/export/starexec/sandbox/solver/bin/starexec_run_C /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_Loopus2011_ex1_2/6,eval_Loopus2011_ex1_3/7,eval_Loopus2011_ex1_bb3_in/6,eval_Loopus2011_ex1_bb4_in/6,eval_Loopus2011_ex1_bb5_in/7]
1. recursive  : [eval_Loopus2011_ex1__critedge_in/5,eval_Loopus2011_ex1_bb1_in/3,eval_Loopus2011_ex1_bb2_in/3,eval_Loopus2011_ex1_bb3_in_loop_cont/6]
2. non_recursive  : [eval_Loopus2011_ex1_stop/1]
3. non_recursive  : [eval_Loopus2011_ex1_bb6_in/1]
4. non_recursive  : [eval_Loopus2011_ex1_bb1_in_loop_cont/2]
5. non_recursive  : [eval_Loopus2011_ex1_bb0_in/2]
6. non_recursive  : [eval_Loopus2011_ex1_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_Loopus2011_ex1_bb3_in/6
1. SCC is partially evaluated into eval_Loopus2011_ex1_bb1_in/3
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_Loopus2011_ex1_bb0_in/2
6. SCC is partially evaluated into eval_Loopus2011_ex1_start/2

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

### Specialization of cost equations eval_Loopus2011_ex1_bb3_in/6 
* CE 6 is refined into CE [9] 
* CE 8 is refined into CE [10] 
* CE 7 is refined into CE [11] 


### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb3_in/6 
* CEs [11] --> Loop 8 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 

### Ranking functions of CR eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D) 
* RF of phase [8]: [V_n-V_i_1]

#### Partial ranking functions of CR eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V_n-V_i_1


### Specialization of cost equations eval_Loopus2011_ex1_bb1_in/3 
* CE 5 is refined into CE [12] 
* CE 3 is refined into CE [13,14] 
* CE 4 is refined into CE [15,16] 


### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb1_in/3 
* CEs [16] --> Loop 11 
* CEs [15] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [12] --> Loop 15 

### Ranking functions of CR eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B) 
* RF of phase [11,13]: [V_n-V_i_0-1]

#### Partial ranking functions of CR eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B) 
* Partial RF of phase [11,13]:
  - RF of loop [11:1]:
    V_n-V_i_0-2
  - RF of loop [13:1]:
    V_n-V_i_0-1


### Specialization of cost equations eval_Loopus2011_ex1_bb0_in/2 
* CE 2 is refined into CE [17,18,19,20] 


### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb0_in/2 
* CEs [20] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR eval_Loopus2011_ex1_bb0_in(V_n,B) 

#### Partial ranking functions of CR eval_Loopus2011_ex1_bb0_in(V_n,B) 


### Specialization of cost equations eval_Loopus2011_ex1_start/2 
* CE 1 is refined into CE [21,22,23,24] 


### Cost equations --> "Loop" of eval_Loopus2011_ex1_start/2 
* CEs [24] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [21] --> Loop 23 

### Ranking functions of CR eval_Loopus2011_ex1_start(V_n,B) 

#### Partial ranking functions of CR eval_Loopus2011_ex1_start(V_n,B) 


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

#### Cost of chains of eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< V_n-V_i_1

  with precondition: [B=2,V_n=D,V_j_0+V_n=V_i_1+C,V_j_0>=0,V_n>=V_i_1+1] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -V_i_1+D

  with precondition: [B=2,V_i_1+C=V_j_0+D,V_j_0>=0,C>=V_j_0+1,V_j_0+V_n>=V_i_1+C+1] 

* Chain [10]: 0
  with precondition: [B=2,V_i_1=V_n,V_j_0=C,V_i_1=D,V_j_0>=0] 

* Chain [9]: 0
  with precondition: [B=2,V_j_0=C,V_i_1=D,V_j_0>=0,V_n>=V_i_1+1] 


#### Cost of chains of eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B):
* Chain [[11,13],14,15]: 3*it(11)+1
  Such that:aux(3) =< V_n-V_i_0
it(11) =< aux(3)

  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 

* Chain [[11,13],12,14,15]: 4*it(11)+2
  Such that:aux(4) =< V_n-V_i_0
it(11) =< aux(4)

  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 

* Chain [15]: 0
  with precondition: [B=3,V_i_0>=0,V_i_0>=V_n] 

* Chain [14,15]: 1
  with precondition: [B=3,V_i_0+1=V_n,V_i_0>=0] 

* Chain [12,14,15]: 1*s(4)+2
  Such that:s(4) =< V_n-V_i_0

  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 


#### Cost of chains of eval_Loopus2011_ex1_bb0_in(V_n,B):
* Chain [19]: 1
  with precondition: [V_n=1] 

* Chain [18]: 0
  with precondition: [0>=V_n] 

* Chain [17]: 4*s(9)+2
  Such that:s(8) =< V_n
s(9) =< s(8)

  with precondition: [V_n>=2] 

* Chain [16]: 4*s(11)+2
  Such that:s(10) =< V_n
s(11) =< s(10)

  with precondition: [V_n>=3] 


#### Cost of chains of eval_Loopus2011_ex1_start(V_n,B):
* Chain [23]: 1
  with precondition: [V_n=1] 

* Chain [22]: 0
  with precondition: [0>=V_n] 

* Chain [21]: 4*s(13)+2
  Such that:s(12) =< V_n
s(13) =< s(12)

  with precondition: [V_n>=2] 

* Chain [20]: 4*s(15)+2
  Such that:s(14) =< V_n
s(15) =< s(14)

  with precondition: [V_n>=3] 


Closed-form bounds of eval_Loopus2011_ex1_start(V_n,B): 
-------------------------------------
* Chain [23] with precondition: [V_n=1] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [22] with precondition: [0>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [21] with precondition: [V_n>=2] 
    - Upper bound: 4*V_n+2 
    - Complexity: n 
* Chain [20] with precondition: [V_n>=3] 
    - Upper bound: 4*V_n+2 
    - Complexity: n 

### Maximum cost of eval_Loopus2011_ex1_start(V_n,B): max([1,nat(V_n)*4+2]) 
Asymptotic class: n 
* Total analysis performed in 193 ms.