/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_subsetdump_2/4,eval_subsetdump_3/5,eval_subsetdump_bb3_in/4,eval_subsetdump_bb4_in/4,eval_subsetdump_bb5_in/5]
1. recursive  : [eval_subsetdump_bb7_in/4,eval_subsetdump_bb8_in/4]
2. recursive  : [eval_subsetdump_0/3,eval_subsetdump_1/4,eval_subsetdump_6/5,eval_subsetdump_7/6,eval_subsetdump_bb1_in/3,eval_subsetdump_bb2_in/3,eval_subsetdump_bb3_in_loop_cont/6,eval_subsetdump_bb6_in/5,eval_subsetdump_bb7_in_loop_cont/6,eval_subsetdump_bb9_in/5]
3. non_recursive  : [eval_subsetdump_stop/1]
4. non_recursive  : [eval_subsetdump_bb10_in/1]
5. non_recursive  : [eval_subsetdump_bb1_in_loop_cont/2]
6. non_recursive  : [eval_subsetdump_bb0_in/2]
7. non_recursive  : [eval_subsetdump_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_subsetdump_bb3_in/4
1. SCC is partially evaluated into eval_subsetdump_bb7_in/4
2. SCC is partially evaluated into eval_subsetdump_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_subsetdump_bb0_in/2
7. SCC is partially evaluated into eval_subsetdump_start/2

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

### Specialization of cost equations eval_subsetdump_bb3_in/4 
* CE 8 is refined into CE [13] 
* CE 10 is refined into CE [14] 
* CE 9 is refined into CE [15] 


### Cost equations --> "Loop" of eval_subsetdump_bb3_in/4 
* CEs [15] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 

### Ranking functions of CR eval_subsetdump_bb3_in(V_limit,V_cnum_1,B,C) 
* RF of phase [11]: [V_limit-V_cnum_1]

#### Partial ranking functions of CR eval_subsetdump_bb3_in(V_limit,V_cnum_1,B,C) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    V_limit-V_cnum_1


### Specialization of cost equations eval_subsetdump_bb7_in/4 
* CE 12 is refined into CE [16] 
* CE 11 is refined into CE [17] 


### Cost equations --> "Loop" of eval_subsetdump_bb7_in/4 
* CEs [17] --> Loop 14 
* CEs [16] --> Loop 15 

### Ranking functions of CR eval_subsetdump_bb7_in(V_cnum_1,V_7,V_rangestart_0,B) 
* RF of phase [14]: [V_cnum_1-V_rangestart_0]

#### Partial ranking functions of CR eval_subsetdump_bb7_in(V_cnum_1,V_7,V_rangestart_0,B) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    V_cnum_1-V_rangestart_0


### Specialization of cost equations eval_subsetdump_bb1_in/3 
* CE 7 is refined into CE [18] 
* CE 3 is refined into CE [19,20,21] 
* CE 4 is refined into CE [22,23,24] 
* CE 5 is refined into CE [25,26,27] 
* CE 6 is refined into CE [28] 


### Cost equations --> "Loop" of eval_subsetdump_bb1_in/3 
* CEs [21,24,27] --> Loop 16 
* CEs [20,23,26,28] --> Loop 17 
* CEs [19,22,25] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR eval_subsetdump_bb1_in(V_limit,V_cnum_0,B) 
* RF of phase [16,17]: [V_limit-V_cnum_0]

#### Partial ranking functions of CR eval_subsetdump_bb1_in(V_limit,V_cnum_0,B) 
* Partial RF of phase [16,17]:
  - RF of loop [16:1]:
    V_limit-V_cnum_0-1
  - RF of loop [17:1]:
    V_limit-V_cnum_0


### Specialization of cost equations eval_subsetdump_bb0_in/2 
* CE 2 is refined into CE [29,30,31] 


### Cost equations --> "Loop" of eval_subsetdump_bb0_in/2 
* CEs [31] --> Loop 20 
* CEs [30] --> Loop 21 
* CEs [29] --> Loop 22 

### Ranking functions of CR eval_subsetdump_bb0_in(V_limit,B) 

#### Partial ranking functions of CR eval_subsetdump_bb0_in(V_limit,B) 


### Specialization of cost equations eval_subsetdump_start/2 
* CE 1 is refined into CE [32,33,34] 


### Cost equations --> "Loop" of eval_subsetdump_start/2 
* CEs [34] --> Loop 23 
* CEs [33] --> Loop 24 
* CEs [32] --> Loop 25 

### Ranking functions of CR eval_subsetdump_start(V_limit,B) 

#### Partial ranking functions of CR eval_subsetdump_start(V_limit,B) 


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

#### Cost of chains of eval_subsetdump_bb3_in(V_limit,V_cnum_1,B,C):
* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< V_limit-V_cnum_1

  with precondition: [B=2,V_limit=C,V_limit>=V_cnum_1+1] 

* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< -V_cnum_1+C

  with precondition: [B=2,C>=V_cnum_1+1,V_limit>=C+1] 

* Chain [12]: 0
  with precondition: [B=2,V_cnum_1=C,V_limit>=V_cnum_1+1] 


#### Cost of chains of eval_subsetdump_bb7_in(V_cnum_1,V_7,V_rangestart_0,B):
* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< V_cnum_1-V_rangestart_0

  with precondition: [B=3,V_cnum_1>=V_rangestart_0+1] 

* Chain [15]: 0
  with precondition: [B=3,V_rangestart_0>=V_cnum_1] 


#### Cost of chains of eval_subsetdump_bb1_in(V_limit,V_cnum_0,B):
* Chain [[16,17],19]: 7*it(16)+0
  Such that:aux(6) =< V_limit-V_cnum_0
it(16) =< aux(6)

  with precondition: [B=4,V_cnum_0>=0,V_limit>=V_cnum_0+1] 

* Chain [[16,17],18,19]: 2*it(16)+5*s(8)+5*s(10)+1
  Such that:aux(10) =< V_limit-V_cnum_0
aux(11) =< V_limit-V_cnum_0+1
aux(5) =< aux(10)
aux(5) =< aux(11)
s(10) =< aux(5)
it(16) =< aux(10)
s(9) =< aux(10)
it(16) =< aux(5)
s(9) =< aux(5)
s(8) =< s(9)

  with precondition: [B=4,V_cnum_0>=0,V_limit>=V_cnum_0+2] 

* Chain [19]: 0
  with precondition: [B=4,V_cnum_0>=0,V_cnum_0>=V_limit] 

* Chain [18,19]: 5*s(10)+1
  Such that:aux(9) =< V_limit-V_cnum_0+1
s(10) =< aux(9)

  with precondition: [B=4,V_cnum_0>=0,V_limit>=V_cnum_0+1] 


#### Cost of chains of eval_subsetdump_bb0_in(V_limit,B):
* Chain [22]: 0
  with precondition: [0>=V_limit] 

* Chain [21]: 7*s(21)+5*s(22)+1
  Such that:s(19) =< V_limit
s(20) =< V_limit+1
s(21) =< s(19)
s(22) =< s(20)

  with precondition: [V_limit>=1] 

* Chain [20]: 5*s(26)+2*s(27)+5*s(29)+1
  Such that:s(23) =< V_limit
s(24) =< V_limit+1
s(25) =< s(23)
s(25) =< s(24)
s(26) =< s(25)
s(27) =< s(23)
s(28) =< s(23)
s(27) =< s(25)
s(28) =< s(25)
s(29) =< s(28)

  with precondition: [V_limit>=2] 


#### Cost of chains of eval_subsetdump_start(V_limit,B):
* Chain [25]: 0
  with precondition: [0>=V_limit] 

* Chain [24]: 7*s(32)+5*s(33)+1
  Such that:s(30) =< V_limit
s(31) =< V_limit+1
s(32) =< s(30)
s(33) =< s(31)

  with precondition: [V_limit>=1] 

* Chain [23]: 5*s(37)+2*s(38)+5*s(40)+1
  Such that:s(34) =< V_limit
s(35) =< V_limit+1
s(36) =< s(34)
s(36) =< s(35)
s(37) =< s(36)
s(38) =< s(34)
s(39) =< s(34)
s(38) =< s(36)
s(39) =< s(36)
s(40) =< s(39)

  with precondition: [V_limit>=2] 


Closed-form bounds of eval_subsetdump_start(V_limit,B): 
-------------------------------------
* Chain [25] with precondition: [0>=V_limit] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24] with precondition: [V_limit>=1] 
    - Upper bound: 12*V_limit+6 
    - Complexity: n 
* Chain [23] with precondition: [V_limit>=2] 
    - Upper bound: 12*V_limit+1 
    - Complexity: n 

### Maximum cost of eval_subsetdump_start(V_limit,B): nat(V_limit)*7+1+max([nat(V_limit)*5,nat(V_limit+1)*5]) 
Asymptotic class: n 
* Total analysis performed in 256 ms.