/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [m1/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [m1_loop_cont/2]
3. non_recursive  : [start/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into m1/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into start/7

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

### Specialization of cost equations m1/7 
* CE 6 is refined into CE [7] 
* CE 2 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 


### Cost equations --> "Loop" of m1/7 
* CEs [8] --> Loop 7 
* CEs [9] --> Loop 8 
* CEs [10] --> Loop 9 
* CEs [11] --> Loop 10 
* CEs [7] --> Loop 11 

### Ranking functions of CR m1(A,B,C,D,E,F,I) 
* RF of phase [7]: [-A+B-C+E+2,-A-C+3*E+4,2*A-C+1,2*A+2*C-3*F+1,2*A-F+1,B-C+1,B-F+1,-C+2*E+3,2*E-F+3]
* RF of phase [8,9]: [-A+B-C+E+1,-A+2*B-C,-A-C+3*E+3,2*A+2*C-3*F,B-F,2*E-F+2]
* RF of phase [10]: [-A+B,-A+B-C+E+2,-A+3*B-2*C+2,-A-C+3*E+4,-A+C-1,-A+E+1,2*A+2*C-3*F+1,B-F+1,C-F,2*E-F+3]

#### Partial ranking functions of CR m1(A,B,C,D,E,F,I) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -A+B-C+E+2
    -A-C+3*E+4
    2*A-C+1
    2*A+2*C-3*F+1
    2*A-F+1
    B-C+1
    B-F+1
    -C+2*E+3
    2*E-F+3
* Partial RF of phase [8,9]:
  - RF of loop [8:1]:
    A+B-E-F
    A+B/2-F+1/2
    A+E-F+2
    2*A+C-2*F+1
    B-C+1
    -C+2*E+3
  - RF of loop [8:1,9:1]:
    B-F
    2*E-F+2
  - RF of loop [9:1]:
    -A+B
    -A+C depends on loops [8:1] 
    -A+E+1
    C-F
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    -A+B
    -A+B-C+E+2
    -A+3*B-2*C+2
    -A-C+3*E+4
    -A+C-1
    -A+E+1
    2*A+2*C-3*F+1
    B-F+1
    C-F
    2*E-F+3


### Specialization of cost equations start/7 
* CE 1 is refined into CE [12,13] 


### Cost equations --> "Loop" of start/7 
* CEs [13] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR start(A,B,C,D,E,F,I) 

#### Partial ranking functions of CR start(A,B,C,D,E,F,I) 


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

#### Cost of chains of m1(A,B,C,D,E,F,I):
* Chain [[8,9],[10],11]: 1*it(8)+1*it(9)+1*it(10)+0
  Such that:aux(1) =< -2*A+E+F+1
it(8) =< A+B-E-F
it(8) =< A+B/2-F+1/2
aux(2) =< -B+2*C-F
aux(5) =< 2*B-E-F
aux(15) =< -A+E
aux(16) =< -A+E+1
aux(17) =< B-F
aux(18) =< B-F+1
aux(19) =< 2*E-F+2
aux(2) =< aux(15)
it(9) =< aux(15)
it(9) =< aux(16)
it(10) =< aux(16)
aux(4) =< aux(17)
aux(4) =< aux(18)
it(10) =< aux(18)
it(8) =< aux(17)
it(9) =< aux(17)
it(8) =< aux(4)
it(9) =< aux(4)
it(8) =< aux(5)
it(9) =< aux(5)
it(8) =< aux(19)
it(9) =< aux(19)
it(9) =< it(8)+aux(2)
it(9) =< it(8)+aux(1)

  with precondition: [I=2,A+C=E+F+1,D>=0,2*E+2>=B,B>=C,C>=E+1,C>=F+1,E+F+1>=C,B+F+1>=C+E] 

* Chain [[8,9],[7],11]: 1*it(7)+1*it(8)+1*it(9)+0
  Such that:aux(1) =< -2*A+E+F+1
aux(5) =< 2*B-E-F
aux(2) =< C-F
aux(20) =< -A+E+1
aux(21) =< A+B-E-F
aux(22) =< B-F
aux(23) =< B-F+1
aux(24) =< 2*E-F+2
aux(2) =< aux(20)
it(9) =< aux(20)
it(7) =< aux(21)
it(8) =< aux(21)
aux(4) =< aux(22)
aux(4) =< aux(23)
it(7) =< aux(23)
it(8) =< aux(22)
it(9) =< aux(22)
it(8) =< aux(4)
it(9) =< aux(4)
it(8) =< aux(5)
it(9) =< aux(5)
it(8) =< aux(24)
it(9) =< aux(24)
it(9) =< it(8)+aux(2)
it(9) =< it(8)+aux(1)

  with precondition: [I=2,A+C=E+F+1,D>=0,2*E+2>=B,B>=C,C>=E+1,C>=F+1,E+F+1>=C,B+F+1>=C+E] 

* Chain [[8,9],11]: 1*it(8)+1*it(9)+0
  Such that:aux(1) =< -2*A+E+F+1
it(8) =< A+B/2-F+1/2
aux(5) =< 2*B-E-F
aux(2) =< C-F
aux(25) =< -A+E+1
aux(26) =< B-F
aux(27) =< 2*E-F+2
aux(2) =< aux(25)
it(9) =< aux(25)
it(8) =< aux(26)
it(9) =< aux(26)
it(8) =< aux(5)
it(9) =< aux(5)
it(8) =< aux(27)
it(9) =< aux(27)
it(9) =< it(8)+aux(2)
it(9) =< it(8)+aux(1)

  with precondition: [I=2,A+C=E+F+1,D>=0,2*E+2>=B,B>=C,C>=E+1,C>=F+1,E+F+1>=C,B+F+1>=C+E] 

* Chain [11]: 0
  with precondition: [I=2,E+F+1=A+C,A>=0,B>=1,D>=0,F>=A,2*E+2>=B,2*B>=F,3*B>=2*E+A+2,3*B>=2*E+F+1,A+B>=2*E,A+2*B>=2*E+F+1] 


#### Cost of chains of start(A,B,C,D,E,F,I):
* Chain [13]: 0
  with precondition: [E+1=C,A=F,A>=0,D>=0,B>=A+1,A+B>=2*E,2*E+2>=A+B] 

* Chain [12]: 1*s(44)+1*s(45)+1*s(47)+1*s(48)+1*s(49)+1*s(50)+1*s(52)+1*s(53)+0
  Such that:s(34) =< -B+2*C-F
s(37) =< B-C+1
s(39) =< B-F
s(40) =< B-F+1
s(41) =< 2*B-C-F+1
s(38) =< B/2+1/2
s(43) =< 2*C-F
aux(37) =< C-F
s(44) =< s(37)
s(45) =< s(38)
s(44) =< s(38)
s(47) =< aux(37)
s(45) =< s(39)
s(47) =< s(39)
s(45) =< s(41)
s(47) =< s(41)
s(45) =< s(43)
s(47) =< s(43)
s(47) =< s(45)+aux(37)
s(48) =< aux(37)
s(49) =< s(37)
s(50) =< s(37)
s(51) =< s(39)
s(51) =< s(40)
s(49) =< s(40)
s(50) =< s(39)
s(48) =< s(39)
s(50) =< s(51)
s(48) =< s(51)
s(50) =< s(41)
s(48) =< s(41)
s(50) =< s(43)
s(48) =< s(43)
s(48) =< s(50)+aux(37)
s(34) =< aux(37)
s(52) =< aux(37)
s(53) =< aux(37)
s(53) =< s(40)
s(44) =< s(39)
s(52) =< s(39)
s(44) =< s(51)
s(52) =< s(51)
s(44) =< s(41)
s(52) =< s(41)
s(44) =< s(43)
s(52) =< s(43)
s(52) =< s(44)+s(34)
s(52) =< s(44)+aux(37)

  with precondition: [E+1=C,A=F,A>=0,D>=0,E>=A,B>=E+1,A+B>=2*E,2*E+2>=A+B] 


Closed-form bounds of start(A,B,C,D,E,F,I): 
-------------------------------------
* Chain [13] with precondition: [E+1=C,A=F,A>=0,D>=0,B>=A+1,A+B>=2*E,2*E+2>=A+B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [12] with precondition: [E+1=C,A=F,A>=0,D>=0,E>=A,B>=E+1,A+B>=2*E,2*E+2>=A+B] 
    - Upper bound: 7/2*B+C-4*F+7/2 
    - Complexity: n 

### Maximum cost of start(A,B,C,D,E,F,I): 7/2*B+C-4*F+7/2 
Asymptotic class: n 
* Total analysis performed in 994 ms.