B+1 
    - Complexity: n 
* Chain [23] with precondition: [A>=31,B>=23] 
    - Upper bound: A+B+1 
    - Complexity: n 
* Chain [22] with precondition: [B>=21] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f3(A,B,C,E): max([nat(B)*2,nat(A)+1+max([nat(B),nat(B)*2+nat(A)+nat(A)])]) 
Asymptotic class: n 
* Total analysis performed in 216 ms.