WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,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->{2,3},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>, 0, .= 0) (<1,0,B>, 0, .= 0) (<1,0,C>, C, .= 0)
(<2,0,A>, A, .= 0) (<2,0,B>, B, .= 0) (<2,0,C>, C, .= 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>, 1 + A, .+ 1) (<6,0,B>, B, .= 0) (<6,0,C>, C, .= 0)
(<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^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,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->{2,3},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>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<3,0,A>, ?) (<3,0,B>, 99) (<3,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
(<8,0,A>, ?) (<8,0,B>, 99) (<8,0,C>, C)
* Step 3: UnsatPaths WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,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->{2,3},7->{2,3},8->{}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<3,0,A>, ?) (<3,0,B>, 99) (<3,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
(<8,0,A>, ?) (<8,0,B>, 99) (<8,0,C>, C)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(1,3)]
* Step 4: LeafRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<3,0,A>, ?) (<3,0,B>, 99) (<3,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
(<8,0,A>, ?) (<8,0,B>, 99) (<8,0,C>, 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^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{2},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = -1*x1 + x3
p(evalfbb2in) = 1 + -1*x1 + x3
p(evalfbb3in) = 1 + -1*x1 + x3
p(evalfbbin) = 1 + -1*x1 + x3
p(evalfentryin) = 1 + x3
p(evalfstart) = 1 + x3
The following rules are strictly oriented:
[C >= 1 + A] ==>
evalfbbin(A,B,C) = 1 + -1*A + C
> -1*A + C
= evalfbb1in(A,B,C)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C) = 1 + C
>= 1 + C
= evalfentryin(A,B,C)
True ==>
evalfentryin(A,B,C) = 1 + C
>= 1 + C
= evalfbb3in(0,0,C)
[99 >= B] ==>
evalfbb3in(A,B,C) = 1 + -1*A + C
>= 1 + -1*A + C
= evalfbbin(A,B,C)
[A >= C] ==>
evalfbbin(A,B,C) = 1 + -1*A + C
>= 1 + -1*A + C
= evalfbb2in(A,B,C)
True ==>
evalfbb1in(A,B,C) = -1*A + C
>= -1*A + C
= evalfbb3in(1 + A,B,C)
True ==>
evalfbb2in(A,B,C) = 1 + -1*A + C
>= 1 + -1*A + C
= evalfbb3in(A,1 + B,C)
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (1 + C,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{2},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 7: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (1,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (?,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (1 + C,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (1 + C,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{2},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,4,7,5], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb1in) = 99 + -1*x2
p(evalfbb2in) = 99 + -1*x2
p(evalfbb3in) = 100 + -1*x2
p(evalfbbin) = 99 + -1*x2
The following rules are strictly oriented:
[99 >= B] ==>
evalfbb3in(A,B,C) = 100 + -1*B
> 99 + -1*B
= evalfbbin(A,B,C)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbbin(A,B,C) = 99 + -1*B
>= 99 + -1*B
= evalfbb1in(A,B,C)
[A >= C] ==>
evalfbbin(A,B,C) = 99 + -1*B
>= 99 + -1*B
= evalfbb2in(A,B,C)
True ==>
evalfbb2in(A,B,C) = 99 + -1*B
>= 99 + -1*B
= evalfbb3in(A,1 + B,C)
We use the following global sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
* Step 8: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (1,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (299 + 199*C,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (1 + C,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (1 + C,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{2},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 9: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1)
1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (1,1)
2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [99 >= B] (299 + 199*C,1)
4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (1 + C,1)
5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (299 + 199*C,1)
6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (1 + C,1)
7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (299 + 199*C,1)
Signature:
{(evalfbb1in,3)
;(evalfbb2in,3)
;(evalfbb3in,3)
;(evalfbbin,3)
;(evalfentryin,3)
;(evalfreturnin,3)
;(evalfstart,3)
;(evalfstop,3)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6},5->{7},6->{2},7->{2}]
Sizebounds:
(<0,0,A>, A) (<0,0,B>, B) (<0,0,C>, C)
(<1,0,A>, 0) (<1,0,B>, 0) (<1,0,C>, C)
(<2,0,A>, ?) (<2,0,B>, 99) (<2,0,C>, C)
(<4,0,A>, C) (<4,0,B>, 99) (<4,0,C>, C)
(<5,0,A>, ?) (<5,0,B>, 99) (<5,0,C>, C)
(<6,0,A>, C) (<6,0,B>, 99) (<6,0,C>, C)
(<7,0,A>, ?) (<7,0,B>, 99) (<7,0,C>, C)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^1))