/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_asctoeg_0/5,eval_asctoeg_1/6,eval_asctoeg_bb2_in/5,eval_asctoeg_bb3_in/5,eval_asctoeg_bb4_in/6]
1. recursive  : [eval_asctoeg_6/5,eval_asctoeg_7/6,eval_asctoeg__critedge_in/4,eval_asctoeg_bb5_in/5]
2. recursive  : [eval_asctoeg__critedge1_in/6,eval_asctoeg__critedge_in_loop_cont/7,eval_asctoeg_bb1_in/3,eval_asctoeg_bb2_in_loop_cont/6]
3. non_recursive  : [eval_asctoeg_stop/1]
4. non_recursive  : [eval_asctoeg_bb6_in/1]
5. non_recursive  : [eval_asctoeg_bb1_in_loop_cont/2]
6. non_recursive  : [eval_asctoeg_bb0_in/2]
7. non_recursive  : [eval_asctoeg_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_asctoeg_bb2_in/5
1. SCC is partially evaluated into eval_asctoeg__critedge_in/4
2. SCC is partially evaluated into eval_asctoeg_bb1_in/3
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_asctoeg_bb0_in/2
7. SCC is partially evaluated into eval_asctoeg_start/2

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

### Specialization of cost equations eval_asctoeg_bb2_in/5 
* CE 5 is refined into CE [11] 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of eval_asctoeg_bb2_in/5 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D) 
* RF of phase [11]: [V_s-V_sp_0]

#### Partial ranking functions of CR eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    V_s-V_sp_0


### Specialization of cost equations eval_asctoeg__critedge_in/4 
* CE 8 is refined into CE [14] 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 


### Cost equations --> "Loop" of eval_asctoeg__critedge_in/4 
* CEs [16] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D) 
* RF of phase [14]: [V_sp_0_sink-1]

#### Partial ranking functions of CR eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    V_sp_0_sink-1


### Specialization of cost equations eval_asctoeg_bb1_in/3 
* CE 4 is refined into CE [17] 
* CE 3 is refined into CE [18,19,20,21,22,23,24,25,26] 


### Cost equations --> "Loop" of eval_asctoeg_bb1_in/3 
* CEs [22] --> Loop 17 
* CEs [18,24] --> Loop 18 
* CEs [26] --> Loop 19 
* CEs [21,23,25] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [19] --> Loop 22 
* CEs [17] --> Loop 23 

### Ranking functions of CR eval_asctoeg_bb1_in(V_s,V_k_0,B) 
* RF of phase [17,18,19,20,21]: [V_k_0]

#### Partial ranking functions of CR eval_asctoeg_bb1_in(V_s,V_k_0,B) 
* Partial RF of phase [17,18,19,20,21]:
  - RF of loop [17:1,18:1,19:1,20:1,21:1]:
    V_k_0


### Specialization of cost equations eval_asctoeg_bb0_in/2 
* CE 2 is refined into CE [27,28,29] 


### Cost equations --> "Loop" of eval_asctoeg_bb0_in/2 
* CEs [29] --> Loop 24 
* CEs [28] --> Loop 25 
* CEs [27] --> Loop 26 

### Ranking functions of CR eval_asctoeg_bb0_in(V_s,B) 

#### Partial ranking functions of CR eval_asctoeg_bb0_in(V_s,B) 


### Specialization of cost equations eval_asctoeg_start/2 
* CE 1 is refined into CE [30,31,32] 


### Cost equations --> "Loop" of eval_asctoeg_start/2 
* CEs [32] --> Loop 27 
* CEs [31] --> Loop 28 
* CEs [30] --> Loop 29 

### Ranking functions of CR eval_asctoeg_start(V_s,B) 

#### Partial ranking functions of CR eval_asctoeg_start(V_s,B) 


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

#### Cost of chains of eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D):
* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< -V_sp_0+D

  with precondition: [B=3,V_s=C,V_s=D,V_sp_0>=0,V_s>=V_sp_0+1] 

* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< -V_sp_0+D

  with precondition: [B=3,C=D,V_sp_0>=0,C>=V_sp_0+1,V_s>=C+1] 

* Chain [12]: 0
  with precondition: [B=3,V_sp_0=C,V_sp_0=D,V_sp_0>=0,V_s>=V_sp_0+1] 


#### Cost of chains of eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< V_sp_0_sink

  with precondition: [B=2,C=1,D=0,V_sp_0_sink>=2] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< V_sp_0_sink-D

  with precondition: [B=2,C=D+1,C>=2,V_sp_0_sink>=C+1] 

* Chain [16]: 0
  with precondition: [B=2,V_sp_0_sink=C,V_sp_0_sink=D+1,1>=V_sp_0_sink] 

* Chain [15]: 0
  with precondition: [B=2,V_sp_0_sink=C,V_sp_0_sink=D+1,V_sp_0_sink>=2] 


#### Cost of chains of eval_asctoeg_bb1_in(V_s,V_k_0,B):
* Chain [[17,18,19,20,21],23]: 6*it(17)+2*s(21)+6*s(24)+2*s(27)+0
  Such that:aux(7) =< V_s
aux(14) =< V_k_0
it(17) =< aux(14)
aux(8) =< aux(7)
s(23) =< it(17)*aux(7)
s(27) =< it(17)*aux(8)
s(25) =< it(17)*aux(8)
s(24) =< s(25)
s(21) =< s(23)

  with precondition: [B=4,V_k_0>=1,V_s>=V_k_0] 

* Chain [23]: 0
  with precondition: [B=4,0>=V_k_0,V_s>=V_k_0] 

* Chain [22,23]: 1*s(30)+1
  Such that:s(30) =< 1

  with precondition: [V_s=1,V_k_0=1,B=4] 


#### Cost of chains of eval_asctoeg_bb0_in(V_s,B):
* Chain [26]: 1*s(31)+1
  Such that:s(31) =< 1

  with precondition: [V_s=1] 

* Chain [25]: 0
  with precondition: [0>=V_s] 

* Chain [24]: 6*s(34)+2*s(37)+6*s(39)+2*s(40)+0
  Such that:aux(15) =< V_s
s(34) =< aux(15)
s(35) =< aux(15)
s(36) =< s(34)*aux(15)
s(37) =< s(34)*s(35)
s(38) =< s(34)*s(35)
s(39) =< s(38)
s(40) =< s(36)

  with precondition: [V_s>=1] 


#### Cost of chains of eval_asctoeg_start(V_s,B):
* Chain [29]: 1*s(41)+1
  Such that:s(41) =< 1

  with precondition: [V_s=1] 

* Chain [28]: 0
  with precondition: [0>=V_s] 

* Chain [27]: 6*s(43)+2*s(46)+6*s(48)+2*s(49)+0
  Such that:s(42) =< V_s
s(43) =< s(42)
s(44) =< s(42)
s(45) =< s(43)*s(42)
s(46) =< s(43)*s(44)
s(47) =< s(43)*s(44)
s(48) =< s(47)
s(49) =< s(45)

  with precondition: [V_s>=1] 


Closed-form bounds of eval_asctoeg_start(V_s,B): 
-------------------------------------
* Chain [29] with precondition: [V_s=1] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [28] with precondition: [0>=V_s] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [27] with precondition: [V_s>=1] 
    - Upper bound: 10*V_s*V_s+6*V_s 
    - Complexity: n^2 

### Maximum cost of eval_asctoeg_start(V_s,B): max([2,nat(V_s)*10*nat(V_s)+nat(V_s)*6]) 
Asymptotic class: n^2 
* Total analysis performed in 308 ms.