/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_ex_paper1_3/5,eval_ex_paper1_4/6,eval_ex_paper1_6/7,eval_ex_paper1_7/7,eval_ex_paper1_bb3_in/5,eval_ex_paper1_bb4_in/6]
1. recursive  : [eval_ex_paper1_bb1_in/4,eval_ex_paper1_bb2_in/4,eval_ex_paper1_bb3_in_loop_cont/5]
2. recursive  : [eval_ex_paper1_10/4,eval_ex_paper1_11/4,eval_ex_paper1_bb7_in/4,eval_ex_paper1_bb8_in/4]
3. recursive  : [eval_ex_paper1_bb5_in/3,eval_ex_paper1_bb6_in/3,eval_ex_paper1_bb7_in_loop_cont/4]
4. non_recursive  : [eval_ex_paper1_stop/1]
5. non_recursive  : [eval_ex_paper1_bb9_in/1]
6. non_recursive  : [eval_ex_paper1_bb5_in_loop_cont/2]
7. non_recursive  : [eval_ex_paper1_bb1_in_loop_cont/4]
8. non_recursive  : [eval_ex_paper1_bb0_in/4]
9. non_recursive  : [eval_ex_paper1_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_ex_paper1_bb3_in/5
1. SCC is partially evaluated into eval_ex_paper1_bb1_in/4
2. SCC is partially evaluated into eval_ex_paper1_bb7_in/4
3. SCC is partially evaluated into eval_ex_paper1_bb5_in/3
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is completely evaluated into other SCCs
7. SCC is partially evaluated into eval_ex_paper1_bb1_in_loop_cont/4
8. SCC is partially evaluated into eval_ex_paper1_bb0_in/4
9. SCC is partially evaluated into eval_ex_paper1_start/4

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

### Specialization of cost equations eval_ex_paper1_bb3_in/5 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of eval_ex_paper1_bb3_in/5 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR eval_ex_paper1_bb3_in(V__01,V__0,V__1,B,C) 
* RF of phase [15]: [V__1]

#### Partial ranking functions of CR eval_ex_paper1_bb3_in(V__01,V__0,V__1,B,C) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    V__1


### Specialization of cost equations eval_ex_paper1_bb1_in/4 
* CE 6 is refined into CE [16] 
* CE 5 is refined into CE [17,18] 


### Cost equations --> "Loop" of eval_ex_paper1_bb1_in/4 
* CEs [18] --> Loop 16 
* CEs [17] --> Loop 17 
* CEs [16] --> Loop 18 

### Ranking functions of CR eval_ex_paper1_bb1_in(V__01,V__0,B,C) 
* RF of phase [16,17]: [V__0]

#### Partial ranking functions of CR eval_ex_paper1_bb1_in(V__01,V__0,B,C) 
* Partial RF of phase [16,17]:
  - RF of loop [16:1,17:1]:
    V__0


### Specialization of cost equations eval_ex_paper1_bb7_in/4 
* CE 13 is refined into CE [19] 
* CE 12 is refined into CE [20] 


### Cost equations --> "Loop" of eval_ex_paper1_bb7_in/4 
* CEs [20] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR eval_ex_paper1_bb7_in(V_z,V__2,V_i_0,B) 
* RF of phase [19]: [V_z-V_i_0]

#### Partial ranking functions of CR eval_ex_paper1_bb7_in(V_z,V__2,V_i_0,B) 
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    V_z-V_i_0


### Specialization of cost equations eval_ex_paper1_bb5_in/3 
* CE 11 is refined into CE [21] 
* CE 10 is refined into CE [22,23] 


### Cost equations --> "Loop" of eval_ex_paper1_bb5_in/3 
* CEs [23] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [21] --> Loop 23 

### Ranking functions of CR eval_ex_paper1_bb5_in(V_z,V__2,B) 
* RF of phase [21]: [V__2]
* RF of phase [22]: [V__2]

#### Partial ranking functions of CR eval_ex_paper1_bb5_in(V_z,V__2,B) 
* Partial RF of phase [21]:
  - RF of loop [21:1]:
    V__2
* Partial RF of phase [22]:
  - RF of loop [22:1]:
    V__2


### Specialization of cost equations eval_ex_paper1_bb1_in_loop_cont/4 
* CE 7 is refined into CE [24,25,26] 


### Cost equations --> "Loop" of eval_ex_paper1_bb1_in_loop_cont/4 
* CEs [26] --> Loop 24 
* CEs [25] --> Loop 25 
* CEs [24] --> Loop 26 

### Ranking functions of CR eval_ex_paper1_bb1_in_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR eval_ex_paper1_bb1_in_loop_cont(A,B,C,D) 


### Specialization of cost equations eval_ex_paper1_bb0_in/4 
* CE 4 is refined into CE [27,28,29] 
* CE 3 is refined into CE [30] 
* CE 2 is refined into CE [31] 


### Cost equations --> "Loop" of eval_ex_paper1_bb0_in/4 
* CEs [29] --> Loop 27 
* CEs [28] --> Loop 28 
* CEs [27] --> Loop 29 
* CEs [30] --> Loop 30 
* CEs [31] --> Loop 31 

### Ranking functions of CR eval_ex_paper1_bb0_in(V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_ex_paper1_bb0_in(V_x,V_y,V_z,B) 


### Specialization of cost equations eval_ex_paper1_start/4 
* CE 1 is refined into CE [32,33,34,35,36] 


### Cost equations --> "Loop" of eval_ex_paper1_start/4 
* CEs [36] --> Loop 32 
* CEs [35] --> Loop 33 
* CEs [34] --> Loop 34 
* CEs [33] --> Loop 35 
* CEs [32] --> Loop 36 

### Ranking functions of CR eval_ex_paper1_start(V_x,V_y,V_z,B) 

#### Partial ranking functions of CR eval_ex_paper1_start(V_x,V_y,V_z,B) 


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

#### Cost of chains of eval_ex_paper1_bb3_in(V__01,V__0,V__1,B,C):
* Chain [[15],14]: 1*it(15)+0
  Such that:it(15) =< V__1-C

  with precondition: [B=3,V__0>=1,C>=0,V__01+1>=V__1,V__1>=C+1] 

* Chain [14]: 0
  with precondition: [B=3,V__1=C,V__0>=1,V__01+1>=V__1] 


#### Cost of chains of eval_ex_paper1_bb1_in(V__01,V__0,B,C):
* Chain [[16,17],18]: 2*it(16)+1*s(3)+0
  Such that:s(3) =< V__01+V__0-C
aux(3) =< V__0
it(16) =< aux(3)

  with precondition: [B=2,V__01>=0,V__0>=1,C>=0,V__0+V__01>=C] 


#### Cost of chains of eval_ex_paper1_bb7_in(V_z,V__2,V_i_0,B):
* Chain [[19],20]: 1*it(19)+0
  Such that:it(19) =< V_z-V_i_0

  with precondition: [B=2,V__2>=1,V_i_0>=0,V_z>=V_i_0+1] 

* Chain [20]: 0
  with precondition: [B=2,V__2>=1,V_i_0>=0,V_i_0>=V_z] 


#### Cost of chains of eval_ex_paper1_bb5_in(V_z,V__2,B):
* Chain [[22],23]: 1*it(22)+0
  Such that:it(22) =< V__2

  with precondition: [B=4,0>=V_z,V__2>=1] 

* Chain [[21],23]: 1*it(21)+1*s(6)+0
  Such that:aux(4) =< V_z
it(21) =< V__2
s(6) =< it(21)*aux(4)

  with precondition: [B=4,V_z>=1,V__2>=1] 

* Chain [23]: 0
  with precondition: [B=4,0>=V__2] 


#### Cost of chains of eval_ex_paper1_bb1_in_loop_cont(A,B,C,D):
* Chain [26]: 1*s(7)+0
  Such that:s(7) =< C

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

* Chain [25]: 0
  with precondition: [A=2,0>=C] 

* Chain [24]: 1*s(9)+1*s(10)+0
  Such that:s(8) =< B
s(9) =< C
s(10) =< s(9)*s(8)

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


#### Cost of chains of eval_ex_paper1_bb0_in(V_x,V_y,V_z,B):
* Chain [31]: 0
  with precondition: [0>=V_x] 

* Chain [30]: 0
  with precondition: [0>=V_y] 

* Chain [29]: 2*s(11)+2*s(13)+0
  Such that:s(12) =< V_x
aux(5) =< V_x+V_y
s(11) =< aux(5)
s(13) =< s(12)

  with precondition: [0>=V_z,V_x>=1,V_y>=1] 

* Chain [28]: 1*s(15)+2*s(17)+0
  Such that:s(16) =< V_x
s(15) =< V_x+V_y
s(17) =< s(16)

  with precondition: [V_x>=1,V_y>=1] 

* Chain [27]: 2*s(18)+2*s(20)+1*s(23)+0
  Such that:s(19) =< V_x
s(21) =< V_z
aux(6) =< V_x+V_y
s(18) =< aux(6)
s(23) =< s(18)*s(21)
s(20) =< s(19)

  with precondition: [V_x>=1,V_y>=1,V_z>=1] 


#### Cost of chains of eval_ex_paper1_start(V_x,V_y,V_z,B):
* Chain [36]: 0
  with precondition: [0>=V_x] 

* Chain [35]: 0
  with precondition: [0>=V_y] 

* Chain [34]: 2*s(26)+2*s(27)+0
  Such that:s(24) =< V_x
s(25) =< V_x+V_y
s(26) =< s(25)
s(27) =< s(24)

  with precondition: [0>=V_z,V_x>=1,V_y>=1] 

* Chain [33]: 1*s(29)+2*s(30)+0
  Such that:s(28) =< V_x
s(29) =< V_x+V_y
s(30) =< s(28)

  with precondition: [V_x>=1,V_y>=1] 

* Chain [32]: 2*s(34)+1*s(35)+2*s(36)+0
  Such that:s(31) =< V_x
s(33) =< V_x+V_y
s(32) =< V_z
s(34) =< s(33)
s(35) =< s(34)*s(32)
s(36) =< s(31)

  with precondition: [V_x>=1,V_y>=1,V_z>=1] 


Closed-form bounds of eval_ex_paper1_start(V_x,V_y,V_z,B): 
-------------------------------------
* Chain [36] with precondition: [0>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [0>=V_y] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=V_z,V_x>=1,V_y>=1] 
    - Upper bound: 4*V_x+2*V_y 
    - Complexity: n 
* Chain [33] with precondition: [V_x>=1,V_y>=1] 
    - Upper bound: 3*V_x+V_y 
    - Complexity: n 
* Chain [32] with precondition: [V_x>=1,V_y>=1,V_z>=1] 
    - Upper bound: (V_x+V_y)*V_z+2*V_x+(2*V_x+2*V_y) 
    - Complexity: n^2 

### Maximum cost of eval_ex_paper1_start(V_x,V_y,V_z,B): nat(V_x+V_y)*nat(V_z)+nat(V_x+V_y)+(nat(V_x)*2+nat(V_x+V_y)) 
Asymptotic class: n^2 
* Total analysis performed in 265 ms.