/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^3))  

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

#### Computed strongly connected components 
0. recursive  : [eval_realshellsort_4/5,eval_realshellsort_5/6,eval_realshellsort_bb4_in/5,eval_realshellsort_bb5_in/5,eval_realshellsort_bb6_in/6]
1. recursive  : [eval_realshellsort_2/5,eval_realshellsort_3/6,eval_realshellsort__critedge_in/7,eval_realshellsort_bb2_in/5,eval_realshellsort_bb3_in/5,eval_realshellsort_bb4_in_loop_cont/8]
2. recursive  : [eval_realshellsort_bb1_in/3,eval_realshellsort_bb2_in_loop_cont/4]
3. non_recursive  : [eval_realshellsort_stop/1]
4. non_recursive  : [eval_realshellsort_bb7_in/1]
5. non_recursive  : [eval_realshellsort_bb1_in_loop_cont/2]
6. non_recursive  : [eval_realshellsort_bb0_in/2]
7. non_recursive  : [eval_realshellsort_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_realshellsort_bb4_in/5
1. SCC is partially evaluated into eval_realshellsort_bb2_in/5
2. SCC is partially evaluated into eval_realshellsort_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_realshellsort_bb0_in/2
7. SCC is partially evaluated into eval_realshellsort_start/2

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

### Specialization of cost equations eval_realshellsort_bb4_in/5 
* CE 11 is refined into CE [12] 
* CE 9 is refined into CE [13] 
* CE 10 is refined into CE [14] 


### Cost equations --> "Loop" of eval_realshellsort_bb4_in/5 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_realshellsort_bb4_in(V_0,V_3,V_j_0,B,C) 
* RF of phase [12]: [-V_0+V_j_0+1,V_j_0]

#### Partial ranking functions of CR eval_realshellsort_bb4_in(V_0,V_3,V_j_0,B,C) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    -V_0+V_j_0+1
    V_j_0


### Specialization of cost equations eval_realshellsort_bb2_in/5 
* CE 8 is refined into CE [15] 
* CE 7 is refined into CE [16,17,18,19] 


### Cost equations --> "Loop" of eval_realshellsort_bb2_in/5 
* CEs [17] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [15] --> Loop 19 

### Ranking functions of CR eval_realshellsort_bb2_in(V_array_size,V_array_size_sink,V_0,V_i_0,B) 
* RF of phase [15]: [V_0-V_i_0,V_array_size/2-V_i_0-1/2,V_array_size_sink/2-V_i_0-1/2]
* RF of phase [16,17,18]: [V_array_size-V_i_0]

#### Partial ranking functions of CR eval_realshellsort_bb2_in(V_array_size,V_array_size_sink,V_0,V_i_0,B) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    V_0-V_i_0
    V_array_size/2-V_i_0-1/2
    V_array_size_sink/2-V_i_0-1/2
* Partial RF of phase [16,17,18]:
  - RF of loop [16:1,17:1,18:1]:
    V_array_size-V_i_0


### Specialization of cost equations eval_realshellsort_bb1_in/3 
* CE 6 is refined into CE [20] 
* CE 5 is refined into CE [21] 
* CE 4 is refined into CE [22] 
* CE 3 is refined into CE [23] 


### Cost equations --> "Loop" of eval_realshellsort_bb1_in/3 
* CEs [23] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [21] --> Loop 22 
* CEs [22] --> Loop 23 

### Ranking functions of CR eval_realshellsort_bb1_in(V_array_size,V_array_size_sink,B) 
* RF of phase [20]: [V_array_size_sink-1]

#### Partial ranking functions of CR eval_realshellsort_bb1_in(V_array_size,V_array_size_sink,B) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    V_array_size_sink-1


### Specialization of cost equations eval_realshellsort_bb0_in/2 
* CE 2 is refined into CE [24,25,26,27] 


### Cost equations --> "Loop" of eval_realshellsort_bb0_in/2 
* CEs [27] --> Loop 24 
* CEs [26] --> Loop 25 
* CEs [25] --> Loop 26 
* CEs [24] --> Loop 27 

### Ranking functions of CR eval_realshellsort_bb0_in(V_array_size,B) 

#### Partial ranking functions of CR eval_realshellsort_bb0_in(V_array_size,B) 


### Specialization of cost equations eval_realshellsort_start/2 
* CE 1 is refined into CE [28,29,30,31] 


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

### Ranking functions of CR eval_realshellsort_start(V_array_size,B) 

#### Partial ranking functions of CR eval_realshellsort_start(V_array_size,B) 


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

#### Cost of chains of eval_realshellsort_bb4_in(V_0,V_3,V_j_0,B,C):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< V_j_0-C

  with precondition: [B=2,V_0>=1,C>=V_0,V_j_0>=V_0+C] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -V_0+V_j_0+1

  with precondition: [B=2,C>=0,V_0>=C+1,V_j_0>=V_0+C] 

* Chain [14]: 0
  with precondition: [B=2,V_j_0=C,V_0>=1,V_j_0>=V_0] 

* Chain [13]: 0
  with precondition: [B=2,V_j_0=C,V_j_0>=0,V_0>=V_j_0+1] 


#### Cost of chains of eval_realshellsort_bb2_in(V_array_size,V_array_size_sink,V_0,V_i_0,B):
* Chain [[15],[16,17,18],19]: 1*it(15)+3*it(16)+1*s(5)+1*s(6)+0
  Such that:it(15) =< V_0-V_i_0
aux(6) =< V_array_size-V_0
it(16) =< aux(6)
aux(2) =< aux(6)
s(5) =< it(16)*aux(6)
s(6) =< it(16)*aux(2)

  with precondition: [B=3,V_i_0>=0,V_array_size_sink>=2*V_0,V_array_size>=V_array_size_sink,2*V_0+1>=V_array_size_sink,V_0>=V_i_0+1] 


#### Cost of chains of eval_realshellsort_bb1_in(V_array_size,V_array_size_sink,B):
* Chain [[20],22]: 2*it(20)+3*s(20)+1*s(21)+1*s(22)+0
  Such that:aux(8) =< V_array_size
aux(11) =< V_array_size_sink
aux(7) =< aux(8)
it(20) =< aux(11)
aux(7) =< aux(8)
s(23) =< it(20)*aux(7)
s(20) =< s(23)
s(16) =< aux(8)
s(21) =< s(20)*aux(8)
s(22) =< s(20)*s(16)

  with precondition: [B=4,V_array_size_sink>=2,V_array_size>=V_array_size_sink] 

* Chain [23]: 0
  with precondition: [V_array_size=0,V_array_size_sink=0,B=4] 

* Chain [22]: 0
  with precondition: [V_array_size_sink=1,B=4,V_array_size>=1] 

* Chain [21]: 0
  with precondition: [B=4,V_array_size_sink=V_array_size,0>=V_array_size_sink+1] 


#### Cost of chains of eval_realshellsort_bb0_in(V_array_size,B):
* Chain [27]: 0
  with precondition: [V_array_size=0] 

* Chain [26]: 0
  with precondition: [V_array_size=1] 

* Chain [25]: 0
  with precondition: [0>=V_array_size+1] 

* Chain [24]: 2*s(27)+3*s(29)+1*s(31)+1*s(32)+0
  Such that:aux(12) =< V_array_size
s(26) =< aux(12)
s(27) =< aux(12)
s(26) =< aux(12)
s(28) =< s(27)*s(26)
s(29) =< s(28)
s(30) =< aux(12)
s(31) =< s(29)*aux(12)
s(32) =< s(29)*s(30)

  with precondition: [V_array_size>=2] 


#### Cost of chains of eval_realshellsort_start(V_array_size,B):
* Chain [31]: 0
  with precondition: [V_array_size=0] 

* Chain [30]: 0
  with precondition: [V_array_size=1] 

* Chain [29]: 0
  with precondition: [0>=V_array_size+1] 

* Chain [28]: 2*s(35)+3*s(37)+1*s(39)+1*s(40)+0
  Such that:s(33) =< V_array_size
s(34) =< s(33)
s(35) =< s(33)
s(34) =< s(33)
s(36) =< s(35)*s(34)
s(37) =< s(36)
s(38) =< s(33)
s(39) =< s(37)*s(33)
s(40) =< s(37)*s(38)

  with precondition: [V_array_size>=2] 


Closed-form bounds of eval_realshellsort_start(V_array_size,B): 
-------------------------------------
* Chain [31] with precondition: [V_array_size=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [V_array_size=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [0>=V_array_size+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [28] with precondition: [V_array_size>=2] 
    - Upper bound: 3*V_array_size*V_array_size+2*V_array_size+2*V_array_size*V_array_size*V_array_size 
    - Complexity: n^3 

### Maximum cost of eval_realshellsort_start(V_array_size,B): nat(V_array_size)*3*nat(V_array_size)+nat(V_array_size)*2+nat(V_array_size)*2*nat(V_array_size)*nat(V_array_size) 
Asymptotic class: n^3 
* Total analysis performed in 353 ms.