/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval1/4,eval2/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [eval1_loop_cont/2]
3. non_recursive  : [start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval1/4
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 eval1/4 
* CE 5 is refined into CE [6] 
* CE 2 is refined into CE [7] 
* CE 3 is refined into CE [8] 
* CE 4 is refined into CE [9] 


### Cost equations --> "Loop" of eval1/4 
* CEs [7] --> Loop 6 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [6] --> Loop 9 

### Ranking functions of CR eval1(A,B,C,D) 
* RF of phase [6]: [A-B]
* RF of phase [7,8]: [2*A-B-C-1]

#### Partial ranking functions of CR eval1(A,B,C,D) 
* Partial RF of phase [6]:
  - RF of loop [6:1]:
    A-B
* Partial RF of phase [7,8]:
  - RF of loop [7:1]:
    A-C
  - RF of loop [8:1]:
    A-B


### Specialization of cost equations start/4 
* CE 1 is refined into CE [10,11,12] 


### Cost equations --> "Loop" of start/4 
* CEs [12] --> Loop 10 
* CEs [11] --> Loop 11 
* CEs [10] --> Loop 12 

### 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 eval1(A,B,C,D):
* Chain [[7,8],[6],9]: 2*it(6)+1*it(7)+0
  Such that:it(7) =< A-C
aux(3) =< A-B
aux(4) =< 2*A-B-C
it(6) =< aux(3)
it(6) =< aux(4)
it(7) =< aux(4)

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

* Chain [[7,8],9]: 1*it(7)+1*it(8)+0
  Such that:it(8) =< A-B
it(7) =< A-C
aux(5) =< 2*A-B-C
it(7) =< aux(5)
it(8) =< aux(5)

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

* Chain [[6],9]: 1*it(6)+0
  Such that:it(6) =< A-B

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

* Chain [9]: 0
  with precondition: [D=2] 


#### Cost of chains of start(A,B,C,D):
* Chain [12]: 0
  with precondition: [] 

* Chain [11]: 1*s(8)+0
  Such that:s(8) =< A-B

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

* Chain [10]: 3*s(12)+2*s(13)+0
  Such that:s(9) =< A-B
s(10) =< A-C
s(11) =< 2*A-B-C
s(12) =< s(9)
s(13) =< s(10)
s(13) =< s(11)
s(12) =< s(11)

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


Closed-form bounds of start(A,B,C,D): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [11] with precondition: [C>=A,A>=B+1] 
    - Upper bound: A-B 
    - Complexity: n 
* Chain [10] with precondition: [A>=B+1,A>=C+1] 
    - Upper bound: 5*A-3*B-2*C 
    - Complexity: n 

### Maximum cost of start(A,B,C,D): nat(A-C)*2+nat(A-B)*2+nat(A-B) 
Asymptotic class: n 
* Total analysis performed in 117 ms.