/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. non_recursive  : [eval_foo_stop/1]
1. non_recursive  : [eval_foo__critedge_in/1]
2. recursive  : [eval_foo_10/8,eval_foo_11/9,eval_foo_7/6,eval_foo_8/7,eval_foo_9/8,eval_foo_bb1_in/6,eval_foo_bb2_in/6,eval_foo_bb3_in/6,eval_foo_bb4_in/8]
3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
4. non_recursive  : [eval_foo_bb0_in/6]
5. non_recursive  : [eval_foo_start/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into eval_foo_bb1_in/6
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_foo_bb0_in/6
5. SCC is partially evaluated into eval_foo_start/6

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

### Specialization of cost equations eval_foo_bb1_in/6 
* CE 6 is refined into CE [10] 
* CE 4 is refined into CE [11] 
* CE 5 is refined into CE [12] 
* CE 9 is refined into CE [13] 
* CE 7 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of eval_foo_bb1_in/6 
* CEs [14] --> Loop 10 
* CEs [15] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [13] --> Loop 15 

### Ranking functions of CR eval_foo_bb1_in(V_n,V__05,V__03,V__01,V__0,B) 
* RF of phase [10,11]: [V_n-V__01,V_n/2-V__05/2-V__01]

#### Partial ranking functions of CR eval_foo_bb1_in(V_n,V__05,V__03,V__01,V__0,B) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1]:
    V_n/3-V__05/3-2/3*V__01
  - RF of loop [10:1,11:1]:
    V_n-V__01
  - RF of loop [11:1]:
    V_n/2-V__03/2-V__01+1/2 depends on loops [10:1] 
    V_n/2-V__05/2-V__01


### Specialization of cost equations eval_foo_bb0_in/6 
* CE 3 is refined into CE [16,17,18,19,20] 
* CE 2 is refined into CE [21] 


### Cost equations --> "Loop" of eval_foo_bb0_in/6 
* CEs [16] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 
* CEs [19] --> Loop 20 
* CEs [21] --> Loop 21 

### Ranking functions of CR eval_foo_bb0_in(V_x,V_tx,V_y,V_ty,V_n,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_tx,V_y,V_ty,V_n,B) 


### Specialization of cost equations eval_foo_start/6 
* CE 1 is refined into CE [22,23,24,25,26,27] 


### Cost equations --> "Loop" of eval_foo_start/6 
* CEs [27] --> Loop 22 
* CEs [26] --> Loop 23 
* CEs [25] --> Loop 24 
* CEs [24] --> Loop 25 
* CEs [23] --> Loop 26 
* CEs [22] --> Loop 27 

### Ranking functions of CR eval_foo_start(V_x,V_tx,V_y,V_ty,V_n,B) 

#### Partial ranking functions of CR eval_foo_start(V_x,V_tx,V_y,V_ty,V_n,B) 


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

#### Cost of chains of eval_foo_bb1_in(V_n,V__05,V__03,V__01,V__0,B):
* Chain [[10,11],15]: 1*it(10)+1*it(11)+0
  Such that:aux(3) =< V_n/2-V__05/2-V__01
it(10) =< V_n/3-V__05/3-2/3*V__01
aux(4) =< 3/2*V_n-V__05/2-2*V__01
aux(5) =< V_n-V__01
it(10) =< aux(5)
it(11) =< aux(5)
it(10) =< aux(3)
it(11) =< aux(3)
it(10) =< aux(4)
it(11) =< aux(4)

  with precondition: [B=2,V__03>=V__05+1,V__0>=V__01+1,V_n>=V__0,V__0>=2*V__01+V__03] 

* Chain [[10,11],14]: 1*it(10)+1*it(11)+0
  Such that:aux(3) =< V_n/2-V__05/2-V__01
it(10) =< V_n/3-V__05/3-2/3*V__01
aux(4) =< 3/2*V_n-V__05/2-2*V__01
aux(6) =< V_n-V__01
it(10) =< aux(6)
it(11) =< aux(6)
it(10) =< aux(3)
it(11) =< aux(3)
it(10) =< aux(4)
it(11) =< aux(4)

  with precondition: [B=2,V__03>=V__05+1,V__0>=V__01+1,V_n>=V__0,V__0>=2*V__01+V__03] 

* Chain [[10,11],13]: 1*it(10)+1*it(11)+0
  Such that:aux(3) =< V_n/2-V__05/2-V__01
it(10) =< V_n/3-V__05/3-2/3*V__01
aux(4) =< 3/2*V_n-V__05/2-2*V__01
aux(7) =< V_n-V__01
it(10) =< aux(7)
it(11) =< aux(7)
it(10) =< aux(3)
it(11) =< aux(3)
it(10) =< aux(4)
it(11) =< aux(4)

  with precondition: [B=2,V__03>=V__05+1,V__0>=V__01+1,V_n>=V__0,V__0>=2*V__01+V__03] 

* Chain [[10,11],12]: 1*it(10)+1*it(11)+0
  Such that:aux(3) =< V_n/2-V__05/2-V__01
it(10) =< V_n/3-V__05/3-2/3*V__01
aux(4) =< 3/2*V_n-V__05/2-2*V__01
aux(8) =< V_n-V__01
it(10) =< aux(8)
it(11) =< aux(8)
it(10) =< aux(3)
it(11) =< aux(3)
it(10) =< aux(4)
it(11) =< aux(4)

  with precondition: [B=2,V__03>=V__05+1,V__0>=V__01+1,V_n>=V__0,V__0>=2*V__01+V__03] 

* Chain [15]: 0
  with precondition: [B=2,V__0>=V_n+1] 

* Chain [14]: 0
  with precondition: [B=2,V__05>=V__03,V_n>=V__0] 

* Chain [13]: 0
  with precondition: [B=2,V_n>=V__0,V__01>=V__0] 

* Chain [12]: 0
  with precondition: [B=2,V_n>=V__0,V__03+2*V__01>=V__0+1] 


#### Cost of chains of eval_foo_bb0_in(V_x,V_tx,V_y,V_ty,V_n,B):
* Chain [21]: 0
  with precondition: [0>=V_x+V_y+1] 

* Chain [20]: 0
  with precondition: [V_tx>=V_x,V_n>=V_x,V_x+V_y>=0] 

* Chain [19]: 4*s(25)+4*s(26)+0
  Such that:s(24) =< -2*V_tx-V_ty/2+3/2*V_n
s(22) =< -V_tx-V_ty/2+V_n/2
s(21) =< -V_tx+V_n
s(23) =< -2/3*V_tx-V_ty/3+V_n/3
s(25) =< s(23)
s(25) =< s(21)
s(26) =< s(21)
s(25) =< s(22)
s(26) =< s(22)
s(25) =< s(24)
s(26) =< s(24)

  with precondition: [V_n>=V_x,V_x>=V_tx+1,V_y>=V_ty+1,V_x+V_y>=0,V_x>=2*V_tx+V_y] 

* Chain [18]: 0
  with precondition: [V_n>=V_x,V_ty>=V_y,V_x+V_y>=0] 

* Chain [17]: 0
  with precondition: [V_n>=V_x,V_x+V_y>=0,V_y+2*V_tx>=V_x+1] 

* Chain [16]: 0
  with precondition: [V_x>=V_n+1,V_x+V_y>=0] 


#### Cost of chains of eval_foo_start(V_x,V_tx,V_y,V_ty,V_n,B):
* Chain [27]: 0
  with precondition: [0>=V_x+V_y+1] 

* Chain [26]: 0
  with precondition: [V_tx>=V_x,V_n>=V_x,V_x+V_y>=0] 

* Chain [25]: 4*s(31)+4*s(32)+0
  Such that:s(27) =< -2*V_tx-V_ty/2+3/2*V_n
s(28) =< -V_tx-V_ty/2+V_n/2
s(29) =< -V_tx+V_n
s(30) =< -2/3*V_tx-V_ty/3+V_n/3
s(31) =< s(30)
s(31) =< s(29)
s(32) =< s(29)
s(31) =< s(28)
s(32) =< s(28)
s(31) =< s(27)
s(32) =< s(27)

  with precondition: [V_n>=V_x,V_x>=V_tx+1,V_y>=V_ty+1,V_x+V_y>=0,V_x>=2*V_tx+V_y] 

* Chain [24]: 0
  with precondition: [V_n>=V_x,V_ty>=V_y,V_x+V_y>=0] 

* Chain [23]: 0
  with precondition: [V_n>=V_x,V_x+V_y>=0,V_y+2*V_tx>=V_x+1] 

* Chain [22]: 0
  with precondition: [V_x>=V_n+1,V_x+V_y>=0] 


Closed-form bounds of eval_foo_start(V_x,V_tx,V_y,V_ty,V_n,B): 
-------------------------------------
* Chain [27] with precondition: [0>=V_x+V_y+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [V_tx>=V_x,V_n>=V_x,V_x+V_y>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [V_n>=V_x,V_x>=V_tx+1,V_y>=V_ty+1,V_x+V_y>=0,V_x>=2*V_tx+V_y] 
    - Upper bound: -20/3*V_tx-4/3*V_ty+16/3*V_n 
    - Complexity: n 
* Chain [24] with precondition: [V_n>=V_x,V_ty>=V_y,V_x+V_y>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [V_n>=V_x,V_x+V_y>=0,V_y+2*V_tx>=V_x+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [V_x>=V_n+1,V_x+V_y>=0] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_foo_start(V_x,V_tx,V_y,V_ty,V_n,B): nat(-2/3*V_tx-V_ty/3+V_n/3)*4+nat(-V_tx+V_n)*4 
Asymptotic class: n 
* Total analysis performed in 255 ms.