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(1,B,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 1 + B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,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>, 1, .= 1) (<1,0,B>, B, .= 0) (<1,0,C>, C, .= 0)
(<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, A, .= 0)
(<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>, 1 + A, .+ 1) (<7,0,B>, B, .= 0) (<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(1,B,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 1 + B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<3,0,A>, ?) (<3,0,B>, B) (<3,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
(<8,0,A>, ?) (<8,0,B>, B) (<8,0,C>, ?)
* Step 3: UnsatPaths 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(1,B,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 1 + B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<3,0,A>, ?) (<3,0,B>, B) (<3,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
(<8,0,A>, ?) (<8,0,B>, B) (<8,0,C>, ?)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(2,5)]
* Step 4: 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(1,B,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 1 + B] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,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},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<3,0,A>, ?) (<3,0,B>, B) (<3,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
(<8,0,A>, ?) (<8,0,B>, B) (<8,0,C>, ?)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [3,8]
* 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(1,B,C) True (?,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + 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},2->{4},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
+ 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(1,B,C)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C) = 2
>= 2
= evalfentryin(A,B,C)
[B >= A] ==>
evalfbb4in(A,B,C) = 1
>= 1
= evalfbb2in(A,B,A)
[B >= C] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb1in(A,B,C)
[C >= 1 + B] ==>
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(1 + A,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(1,B,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (?,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + 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},2->{4},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = -1*x1 + x2
p(evalfbb2in) = -1*x1 + x2
p(evalfbb3in) = -1*x1 + x2
p(evalfbb4in) = 1 + -1*x1 + x2
p(evalfentryin) = x2
p(evalfstart) = x2
The following rules are strictly oriented:
[B >= A] ==>
evalfbb4in(A,B,C) = 1 + -1*A + B
> -1*A + B
= evalfbb2in(A,B,A)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C) = B
>= B
= evalfentryin(A,B,C)
True ==>
evalfentryin(A,B,C) = B
>= B
= evalfbb4in(1,B,C)
[B >= C] ==>
evalfbb2in(A,B,C) = -1*A + B
>= -1*A + B
= evalfbb1in(A,B,C)
[C >= 1 + B] ==>
evalfbb2in(A,B,C) = -1*A + B
>= -1*A + B
= evalfbb3in(A,B,C)
True ==>
evalfbb1in(A,B,C) = -1*A + B
>= -1*A + B
= evalfbb2in(A,B,1 + C)
True ==>
evalfbb3in(A,B,C) = -1*A + B
>= -1*A + B
= evalfbb4in(1 + A,B,C)
* Step 7: 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(1,B,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (B,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + 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},2->{4},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [7,5,6,4], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = 1
p(evalfbb2in) = 1
p(evalfbb3in) = 1
p(evalfbb4in) = 0
The following rules are strictly oriented:
True ==>
evalfbb3in(A,B,C) = 1
> 0
= evalfbb4in(1 + A,B,C)
The following rules are weakly oriented:
[B >= C] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb1in(A,B,C)
[C >= 1 + B] ==>
evalfbb2in(A,B,C) = 1
>= 1
= evalfbb3in(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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
* 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(1,B,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (B,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,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},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
+ 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 + B] ==>
evalfbb2in(A,B,C) = 1
> 0
= evalfbb3in(A,B,C)
The following rules are weakly oriented:
[B >= 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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
* Step 9: ChainProcessor 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(1,B,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (B,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (B,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,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},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>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
+ Applied Processor:
ChainProcessor False [0,1,2,4,5,6,7]
+ Details:
We chained rule 0 to obtain the rules [8] .
* Step 10: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
1. evalfentryin(A,B,C) -> evalfbb4in(1,B,C) True (2,1)
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (B,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (B,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[1->{2},2->{4,5},4->{6},5->{7},6->{4,5},7->{2},8->{2}]
Sizebounds:
(<1,0,A>, 1) (<1,0,B>, B) (<1,0,C>, C)
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
(<8,0,A>, 1) (<8,0,B>, B) (<8,0,C>, C)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [1]
* Step 11: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,A) [B >= A] (B,1)
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (B,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[2->{4,5},4->{6},5->{7},6->{4,5},7->{2},8->{2}]
Sizebounds:
(<2,0,A>, B) (<2,0,B>, B) (<2,0,C>, ?)
(<4,0,A>, ?) (<4,0,B>, B) (<4,0,C>, B)
(<5,0,A>, ?) (<5,0,B>, B) (<5,0,C>, ?)
(<6,0,A>, ?) (<6,0,B>, B) (<6,0,C>, B)
(<7,0,A>, ?) (<7,0,B>, B) (<7,0,C>, ?)
(<8,0,A>, 1) (<8,0,B>, B) (<8,0,C>, C)
+ Applied Processor:
ChainProcessor False [2,4,5,6,7,8]
+ Details:
We chained rule 2 to obtain the rules [9,10] .
* Step 12: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [B >= C] (?,1)
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (B,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
9. evalfbb4in(A,B,C) -> evalfbb1in(A,B,A) [B >= A && B >= A] (B,2)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[4->{6},5->{7},6->{4,5},7->{9,10},8->{9,10},9->{6},10->{7}]
Sizebounds:
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, B)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?)
(< 8,0,A>, 1) (< 8,0,B>, B) (< 8,0,C>, C)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
+ Applied Processor:
ChainProcessor False [4,5,6,7,8,9,10]
+ Details:
We chained rule 4 to obtain the rules [11] .
* Step 13: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + B] (B,1)
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
9. evalfbb4in(A,B,C) -> evalfbb1in(A,B,A) [B >= A && B >= A] (B,2)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[5->{7},6->{5,11},7->{9,10},8->{9,10},9->{6},10->{7},11->{5,11}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?)
(< 8,0,A>, 1) (< 8,0,B>, B) (< 8,0,C>, C)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
+ Applied Processor:
ChainProcessor False [5,6,7,8,9,10,11]
+ Details:
We chained rule 5 to obtain the rules [12] .
* Step 14: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (B,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
9. evalfbb4in(A,B,C) -> evalfbb1in(A,B,A) [B >= A && B >= A] (B,2)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
12. evalfbb2in(A,B,C) -> evalfbb4in(1 + A,B,C) [C >= 1 + B] (B,2)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,12},7->{9,10},8->{9,10},9->{6},10->{7},11->{11,12},12->{9,10}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?)
(< 8,0,A>, 1) (< 8,0,B>, B) (< 8,0,C>, C)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?)
+ Applied Processor:
ChainProcessor False [6,7,8,9,10,11,12]
+ Details:
We chained rule 7 to obtain the rules [13,14] .
* Step 15: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
8. evalfstart(A,B,C) -> evalfbb4in(1,B,C) True (1,2)
9. evalfbb4in(A,B,C) -> evalfbb1in(A,B,A) [B >= A && B >= A] (B,2)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
12. evalfbb2in(A,B,C) -> evalfbb4in(1 + A,B,C) [C >= 1 + B] (B,2)
13. evalfbb3in(A,B,C) -> evalfbb1in(1 + A,B,1 + A) [B >= 1 + A && B >= 1 + A] (B,3)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,12},8->{9,10},9->{6},10->{13,14},11->{11,12},12->{9,10},13->{6},14->{13,14}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(< 8,0,A>, 1) (< 8,0,B>, B) (< 8,0,C>, C)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
+ Applied Processor:
ChainProcessor False [6,8,9,10,11,12,13,14]
+ Details:
We chained rule 8 to obtain the rules [15,16] .
* Step 16: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
9. evalfbb4in(A,B,C) -> evalfbb1in(A,B,A) [B >= A && B >= A] (B,2)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
12. evalfbb2in(A,B,C) -> evalfbb4in(1 + A,B,C) [C >= 1 + B] (B,2)
13. evalfbb3in(A,B,C) -> evalfbb1in(1 + A,B,1 + A) [B >= 1 + A && B >= 1 + A] (B,3)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
15. evalfstart(A,B,C) -> evalfbb1in(1,B,1) [B >= 1 && B >= 1] (1,4)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,12},9->{6},10->{13,14},11->{11,12},12->{9,10},13->{6},14->{13,14},15->{6},16->{13,14}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
+ Applied Processor:
ChainProcessor False [6,9,10,11,12,13,14,15,16]
+ Details:
We chained rule 9 to obtain the rules [17] .
* Step 17: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
12. evalfbb2in(A,B,C) -> evalfbb4in(1 + A,B,C) [C >= 1 + B] (B,2)
13. evalfbb3in(A,B,C) -> evalfbb1in(1 + A,B,1 + A) [B >= 1 + A && B >= 1 + A] (B,3)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
15. evalfstart(A,B,C) -> evalfbb1in(1,B,1) [B >= 1 && B >= 1] (1,4)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
17. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1 + A) [B >= A && B >= A] (B,3)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,12},10->{13,14},11->{11,12},12->{10,17},13->{6},14->{13,14},15->{6},16->{13,14},17->{11,12}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, B)
+ Applied Processor:
ChainProcessor False [6,10,11,12,13,14,15,16,17]
+ Details:
We chained rule 12 to obtain the rules [18,19] .
* Step 18: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
10. evalfbb4in(A,B,C) -> evalfbb3in(A,B,A) [B >= A && A >= 1 + B] (B,2)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
13. evalfbb3in(A,B,C) -> evalfbb1in(1 + A,B,1 + A) [B >= 1 + A && B >= 1 + A] (B,3)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
15. evalfstart(A,B,C) -> evalfbb1in(1,B,1) [B >= 1 && B >= 1] (1,4)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
17. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1 + A) [B >= A && B >= A] (B,3)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,18,19},10->{13,14},11->{11,18,19},13->{6},14->{13,14},15->{6},16->{13,14},17->{11,18,19},18->{13
,14},19->{11,18,19}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, B)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [10,17]
* Step 19: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
13. evalfbb3in(A,B,C) -> evalfbb1in(1 + A,B,1 + A) [B >= 1 + A && B >= 1 + A] (B,3)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
15. evalfstart(A,B,C) -> evalfbb1in(1,B,1) [B >= 1 && B >= 1] (1,4)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,18,19},11->{11,18,19},13->{6},14->{13,14},15->{6},16->{13,14},18->{13,14},19->{11,18,19}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
+ Applied Processor:
ChainProcessor False [6,11,13,14,15,16,18,19]
+ Details:
We chained rule 13 to obtain the rules [20] .
* Step 20: ChainProcessor WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
15. evalfstart(A,B,C) -> evalfbb1in(1,B,1) [B >= 1 && B >= 1] (1,4)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
20. evalfbb3in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [B >= 1 + A && B >= 1 + A] (B,4)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,18,19},11->{11,18,19},14->{14,20},15->{6},16->{14,20},18->{14,20},19->{11,18,19},20->{11,18,19}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, B)
+ Applied Processor:
ChainProcessor False [6,11,14,15,16,18,19,20]
+ Details:
We chained rule 15 to obtain the rules [21] .
* Step 21: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1)
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
20. evalfbb3in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [B >= 1 + A && B >= 1 + A] (B,4)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[6->{11,18,19},11->{11,18,19},14->{14,20},16->{14,20},18->{14,20},19->{11,18,19},20->{11,18,19},21->{11,18
,19}]
Sizebounds:
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, B)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, B)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, B)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [6]
* Step 22: UnsatPaths WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
20. evalfbb3in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [B >= 1 + A && B >= 1 + A] (B,4)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,18,19},14->{14,20},16->{14,20},18->{14,20},19->{11,18,19},20->{11,18,19},21->{11,18,19}]
Sizebounds:
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, B)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, B)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(11,18)
,(14,14)
,(14,20)
,(16,14)
,(16,20)
,(18,14)
,(18,20)
,(19,18)
,(19,19)
,(20,18)
,(20,19)
,(21,18)
,(21,19)]
* Step 23: UnreachableRules WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
14. evalfbb3in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [B >= 1 + A && 1 + A >= 1 + B] (B,3)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
18. evalfbb2in(A,B,C) -> evalfbb3in(1 + A,B,1 + A) [C >= 1 + B && B >= 1 + A && 1 + A >= 1 + B] (B,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
20. evalfbb3in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [B >= 1 + A && B >= 1 + A] (B,4)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},14->{},16->{},18->{},19->{11},20->{11},21->{11}]
Sizebounds:
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, B)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, B)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [14,18,20]
* Step 24: LocalSizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},16->{},19->{11},21->{11}]
Sizebounds:
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, B)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, B)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, B)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, 1 + C, .+ 1)
(<16,0,A>, 1, .= 1) (<16,0,B>, B, .= 0) (<16,0,C>, 1, .= 1)
(<19,0,A>, 1 + A, .+ 1) (<19,0,B>, B, .= 0) (<19,0,C>, 2 + A, .+ 2)
(<21,0,A>, 1, .= 1) (<21,0,B>, B, .= 0) (<21,0,C>, 2, .= 2)
* Step 25: SizeboundsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},16->{},19->{11},21->{11}]
Sizebounds:
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?)
(<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?)
(<19,0,A>, ?) (<19,0,B>, ?) (<19,0,C>, ?)
(<21,0,A>, ?) (<21,0,B>, ?) (<21,0,C>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<11,0,A>, 1 + B) (<11,0,B>, B) (<11,0,C>, 1 + B)
(<16,0,A>, 1) (<16,0,B>, B) (<16,0,C>, 1)
(<19,0,A>, 1 + B) (<19,0,B>, B) (<19,0,C>, 3 + B)
(<21,0,A>, 1) (<21,0,B>, B) (<21,0,C>, 2)
* Step 26: LocationConstraintsProc WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},16->{},19->{11},21->{11}]
Sizebounds:
(<11,0,A>, 1 + B) (<11,0,B>, B) (<11,0,C>, 1 + B)
(<16,0,A>, 1) (<16,0,B>, B) (<16,0,C>, 1)
(<19,0,A>, 1 + B) (<19,0,B>, B) (<19,0,C>, 3 + B)
(<21,0,A>, 1) (<21,0,B>, B) (<21,0,C>, 2)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 11 : [B >= 1 && B >= 1] 16 : True 19 : [B >= 1
&& False] 21 : True .
* Step 27: PolyRank WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (?,2)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},16->{},19->{11},21->{11}]
Sizebounds:
(<11,0,A>, 1 + B) (<11,0,B>, B) (<11,0,C>, 1 + B)
(<16,0,A>, 1) (<16,0,B>, B) (<16,0,C>, 1)
(<19,0,A>, 1 + B) (<19,0,B>, B) (<19,0,C>, 3 + B)
(<21,0,A>, 1) (<21,0,B>, B) (<21,0,C>, 2)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb2in) = 1 + x2 + -1*x3
The following rules are strictly oriented:
[B >= C] ==>
evalfbb2in(A,B,C) = 1 + B + -1*C
> B + -1*C
= evalfbb2in(A,B,1 + C)
The following rules are weakly oriented:
We use the following global sizebounds:
(<11,0,A>, 1 + B) (<11,0,B>, B) (<11,0,C>, 1 + B)
(<16,0,A>, 1) (<16,0,B>, B) (<16,0,C>, 1)
(<19,0,A>, 1 + B) (<19,0,B>, B) (<19,0,C>, 3 + B)
(<21,0,A>, 1) (<21,0,B>, B) (<21,0,C>, 2)
* Step 28: KnowledgePropagation WORST_CASE(?,O(n^2))
+ Considered Problem:
Rules:
11. evalfbb2in(A,B,C) -> evalfbb2in(A,B,1 + C) [B >= C] (3 + 5*B + 2*B^2,2)
16. evalfstart(A,B,C) -> evalfbb3in(1,B,1) [B >= 1 && 1 >= 1 + B] (1,4)
19. evalfbb2in(A,B,C) -> evalfbb2in(1 + A,B,2 + A) [C >= 1 + B && B >= 1 + A && B >= 1 + A] (B,5)
21. evalfstart(A,B,C) -> evalfbb2in(1,B,2) [B >= 1 && B >= 1] (1,5)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbb4in,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[11->{11,19},16->{},19->{11},21->{11}]
Sizebounds:
(<11,0,A>, 1 + B) (<11,0,B>, B) (<11,0,C>, 1 + B)
(<16,0,A>, 1) (<16,0,B>, B) (<16,0,C>, 1)
(<19,0,A>, 1 + B) (<19,0,B>, B) (<19,0,C>, 3 + B)
(<21,0,A>, 1) (<21,0,B>, B) (<21,0,C>, 2)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^2))