/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_foo_bb4_in/6,eval_foo_bb5_in/6]
1. recursive  : [eval_foo_bb2_in/7,eval_foo_bb3_in/7,eval_foo_bb4_in_loop_cont/8]
2. recursive  : [eval_foo_bb1_in/5,eval_foo_bb2_in_loop_cont/8,eval_foo_bb6_in/7]
3. non_recursive  : [eval_foo_stop/1]
4. non_recursive  : [eval_foo_bb7_in/1]
5. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
6. non_recursive  : [eval_foo_bb0_in/4]
7. non_recursive  : [eval_foo_start/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_foo_bb4_in/6
1. SCC is partially evaluated into eval_foo_bb2_in/7
2. SCC is partially evaluated into eval_foo_bb1_in/5
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_foo_bb0_in/4
7. SCC is partially evaluated into eval_foo_start/7

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

### Specialization of cost equations eval_foo_bb4_in/6 
* CE 11 is refined into CE [12] 
* CE 10 is refined into CE [13] 


### Cost equations --> "Loop" of eval_foo_bb4_in/6 
* CEs [13] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR eval_foo_bb4_in(V_N,V__01,V__1,V__02,B,C) 
* RF of phase [12]: [V_N-V__02]

#### Partial ranking functions of CR eval_foo_bb4_in(V_N,V__01,V__1,V__02,B,C) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V_N-V__02


### Specialization of cost equations eval_foo_bb2_in/7 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15,16] 


### Cost equations --> "Loop" of eval_foo_bb2_in/7 
* CEs [16] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14] --> Loop 16 

### Ranking functions of CR eval_foo_bb2_in(V_m,V_N,V__01,V__1,B,C,D) 
* RF of phase [14]: [V_m-V__01]

#### Partial ranking functions of CR eval_foo_bb2_in(V_m,V_N,V__01,V__1,B,C,D) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    V_m-V__01


### Specialization of cost equations eval_foo_bb1_in/5 
* CE 7 is refined into CE [17] 
* CE 6 is refined into CE [18,19,20,21] 


### Cost equations --> "Loop" of eval_foo_bb1_in/5 
* CEs [21] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [20] --> Loop 20 
* CEs [17] --> Loop 21 

### Ranking functions of CR eval_foo_bb1_in(V_m,V_n,V_N,V__0,B) 
* RF of phase [17]: [V_n-V__0]
* RF of phase [20]: [V_n-V__0]

#### Partial ranking functions of CR eval_foo_bb1_in(V_m,V_n,V_N,V__0,B) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    V_n-V__0
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    V_n-V__0


### Specialization of cost equations eval_foo_bb0_in/4 
* CE 5 is refined into CE [22,23,24,25,26,27,28] 
* CE 4 is refined into CE [29] 
* CE 2 is refined into CE [30] 
* CE 3 is refined into CE [31] 


### Cost equations --> "Loop" of eval_foo_bb0_in/4 
* CEs [26] --> Loop 22 
* CEs [25] --> Loop 23 
* CEs [29] --> Loop 24 
* CEs [30] --> Loop 25 
* CEs [31] --> Loop 26 
* CEs [28] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [24] --> Loop 29 
* CEs [23] --> Loop 30 
* CEs [22] --> Loop 31 

### Ranking functions of CR eval_foo_bb0_in(V_m,V_n,V_N,B) 

#### Partial ranking functions of CR eval_foo_bb0_in(V_m,V_n,V_N,B) 


### Specialization of cost equations eval_foo_start/7 
* CE 1 is refined into CE [32,33,34,35,36,37,38,39,40,41] 


### Cost equations --> "Loop" of eval_foo_start/7 
* CEs [41] --> Loop 32 
* CEs [40] --> Loop 33 
* CEs [39] --> Loop 34 
* CEs [38] --> Loop 35 
* CEs [37] --> Loop 36 
* CEs [36] --> Loop 37 
* CEs [35] --> Loop 38 
* CEs [34] --> Loop 39 
* CEs [33] --> Loop 40 
* CEs [32] --> Loop 41 

### Ranking functions of CR eval_foo_start(V_i,V_j,V_k,V_m,V_n,V_N,B) 

#### Partial ranking functions of CR eval_foo_start(V_i,V_j,V_k,V_m,V_n,V_N,B) 


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

#### Cost of chains of eval_foo_bb4_in(V_N,V__01,V__1,V__02,B,C):
* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -V__02+C

  with precondition: [B=2,V_N=C,V_N>=0,V__01>=0,V__02>=V__1,V_N>=V__02+1] 

* Chain [13]: 0
  with precondition: [B=2,V__02=C,V_N>=0,V__01>=0,V__02>=V_N,V__02>=V__1] 


#### Cost of chains of eval_foo_bb2_in(V_m,V_N,V__01,V__1,B,C,D):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< -V__01+C

  with precondition: [B=3,V_m=C,V__1=D,V_N>=0,V__01>=0,V__1>=V_N,V_m>=V__01+1] 

* Chain [16]: 0
  with precondition: [B=3,V__01=V_m,D=V__1,V__01=C,V_N>=0,V__01>=0] 

* Chain [15,[14],16]: 1*it(14)+1*s(1)+1
  Such that:s(1) =< -V__1+D
it(14) =< C

  with precondition: [V__01=0,B=3,V_m=C,V_N=D,V_m>=2,V_N>=0,V_N>=V__1+1] 

* Chain [15,16]: 1*s(1)+1
  Such that:s(1) =< -V__1+D

  with precondition: [V_m=1,V__01=0,B=3,C=1,V_N=D,V_N>=0,V_N>=V__1+1] 


#### Cost of chains of eval_foo_bb1_in(V_m,V_n,V_N,V__0,B):
* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< V_n-V__0

  with precondition: [V_m=0,B=4,V_N>=0,V__0>=0,V_n>=V__0+1] 

* Chain [[17],21]: 1*it(17)+1*s(4)+0
  Such that:aux(1) =< V_m
it(17) =< V_n-V__0
s(4) =< it(17)*aux(1)

  with precondition: [B=4,V_m>=1,V_N>=0,V__0>=V_N,V_n>=V__0+1] 

* Chain [21]: 0
  with precondition: [B=4,V_m>=0,V_n>=0,V_N>=0,V__0>=V_n] 

* Chain [19,[17],21]: 1*it(17)+1*s(4)+1*s(5)+2
  Such that:aux(1) =< 1
it(17) =< V_n-V_N
s(5) =< V_N+1
s(4) =< it(17)*aux(1)

  with precondition: [V_m=1,V__0=0,B=4,V_N>=1,V_n>=V_N+2] 

* Chain [19,21]: 1*s(5)+2
  Such that:s(5) =< V_N+1

  with precondition: [V_m=1,V__0=0,B=4,V_n>=1,V_N>=1,V_N+1>=V_n] 

* Chain [18,[17],21]: 1*it(17)+1*s(4)+1*s(6)+1*s(7)+2
  Such that:it(17) =< V_n-V_N
s(6) =< V_N+1
aux(2) =< V_m
s(7) =< aux(2)
s(4) =< it(17)*aux(2)

  with precondition: [V__0=0,B=4,V_m>=2,V_N>=1,V_n>=V_N+2] 

* Chain [18,21]: 1*s(6)+1*s(7)+2
  Such that:s(7) =< V_m
s(6) =< V_N+1

  with precondition: [V__0=0,B=4,V_m>=2,V_n>=1,V_N>=1,V_N+1>=V_n] 


#### Cost of chains of eval_foo_bb0_in(V_m,V_n,V_N,B):
* Chain [31]: 1*s(8)+0
  Such that:s(8) =< V_n

  with precondition: [V_m=0,V_n>=1,V_N>=0] 

* Chain [30]: 1*s(9)+2
  Such that:s(9) =< V_N+1

  with precondition: [V_m=1,V_n>=1,V_N>=1,V_N+1>=V_n] 

* Chain [29]: 1*s(11)+1*s(12)+1*s(13)+2
  Such that:s(10) =< 1
s(11) =< V_n-V_N
s(12) =< V_N+1
s(13) =< s(11)*s(10)

  with precondition: [V_m=1,V_N>=1,V_n>=V_N+2] 

* Chain [28]: 0
  with precondition: [V_n=0,V_m>=0,V_N>=0] 

* Chain [27]: 1*s(15)+1*s(16)+0
  Such that:s(14) =< V_m
s(15) =< V_n
s(16) =< s(15)*s(14)

  with precondition: [V_N=0,V_m>=1,V_n>=1] 

* Chain [26]: 0
  with precondition: [0>=V_m+1] 

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

* Chain [24]: 0
  with precondition: [0>=V_N+1] 

* Chain [23]: 1*s(17)+1*s(18)+2
  Such that:s(17) =< V_m
s(18) =< V_N+1

  with precondition: [V_m>=2,V_n>=1,V_N>=1,V_N+1>=V_n] 

* Chain [22]: 1*s(19)+1*s(20)+1*s(22)+1*s(23)+2
  Such that:s(21) =< V_m
s(19) =< V_n-V_N
s(20) =< V_N+1
s(22) =< s(21)
s(23) =< s(19)*s(21)

  with precondition: [V_m>=2,V_N>=1,V_n>=V_N+2] 


#### Cost of chains of eval_foo_start(V_i,V_j,V_k,V_m,V_n,V_N,B):
* Chain [41]: 1*s(24)+0
  Such that:s(24) =< V_n

  with precondition: [V_m=0,V_n>=1,V_N>=0] 

* Chain [40]: 1*s(25)+2
  Such that:s(25) =< V_N+1

  with precondition: [V_m=1,V_n>=1,V_N>=1,V_N+1>=V_n] 

* Chain [39]: 1*s(27)+1*s(28)+1*s(29)+2
  Such that:s(26) =< 1
s(27) =< V_n-V_N
s(28) =< V_N+1
s(29) =< s(27)*s(26)

  with precondition: [V_m=1,V_N>=1,V_n>=V_N+2] 

* Chain [38]: 0
  with precondition: [V_n=0,V_m>=0,V_N>=0] 

* Chain [37]: 1*s(31)+1*s(32)+0
  Such that:s(30) =< V_m
s(31) =< V_n
s(32) =< s(31)*s(30)

  with precondition: [V_N=0,V_m>=1,V_n>=1] 

* Chain [36]: 0
  with precondition: [0>=V_m+1] 

* Chain [35]: 0
  with precondition: [0>=V_n+1] 

* Chain [34]: 0
  with precondition: [0>=V_N+1] 

* Chain [33]: 1*s(33)+1*s(34)+2
  Such that:s(33) =< V_m
s(34) =< V_N+1

  with precondition: [V_m>=2,V_n>=1,V_N>=1,V_N+1>=V_n] 

* Chain [32]: 1*s(36)+1*s(37)+1*s(38)+1*s(39)+2
  Such that:s(35) =< V_m
s(36) =< V_n-V_N
s(37) =< V_N+1
s(38) =< s(35)
s(39) =< s(36)*s(35)

  with precondition: [V_m>=2,V_N>=1,V_n>=V_N+2] 


Closed-form bounds of eval_foo_start(V_i,V_j,V_k,V_m,V_n,V_N,B): 
-------------------------------------
* Chain [41] with precondition: [V_m=0,V_n>=1,V_N>=0] 
    - Upper bound: V_n 
    - Complexity: n 
* Chain [40] with precondition: [V_m=1,V_n>=1,V_N>=1,V_N+1>=V_n] 
    - Upper bound: V_N+3 
    - Complexity: n 
* Chain [39] with precondition: [V_m=1,V_N>=1,V_n>=V_N+2] 
    - Upper bound: 2*V_n-V_N+3 
    - Complexity: n 
* Chain [38] with precondition: [V_n=0,V_m>=0,V_N>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [37] with precondition: [V_N=0,V_m>=1,V_n>=1] 
    - Upper bound: V_n*V_m+V_n 
    - Complexity: n^2 
* Chain [36] with precondition: [0>=V_m+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [0>=V_n+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=V_N+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [V_m>=2,V_n>=1,V_N>=1,V_N+1>=V_n] 
    - Upper bound: V_m+V_N+3 
    - Complexity: n 
* Chain [32] with precondition: [V_m>=2,V_N>=1,V_n>=V_N+2] 
    - Upper bound: V_n-V_N+(V_m+2+(V_n-V_N)*V_m+(V_N+1)) 
    - Complexity: n^2 

### Maximum cost of eval_foo_start(V_i,V_j,V_k,V_m,V_n,V_N,B): max([nat(V_n)*nat(V_m)+nat(V_n),nat(V_N+1)+2+max([nat(V_n-V_N)*2,nat(V_n-V_N)*nat(V_m)+nat(V_n-V_N)+nat(V_m)])]) 
Asymptotic class: n^2 
* Total analysis performed in 384 ms.