/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  : [f/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f_loop_cont/2]
3. non_recursive  : [start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into start/4

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

### Specialization of cost equations f/4 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 
* CE 2 is refined into CE [7] 


### Cost equations --> "Loop" of f/4 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f(A,B,C,D) 
* RF of phase [5,6]: [2*A-B-C-1]

#### Partial ranking functions of CR f(A,B,C,D) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A-C
  - RF of loop [6:1]:
    A-B


### Specialization of cost equations start/4 
* CE 1 is refined into CE [8,9] 


### Cost equations --> "Loop" of start/4 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

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

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


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

#### Cost of chains of f(A,B,C,D):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:it(6) =< A-B
it(5) =< A-C
aux(3) =< 2*A-B-C
it(5) =< aux(3)
it(6) =< aux(3)

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

* Chain [7]: 0
  with precondition: [D=2] 


#### Cost of chains of start(A,B,C,D):
* Chain [9]: 0
  with precondition: [] 

* Chain [8]: 1*s(1)+1*s(2)+0
  Such that:s(1) =< A-B
s(2) =< A-C
s(3) =< 2*A-B-C
s(2) =< s(3)
s(1) =< s(3)

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


Closed-form bounds of start(A,B,C,D): 
-------------------------------------
* Chain [9] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [8] with precondition: [A>=B+1,A>=C+1] 
    - Upper bound: 2*A-B-C 
    - Complexity: n 

### Maximum cost of start(A,B,C,D): nat(A-C)+nat(A-B) 
Asymptotic class: n 
* Total analysis performed in 64 ms.