/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_t13_bb4_in/6,eval_t13_bb5_in/6]
1. recursive  : [eval_t13_1/4,eval_t13_2/5,eval_t13_bb1_in/3,eval_t13_bb2_in/3,eval_t13_bb3_in/5,eval_t13_bb4_in_loop_cont/4]
2. non_recursive  : [eval_t13_stop/1]
3. non_recursive  : [eval_t13_bb6_in/1]
4. non_recursive  : [eval_t13_bb1_in_loop_cont/2]
5. non_recursive  : [eval_t13_bb0_in/3]
6. non_recursive  : [eval_t13_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_t13_bb4_in/6
1. SCC is partially evaluated into eval_t13_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_t13_bb0_in/3
6. SCC is partially evaluated into eval_t13_start/3

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

### Specialization of cost equations eval_t13_bb4_in/6 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 


### Cost equations --> "Loop" of eval_t13_bb4_in/6 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C) 
* RF of phase [8]: [V__1]

#### Partial ranking functions of CR eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V__1


### Specialization of cost equations eval_t13_bb1_in/3 
* CE 5 is refined into CE [10] 
* CE 4 is refined into CE [11,12] 
* CE 3 is refined into CE [13] 


### Cost equations --> "Loop" of eval_t13_bb1_in/3 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR eval_t13_bb1_in(V__01,V__0,B) 
* RF of phase [10,11,12]: [V__0]

#### Partial ranking functions of CR eval_t13_bb1_in(V__01,V__0,B) 
* Partial RF of phase [10,11,12]:
  - RF of loop [10:1,11:1,12:1]:
    V__0
  - RF of loop [12:1]:
    V__01 depends on loops [11:1] 


### Specialization of cost equations eval_t13_bb0_in/3 
* CE 2 is refined into CE [14,15] 


### Cost equations --> "Loop" of eval_t13_bb0_in/3 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR eval_t13_bb0_in(V_x,V_y,B) 

#### Partial ranking functions of CR eval_t13_bb0_in(V_x,V_y,B) 


### Specialization of cost equations eval_t13_start/3 
* CE 1 is refined into CE [16,17] 


### Cost equations --> "Loop" of eval_t13_start/3 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_t13_start(V_x,V_y,B) 

#### Partial ranking functions of CR eval_t13_start(V_x,V_y,B) 


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

#### Cost of chains of eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C):
* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< V__1

  with precondition: [B=2,C=0,0>=V_2,V__0>=1,V__1>=1,V__01>=V__1] 

* Chain [9]: 0
  with precondition: [B=2,V__1=C,0>=V_2,0>=V__1,V__0>=1,V__01>=V__1] 


#### Cost of chains of eval_t13_bb1_in(V__01,V__0,B):
* Chain [[10,11,12],13]: 2*it(10)+1*it(12)+1*s(3)+0
  Such that:aux(6) =< V__01
aux(5) =< V__01+V__0
aux(10) =< V__0
it(10) =< aux(10)
it(12) =< aux(10)
s(3) =< it(10)+aux(6)
it(12) =< it(10)+aux(6)
s(3) =< it(12)*aux(5)

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

* Chain [13]: 0
  with precondition: [B=3,0>=V__0] 


#### Cost of chains of eval_t13_bb0_in(V_x,V_y,B):
* Chain [15]: 0
  with precondition: [0>=V_x] 

* Chain [14]: 2*s(7)+1*s(8)+1*s(9)+0
  Such that:s(6) =< V_x
s(5) =< V_x+V_y
s(4) =< V_y
s(7) =< s(6)
s(8) =< s(6)
s(9) =< s(7)+s(4)
s(8) =< s(7)+s(4)
s(9) =< s(8)*s(5)

  with precondition: [V_x>=1] 


#### Cost of chains of eval_t13_start(V_x,V_y,B):
* Chain [17]: 0
  with precondition: [0>=V_x] 

* Chain [16]: 2*s(13)+1*s(14)+1*s(15)+0
  Such that:s(10) =< V_x
s(11) =< V_x+V_y
s(12) =< V_y
s(13) =< s(10)
s(14) =< s(10)
s(15) =< s(13)+s(12)
s(14) =< s(13)+s(12)
s(15) =< s(14)*s(11)

  with precondition: [V_x>=1] 


Closed-form bounds of eval_t13_start(V_x,V_y,B): 
-------------------------------------
* Chain [17] with precondition: [0>=V_x] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [V_x>=1] 
    - Upper bound: 4*V_x+nat(V_y) 
    - Complexity: n 

### Maximum cost of eval_t13_start(V_x,V_y,B): nat(V_x)*4+nat(V_y) 
Asymptotic class: n 
* Total analysis performed in 137 ms.