/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_realheapsort_step1_2/3,eval_realheapsort_step1_3/4,eval_realheapsort_step1_4/5,eval_realheapsort_step1_5/5,eval_realheapsort_step1_6/5,eval_realheapsort_step1_bb2_in/3,eval_realheapsort_step1_bb3_in/3,eval_realheapsort_step1_bb4_in/5]
1. recursive  : [eval_realheapsort_step1__critedge_in/4,eval_realheapsort_step1_bb1_in/3,eval_realheapsort_step1_bb2_in_loop_cont/5]
2. non_recursive  : [eval_realheapsort_step1_stop/1]
3. non_recursive  : [eval_realheapsort_step1_bb5_in/1]
4. non_recursive  : [eval_realheapsort_step1_bb1_in_loop_cont/2]
5. non_recursive  : [eval_realheapsort_step1_bb0_in/2]
6. non_recursive  : [eval_realheapsort_step1_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_realheapsort_step1_bb2_in/3
1. SCC is partially evaluated into eval_realheapsort_step1_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_realheapsort_step1_bb0_in/2
6. SCC is partially evaluated into eval_realheapsort_step1_start/2

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

### Specialization of cost equations eval_realheapsort_step1_bb2_in/3 
* CE 7 is refined into CE [9] 
* CE 8 is refined into CE [10] 
* CE 6 is refined into CE [11] 


### Cost equations --> "Loop" of eval_realheapsort_step1_bb2_in/3 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR eval_realheapsort_step1_bb2_in(V_j_0,B,C) 
* RF of phase [9]: [V_j_0]

#### Partial ranking functions of CR eval_realheapsort_step1_bb2_in(V_j_0,B,C) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    V_j_0


### Specialization of cost equations eval_realheapsort_step1_bb1_in/3 
* CE 5 is refined into CE [12] 
* CE 4 is refined into CE [13,14,15] 


### Cost equations --> "Loop" of eval_realheapsort_step1_bb1_in/3 
* CEs [13,14] --> Loop 12 
* CEs [15] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR eval_realheapsort_step1_bb1_in(V_N,V_k_0,B) 
* RF of phase [12,13]: [V_N-V_k_0]

#### Partial ranking functions of CR eval_realheapsort_step1_bb1_in(V_N,V_k_0,B) 
* Partial RF of phase [12,13]:
  - RF of loop [12:1,13:1]:
    V_N-V_k_0


### Specialization of cost equations eval_realheapsort_step1_bb0_in/2 
* CE 3 is refined into CE [16] 
* CE 2 is refined into CE [17] 


### Cost equations --> "Loop" of eval_realheapsort_step1_bb0_in/2 
* CEs [16] --> Loop 15 
* CEs [17] --> Loop 16 

### Ranking functions of CR eval_realheapsort_step1_bb0_in(V_N,B) 

#### Partial ranking functions of CR eval_realheapsort_step1_bb0_in(V_N,B) 


### Specialization of cost equations eval_realheapsort_step1_start/2 
* CE 1 is refined into CE [18,19] 


### Cost equations --> "Loop" of eval_realheapsort_step1_start/2 
* CEs [19] --> Loop 17 
* CEs [18] --> Loop 18 

### Ranking functions of CR eval_realheapsort_step1_start(V_N,B) 

#### Partial ranking functions of CR eval_realheapsort_step1_start(V_N,B) 


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

#### Cost of chains of eval_realheapsort_step1_bb2_in(V_j_0,B,C):
* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< V_j_0

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

* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< V_j_0-C

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

* Chain [10]: 0
  with precondition: [B=2,V_j_0=C,V_j_0>=1] 


#### Cost of chains of eval_realheapsort_step1_bb1_in(V_N,V_k_0,B):
* Chain [[12,13],14]: 2*it(12)+1*s(5)+1*s(6)+0
  Such that:aux(1) =< V_N
aux(5) =< V_N-V_k_0
it(12) =< aux(5)
aux(2) =< aux(1)
s(5) =< it(12)*aux(1)
s(6) =< it(12)*aux(2)

  with precondition: [B=3,V_N>=3,V_k_0>=1,V_N>=V_k_0+1] 


#### Cost of chains of eval_realheapsort_step1_bb0_in(V_N,B):
* Chain [16]: 0
  with precondition: [2>=V_N] 

* Chain [15]: 2*s(9)+1*s(11)+1*s(12)+0
  Such that:aux(6) =< V_N
s(9) =< aux(6)
s(10) =< aux(6)
s(11) =< s(9)*aux(6)
s(12) =< s(9)*s(10)

  with precondition: [V_N>=3] 


#### Cost of chains of eval_realheapsort_step1_start(V_N,B):
* Chain [18]: 0
  with precondition: [2>=V_N] 

* Chain [17]: 2*s(14)+1*s(16)+1*s(17)+0
  Such that:s(13) =< V_N
s(14) =< s(13)
s(15) =< s(13)
s(16) =< s(14)*s(13)
s(17) =< s(14)*s(15)

  with precondition: [V_N>=3] 


Closed-form bounds of eval_realheapsort_step1_start(V_N,B): 
-------------------------------------
* Chain [18] with precondition: [2>=V_N] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [17] with precondition: [V_N>=3] 
    - Upper bound: 2*V_N*V_N+2*V_N 
    - Complexity: n^2 

### Maximum cost of eval_realheapsort_step1_start(V_N,B): nat(V_N)*2*nat(V_N)+nat(V_N)*2 
Asymptotic class: n^2 
* Total analysis performed in 135 ms.