/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^2))  

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

#### Computed strongly connected components 
0. recursive  : [eval_exp_paper3_2/6,eval_exp_paper3_3/7,eval_exp_paper3_bb3_in/6,eval_exp_paper3_bb4_in/7]
1. recursive  : [eval_exp_paper3_0/4,eval_exp_paper3_1/5,eval_exp_paper3_6/5,eval_exp_paper3_7/6,eval_exp_paper3_bb1_in/4,eval_exp_paper3_bb2_in/4,eval_exp_paper3_bb3_in_loop_cont/10,eval_exp_paper3_bb5_in/5,eval_exp_paper3_bb6_in/9]
2. non_recursive  : [eval_exp_paper3_stop/1]
3. non_recursive  : [eval_exp_paper3_bb7_in/1]
4. non_recursive  : [eval_exp_paper3_bb1_in_loop_cont/2]
5. non_recursive  : [eval_exp_paper3_bb0_in/4]
6. non_recursive  : [eval_exp_paper3_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_exp_paper3_bb3_in/6
1. SCC is partially evaluated into eval_exp_paper3_bb1_in/4
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_exp_paper3_bb0_in/4
6. SCC is partially evaluated into eval_exp_paper3_start/4

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

### Specialization of cost equations eval_exp_paper3_bb3_in/6 
* CE 9 is refined into CE [10] 
* CE 8 is refined into CE [11] 
* CE 7 is refined into CE [12] 


### Cost equations --> "Loop" of eval_exp_paper3_bb3_in/6 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [10] --> Loop 12 

### Ranking functions of CR eval_exp_paper3_bb3_in(V__1,B,C,D,E,F) 
* RF of phase [12]: [V__1]

#### Partial ranking functions of CR eval_exp_paper3_bb3_in(V__1,B,C,D,E,F) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V__1


### Specialization of cost equations eval_exp_paper3_bb1_in/4 
* CE 6 is refined into CE [13] 
* CE 3 is refined into CE [14,15,16,17] 
* CE 5 is refined into CE [18] 
* CE 4 is refined into CE [19] 


### Cost equations --> "Loop" of eval_exp_paper3_bb1_in/4 
* CEs [17] --> Loop 13 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [14] --> Loop 18 
* CEs [13] --> Loop 19 

### Ranking functions of CR eval_exp_paper3_bb1_in(V_z,V__01,V__0,B) 
* RF of phase [13,14,15,16,17,18]: [V__0]

#### Partial ranking functions of CR eval_exp_paper3_bb1_in(V_z,V__01,V__0,B) 
* Partial RF of phase [13,14,15,16,17,18]:
  - RF of loop [13:1,14:1,15:1,16:1,17:1,18:1]:
    V__0
  - RF of loop [13:1,18:1]:
    V__01 depends on loops [16:1,17:1] 


### Specialization of cost equations eval_exp_paper3_bb0_in/4 
* CE 2 is refined into CE [20,21] 


### Cost equations --> "Loop" of eval_exp_paper3_bb0_in/4 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR eval_exp_paper3_bb0_in(V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_exp_paper3_bb0_in(V_x,V_y,V_z,B) 


### Specialization of cost equations eval_exp_paper3_start/4 
* CE 1 is refined into CE [22,23] 


### Cost equations --> "Loop" of eval_exp_paper3_start/4 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 

### Ranking functions of CR eval_exp_paper3_start(V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_exp_paper3_start(V_x,V_y,V_z,B) 


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

#### Cost of chains of eval_exp_paper3_bb3_in(V__1,B,C,D,E,F):
* Chain [[12],11]: 1*it(12)+0
  Such that:it(12) =< V__1

  with precondition: [B=2,C=0,F=0,V__1>=1] 

* Chain [[12],10]: 1*it(12)+0
  Such that:it(12) =< V__1-F

  with precondition: [B=2,C=F,0>=D,C>=0,V__1>=C+1] 

* Chain [11]: 0
  with precondition: [B=2,V__1=C,V__1=F,0>=V__1] 

* Chain [10]: 0
  with precondition: [B=2,V__1=C,V__1=F,0>=D] 


#### Cost of chains of eval_exp_paper3_bb1_in(V_z,V__01,V__0,B):
* Chain [[13,14,15,16,17,18],19]: 2*it(13)+4*it(14)+1*s(5)+1*s(6)+0
  Such that:aux(6) =< V_z
aux(11) =< V__01
aux(14) =< V__0
it(13) =< aux(14)
it(14) =< aux(14)
aux(7) =< aux(6)
aux(4) =< max([aux(11),aux(6)])+it(14)
aux(10) =< aux(4)
aux(1) =< it(14)*aux(7)
it(13) =< aux(1)+it(14)+aux(11)
s(6) =< aux(1)+it(14)+aux(11)
s(5) =< aux(1)+it(14)+aux(11)
s(6) =< it(13)*aux(10)
s(5) =< it(13)*aux(4)

  with precondition: [B=3,V__0>=1] 

* Chain [19]: 0
  with precondition: [B=3,0>=V__0] 


#### Cost of chains of eval_exp_paper3_bb0_in(V_x,V_y,V_z,B):
* Chain [21]: 0
  with precondition: [0>=V_x] 

* Chain [20]: 2*s(10)+4*s(11)+1*s(16)+1*s(17)+0
  Such that:s(9) =< V_x
s(8) =< V_y
s(7) =< V_z
s(10) =< s(9)
s(11) =< s(9)
s(12) =< s(7)
s(13) =< max([s(8),s(7)])+s(11)
s(14) =< s(13)
s(15) =< s(11)*s(12)
s(10) =< s(15)+s(11)+s(8)
s(16) =< s(15)+s(11)+s(8)
s(17) =< s(15)+s(11)+s(8)
s(16) =< s(10)*s(14)
s(17) =< s(10)*s(13)

  with precondition: [V_x>=1] 


#### Cost of chains of eval_exp_paper3_start(V_x,V_y,V_z,B):
* Chain [23]: 0
  with precondition: [0>=V_x] 

* Chain [22]: 2*s(21)+4*s(22)+1*s(27)+1*s(28)+0
  Such that:s(18) =< V_x
s(19) =< V_y
s(20) =< V_z
s(21) =< s(18)
s(22) =< s(18)
s(23) =< s(20)
s(24) =< max([s(19),s(20)])+s(22)
s(25) =< s(24)
s(26) =< s(22)*s(23)
s(21) =< s(26)+s(22)+s(19)
s(27) =< s(26)+s(22)+s(19)
s(28) =< s(26)+s(22)+s(19)
s(27) =< s(21)*s(25)
s(28) =< s(21)*s(24)

  with precondition: [V_x>=1] 


Closed-form bounds of eval_exp_paper3_start(V_x,V_y,V_z,B): 
-------------------------------------
* Chain [23] with precondition: [0>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [V_x>=1] 
    - Upper bound: 2*V_x*nat(V_z)+8*V_x+nat(V_y)*2 
    - Complexity: n^2 

### Maximum cost of eval_exp_paper3_start(V_x,V_y,V_z,B): nat(V_x)*2*nat(V_z)+nat(V_x)*8+nat(V_y)*2 
Asymptotic class: n^2 
* Total analysis performed in 235 ms.