/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  : [eval/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [eval_loop_cont/2]
3. non_recursive  : [start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval/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 eval/4 
* CE 3 is refined into CE [4] 
* CE 2 is refined into CE [5] 


### Cost equations --> "Loop" of eval/4 
* CEs [5] --> Loop 4 
* CEs [4] --> Loop 5 

### Ranking functions of CR eval(A,B,C,D) 
* RF of phase [4]: [A-B,A-C]

#### Partial ranking functions of CR eval(A,B,C,D) 
* Partial RF of phase [4]:
  - RF of loop [4:1]:
    A-B
    A-C


### Specialization of cost equations start/4 
* CE 1 is refined into CE [6,7] 


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

### 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 eval(A,B,C,D):
* Chain [[4],5]: 1*it(4)+0
  Such that:it(4) =< A-B
it(4) =< A-C

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

* Chain [5]: 0
  with precondition: [D=2] 


#### Cost of chains of start(A,B,C,D):
* Chain [7]: 0
  with precondition: [] 

* Chain [6]: 1*s(1)+0
  Such that:s(1) =< A-B
s(1) =< A-C

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


Closed-form bounds of start(A,B,C,D): 
-------------------------------------
* Chain [7] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [6] with precondition: [A>=B+1,A>=C+1] 
    - Upper bound: A-B 
    - Complexity: n 

### Maximum cost of start(A,B,C,D): nat(A-B) 
Asymptotic class: n 
* Total analysis performed in 39 ms.