WORST_CASE(?,O(n^2))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(<0,0,A>, A, .= 0) (<0,0,B>, B, .= 0) (<0,0,C>, C, .= 0)
(<1,0,A>, B, .= 0) (<1,0,B>, A, .= 0) (<1,0,C>, C, .= 0)
(<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, 1, .= 1)
(<3,0,A>, A, .= 0) (<3,0,B>, B, .= 0) (<3,0,C>, C, .= 0)
(<4,0,A>, A, .= 0) (<4,0,B>, B, .= 0) (<4,0,C>, C, .= 0)
(<5,0,A>, A, .= 0) (<5,0,B>, B, .= 0) (<5,0,C>, C, .= 0)
(<6,0,A>, A, .= 0) (<6,0,B>, B, .= 0) (<6,0,C>, 1 + C, .+ 1)
(<7,0,A>, A, .= 0) (<7,0,B>, 1 + B, .+ 1) (<7,0,C>, C, .= 0)
(<8,0,A>, A, .= 0) (<8,0,B>, B, .= 0) (<8,0,C>, C, .= 0)
* Step 2: SizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}]
Sizebounds:
(<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?)
(<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?)
(<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?)
(<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, ?) (<4,0,C>, ?)
(<5,0,A>, ?) (<5,0,B>, ?) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, ?) (<6,0,C>, ?)
(<7,0,A>, ?) (<7,0,B>, ?) (<7,0,C>, ?)
(<8,0,A>, ?) (<8,0,B>, ?) (<8,0,C>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<3,0,A>, B) (<3,0,B>, ?) (<3,0,C>, 1 + B + C)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
(<8,0,A>, B) (<8,0,B>, ?) (<8,0,C>, 1 + B + C)
* Step 3: LeafRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<3,0,A>, B) (<3,0,B>, ?) (<3,0,C>, 1 + B + C)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
(<8,0,A>, B) (<8,0,B>, ?) (<8,0,C>, 1 + B + C)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [3,8]
* Step 4: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = 1
p(evalfbb2in) = 1
p(evalfbb3in) = 1
p(evalfbb4in) = 1
p(evalfentryin) = 2
p(evalfstart) = 2
The following rules are strictly oriented:
True ==>
evalfentryin(A,B,C) = 2
> 1
= evalfbb4in(B,A,C)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C) = 2
>= 2
= evalfentryin(A,B,C)
[B >= 1] ==>
evalfbb4in(A,B,C) = 1
>= 1
= evalfbb2in(A,B,1)
[A >= C] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb1in(A,B,C)
[C >= 1 + A] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb3in(A,B,C)
True ==>
evalfbb1in(A,B,C) = 1
>= 1
= evalfbb2in(A,B,1 + C)
True ==>
evalfbb3in(A,B,C) = 1
>= 1
= evalfbb4in(A,-1 + B,C)
* Step 5: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = -1 + x2
p(evalfbb2in) = -1 + x2
p(evalfbb3in) = -1 + x2
p(evalfbb4in) = x2
p(evalfentryin) = x1
p(evalfstart) = x1
The following rules are strictly oriented:
[B >= 1] ==>
evalfbb4in(A,B,C) = B
> -1 + B
= evalfbb2in(A,B,1)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C) = A
>= A
= evalfentryin(A,B,C)
True ==>
evalfentryin(A,B,C) = A
>= A
= evalfbb4in(B,A,C)
[A >= C] ==>
evalfbb2in(A,B,C) = -1 + B
>= -1 + B
= evalfbb1in(A,B,C)
[C >= 1 + A] ==>
evalfbb2in(A,B,C) = -1 + B
>= -1 + B
= evalfbb3in(A,B,C)
True ==>
evalfbb1in(A,B,C) = -1 + B
>= -1 + B
= evalfbb2in(A,B,1 + C)
True ==>
evalfbb3in(A,B,C) = -1 + B
>= -1 + B
= evalfbb4in(A,-1 + B,C)
* Step 6: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (A,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,6,4], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = 1
p(evalfbb2in) = 1
p(evalfbb3in) = 0
The following rules are strictly oriented:
[C >= 1 + A] ==>
evalfbb2in(A,B,C) = 1
> 0
= evalfbb3in(A,B,C)
The following rules are weakly oriented:
[A >= C] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb1in(A,B,C)
True ==>
evalfbb1in(A,B,C) = 1
>= 1
= evalfbb2in(A,B,1 + C)
We use the following global sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
* Step 7: KnowledgePropagation WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (A,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (A,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 8: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (A,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (A,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (A,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,6,4], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = 1 + x1 + -1*x3
p(evalfbb2in) = 2 + x1 + -1*x3
p(evalfbb3in) = 2 + x1 + -1*x3
The following rules are strictly oriented:
[A >= C] ==>
evalfbb2in(A,B,C) = 2 + A + -1*C
> 1 + A + -1*C
= evalfbb1in(A,B,C)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb2in(A,B,C) = 2 + A + -1*C
>= 2 + A + -1*C
= evalfbb3in(A,B,C)
True ==>
evalfbb1in(A,B,C) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb2in(A,B,1 + C)
We use the following global sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
* Step 9: KnowledgePropagation WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (A,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (3*A + A*B,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (A,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (A,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 10: LocalSizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (A,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (3*A + A*B,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (A,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (3*A + A*B,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (A,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, B) (<1,0,B>, A) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, ?) (<2,0,C>, 1)
(<4,0,A>, B) (<4,0,B>, ?) (<4,0,C>, B)
(<5,0,A>, B) (<5,0,B>, ?) (<5,0,C>, 1 + B)
(<6,0,A>, B) (<6,0,B>, ?) (<6,0,C>, B)
(<7,0,A>, B) (<7,0,B>, ?) (<7,0,C>, 1 + B)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^2))