/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  : [f2/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2_loop_cont/2]
3. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/3
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f2/3 
* CE 13 is refined into CE [14] 
* CE 7 is refined into CE [15] 
* CE 8 is refined into CE [16] 
* CE 5 is refined into CE [17] 
* CE 6 is refined into CE [18] 
* CE 9 is refined into CE [19] 
* CE 10 is refined into CE [20] 
* CE 11 is refined into CE [21] 
* CE 12 is refined into CE [22] 


### Cost equations --> "Loop" of f2/3 
* CEs [15] --> Loop 14 
* CEs [16] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [18] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [20] --> Loop 19 
* CEs [21] --> Loop 20 
* CEs [22] --> Loop 21 
* CEs [14] --> Loop 22 

### Ranking functions of CR f2(A,B,C) 
* RF of phase [14]: [A-1]
* RF of phase [15]: [A-B]
* RF of phase [16]: [B-1]
* RF of phase [17]: [A+B-1]
* RF of phase [18]: [-A-B]
* RF of phase [19]: [-B-1]
* RF of phase [20]: [-A+B]
* RF of phase [21]: [-A-1]

#### Partial ranking functions of CR f2(A,B,C) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    A-1
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    A-B
* Partial RF of phase [16]:
  - RF of loop [16:1]:
    B-1
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    A+B-1
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    -A-B
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    -B-1
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    -A+B
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    -A-1


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [23,24,25,26] 
* CE 2 is refined into CE [27,28,29] 
* CE 3 is refined into CE [30,31,32,33] 
* CE 4 is refined into CE [34,35,36,37] 


### Cost equations --> "Loop" of f0/3 
* CEs [26] --> Loop 23 
* CEs [31,33] --> Loop 24 
* CEs [29] --> Loop 25 
* CEs [24,25] --> Loop 26 
* CEs [23] --> Loop 27 
* CEs [37] --> Loop 28 
* CEs [28] --> Loop 29 
* CEs [27] --> Loop 30 
* CEs [32] --> Loop 31 
* CEs [35,36] --> Loop 32 
* CEs [30] --> Loop 33 
* CEs [34] --> Loop 34 

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

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


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

#### Cost of chains of f2(A,B,C):
* Chain [[21],22]: 1*it(21)+0
  Such that:it(21) =< -A

  with precondition: [C=2,0>=A+2,A+B>=0] 

* Chain [[20],[16],22]: 1*it(16)+1*it(20)+0
  Such that:it(20) =< -A+B
it(16) =< B

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

* Chain [[20],22]: 1*it(20)+0
  Such that:it(20) =< -A+B

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

* Chain [[19],22]: 1*it(19)+0
  Such that:it(19) =< -B

  with precondition: [C=2,0>=B+2,B>=A] 

* Chain [[18],[21],22]: 1*it(18)+1*it(21)+0
  Such that:it(21) =< -A
it(18) =< -A-B

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

* Chain [[18],22]: 1*it(18)+0
  Such that:it(18) =< -A-B

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

* Chain [[17],[14],22]: 1*it(14)+1*it(17)+0
  Such that:it(14) =< A
it(17) =< A+B

  with precondition: [C=2,0>=B,A+B>=2] 

* Chain [[17],22]: 1*it(17)+0
  Such that:it(17) =< A+B

  with precondition: [C=2,0>=B,A+B>=2] 

* Chain [[16],22]: 1*it(16)+0
  Such that:it(16) =< B

  with precondition: [C=2,B>=2,A>=B] 

* Chain [[15],[19],22]: 1*it(15)+1*it(19)+0
  Such that:it(15) =< A-B
it(19) =< -B

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

* Chain [[15],22]: 1*it(15)+0
  Such that:it(15) =< A-B

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

* Chain [[14],22]: 1*it(14)+0
  Such that:it(14) =< A

  with precondition: [C=2,A>=2,1>=A+B] 

* Chain [22]: 0
  with precondition: [C=2] 


#### Cost of chains of f0(A,B,C):
* Chain [34]: 0
  with precondition: [0>=A+1,0>=B+1] 

* Chain [33]: 0
  with precondition: [0>=A+1,B>=1] 

* Chain [32]: 2*s(4)+1*s(5)+0
  Such that:s(5) =< -B
aux(2) =< A-B
s(4) =< aux(2)

  with precondition: [0>=A+1,A>=B+1] 

* Chain [31]: 1*s(7)+0
  Such that:s(7) =< -A

  with precondition: [0>=A+2,A+B>=0] 

* Chain [30]: 0
  with precondition: [0>=B+1,A>=1] 

* Chain [29]: 1*s(8)+2*s(10)+0
  Such that:s(8) =< A
s(9) =< A+B
s(10) =< s(9)

  with precondition: [0>=B+1,A+B>=2] 

* Chain [28]: 1*s(11)+0
  Such that:s(11) =< -B

  with precondition: [0>=B+2,B>=A] 

* Chain [27]: 0
  with precondition: [A>=1,B>=1] 

* Chain [26]: 2*s(12)+1*s(13)+0
  Such that:s(13) =< B
aux(3) =< -A+B
s(12) =< aux(3)

  with precondition: [A>=1,B>=A+1] 

* Chain [25]: 1*s(15)+0
  Such that:s(15) =< A

  with precondition: [A>=2,1>=A+B] 

* Chain [24]: 1*s(16)+2*s(17)+0
  Such that:s(16) =< -A
aux(4) =< -A-B
s(17) =< aux(4)

  with precondition: [B>=1,0>=A+B+1] 

* Chain [23]: 1*s(19)+0
  Such that:s(19) =< B

  with precondition: [B>=2,A>=B] 


Closed-form bounds of f0(A,B,C): 
-------------------------------------
* Chain [34] with precondition: [0>=A+1,0>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [0>=A+1,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [0>=A+1,A>=B+1] 
    - Upper bound: 2*A-3*B 
    - Complexity: n 
* Chain [31] with precondition: [0>=A+2,A+B>=0] 
    - Upper bound: -A 
    - Complexity: n 
* Chain [30] with precondition: [0>=B+1,A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [0>=B+1,A+B>=2] 
    - Upper bound: 3*A+2*B 
    - Complexity: n 
* Chain [28] with precondition: [0>=B+2,B>=A] 
    - Upper bound: -B 
    - Complexity: n 
* Chain [27] with precondition: [A>=1,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [A>=1,B>=A+1] 
    - Upper bound: -2*A+3*B 
    - Complexity: n 
* Chain [25] with precondition: [A>=2,1>=A+B] 
    - Upper bound: A 
    - Complexity: n 
* Chain [24] with precondition: [B>=1,0>=A+B+1] 
    - Upper bound: -3*A-2*B 
    - Complexity: n 
* Chain [23] with precondition: [B>=2,A>=B] 
    - Upper bound: B 
    - Complexity: n 

### Maximum cost of f0(A,B,C): max([max([max([nat(A-B)*2+nat(-B),nat(-A-B)*2+nat(-A)]),nat(-A+B)*2+nat(B)]),nat(A+B)*2+nat(A)]) 
Asymptotic class: n 
* Total analysis performed in 309 ms.