WORST_CASE(?,O(n^6))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [A >= 1 + B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
13. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{2,3},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 0,0,A>, A, .= 0) (< 0,0,B>, B, .= 0) (< 0,0,C>, C, .= 0) (< 0,0,D>, D, .= 0) (< 0,0,E>, E, .= 0)
(< 1,0,A>, 1, .= 1) (< 1,0,B>, B, .= 0) (< 1,0,C>, C, .= 0) (< 1,0,D>, D, .= 0) (< 1,0,E>, E, .= 0)
(< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, 1, .= 1) (< 2,0,D>, D, .= 0) (< 2,0,E>, E, .= 0)
(< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,D>, D, .= 0) (< 3,0,E>, E, .= 0)
(< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,D>, 1 + A, .+ 1) (< 4,0,E>, E, .= 0)
(< 5,0,A>, 1 + A, .+ 1) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,D>, D, .= 0) (< 5,0,E>, E, .= 0)
(< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0) (< 6,0,D>, D, .= 0) (< 6,0,E>, 1, .= 1)
(< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0) (< 7,0,D>, D, .= 0) (< 7,0,E>, E, .= 0)
(< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, C, .= 0) (< 8,0,D>, D, .= 0) (< 8,0,E>, E, .= 0)
(< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, C, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,E>, E, .= 0)
(<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,D>, D, .= 0) (<10,0,E>, 1 + E, .+ 1)
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0) (<11,0,D>, 1 + D, .+ 1) (<11,0,E>, E, .= 0)
(<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, 1 + C, .+ 1) (<12,0,D>, D, .= 0) (<12,0,E>, E, .= 0)
(<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,D>, D, .= 0) (<13,0,E>, E, .= 0)
* Step 2: SizeboundsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [A >= 1 + B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
13. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{2,3},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{}]
Sizebounds:
(< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 0,0,D>, ?) (< 0,0,E>, ?)
(< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (< 1,0,D>, ?) (< 1,0,E>, ?)
(< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?)
(< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 3,0,A>, ?) (< 3,0,B>, B) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 3: LeafRules WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [A >= 1 + B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
13. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{2,3},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 3,0,A>, ?) (< 3,0,B>, B) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [3,13]
* Step 4: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 2 + -1*x1 + x2
p(evalfbb3in) = 1 + -1*x1 + x2
p(evalfbb4in) = 1 + -1*x1 + x2
p(evalfbb5in) = 1 + -1*x1 + x2
p(evalfbb6in) = 1 + -1*x1 + x2
p(evalfbb7in) = 1 + -1*x1 + x2
p(evalfbb8in) = 1 + -1*x1 + x2
p(evalfentryin) = 1 + x2
p(evalfstart) = 1 + x2
The following rules are strictly oriented:
[B >= A] ==>
evalfbb10in(A,B,C,D,E) = 2 + -1*A + B
> 1 + -1*A + B
= evalfbb8in(A,B,1,D,E)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfentryin(A,B,C,D,E)
True ==>
evalfentryin(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb10in(1,B,C,D,E)
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb6in(A,B,C,1 + A,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb10in(1 + A,B,C,D,E)
[B >= D] ==>
evalfbb6in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = 1 + -1*A + B
>= 1 + -1*A + B
= evalfbb8in(A,B,1 + C,D,E)
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 6: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,12,7,4,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 0
p(evalfbb3in) = 1
p(evalfbb4in) = 1
p(evalfbb5in) = 1
p(evalfbb6in) = 1
p(evalfbb7in) = 1
p(evalfbb8in) = 1
The following rules are strictly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1
> 0
= evalfbb10in(1 + A,B,C,D,E)
The following rules are weakly oriented:
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,1 + A,E)
[B >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = 1
>= 1
= evalfbb8in(A,B,1 + C,D,E)
We use the following global sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
* Step 7: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,12,7,4,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + x1 + -1*x3
p(evalfbb3in) = 1 + x1 + -1*x3
p(evalfbb4in) = 1 + x1 + -1*x3
p(evalfbb5in) = 1 + x1 + -1*x3
p(evalfbb6in) = 1 + x1 + -1*x3
p(evalfbb7in) = 1 + x1 + -1*x3
p(evalfbb8in) = 2 + x1 + -1*x3
The following rules are strictly oriented:
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 2 + A + -1*C
> 1 + A + -1*C
= evalfbb6in(A,B,C,1 + A,E)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 2 + A + -1*C
>= 2 + A + -1*C
= evalfbb10in(1 + A,B,C,D,E)
[B >= D] ==>
evalfbb6in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = 1 + A + -1*C
>= 1 + A + -1*C
= evalfbb8in(A,B,1 + C,D,E)
We use the following global sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
* Step 8: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,5,12,7,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 0
p(evalfbb3in) = 1
p(evalfbb4in) = 1
p(evalfbb5in) = 1
p(evalfbb6in) = 1
p(evalfbb7in) = 1
p(evalfbb8in) = 0
The following rules are strictly oriented:
True ==>
evalfbb7in(A,B,C,D,E) = 1
> 0
= evalfbb8in(A,B,1 + C,D,E)
The following rules are weakly oriented:
[B >= A] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1,D,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(1 + A,B,C,D,E)
[B >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,1 + D,E)
We use the following global sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
* Step 9: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (?,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,5,12,7,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 0
p(evalfbb3in) = 1
p(evalfbb4in) = 1
p(evalfbb5in) = 1
p(evalfbb6in) = 1
p(evalfbb7in) = 0
p(evalfbb8in) = 0
The following rules are strictly oriented:
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 1
> 0
= evalfbb7in(A,B,C,D,E)
The following rules are weakly oriented:
[B >= A] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1,D,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(1 + A,B,C,D,E)
[B >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1 + C,D,E)
We use the following global sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
* Step 10: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1)
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
+ Applied Processor:
ChainProcessor False [0,1,2,4,5,6,7,8,9,10,11,12]
+ Details:
We chained rule 0 to obtain the rules [13] .
* Step 11: UnreachableRules WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[1->{2},2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{2}]
Sizebounds:
(< 1,0,A>, 1) (< 1,0,B>, B) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [1]
* Step 12: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= A] (1 + B,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[2->{4,5},4->{6,7},5->{2},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{2}]
Sizebounds:
(< 2,0,A>, B) (< 2,0,B>, B) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
+ Applied Processor:
ChainProcessor False [2,4,5,6,7,8,9,10,11,12,13]
+ Details:
We chained rule 2 to obtain the rules [14,15] .
* Step 13: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [A >= C] (3 + 4*B + B^2,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[4->{6,7},5->{14,15},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{14,15},14->{6,7}
,15->{14,15}]
Sizebounds:
(< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
+ Applied Processor:
ChainProcessor False [4,5,6,7,8,9,10,11,12,13,14,15]
+ Details:
We chained rule 4 to obtain the rules [16,17] .
* Step 14: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{5,16,17},13->{14,15},14->{6,7}
,15->{14,15},16->{8,9},17->{12}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, B) (< 6,0,E>, 1)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,6,7,8,9,10,11,12,13,14,15,16,17]
+ Details:
We chained rule 6 to obtain the rules [18,19] .
* Step 15: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B] (3 + 4*B + B^2,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},7->{12},8->{10},9->{11},10->{8,9},11->{7,18,19},12->{5,16,17},13->{14,15},14->{7,18,19}
,15->{14,15},16->{8,9},17->{12},18->{10},19->{11}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,7,8,9,10,11,12,13,14,15,16,17,18,19]
+ Details:
We chained rule 7 to obtain the rules [20] .
* Step 16: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [D >= E] (?,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},8->{10},9->{11},10->{8,9},11->{18,19,20},12->{5,16,17},13->{14,15},14->{18,19,20},15->{14,15}
,16->{8,9},17->{12},18->{10},19->{11},20->{5,16,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,8,9,10,11,12,13,14,15,16,17,18,19,20]
+ Details:
We chained rule 8 to obtain the rules [21] .
* Step 17: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (?,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},9->{11},10->{9,21},11->{18,19,20},12->{5,16,17},13->{14,15},14->{18,19,20},15->{14,15},16->{9
,21},17->{12},18->{10},19->{11},20->{5,16,17},21->{9,21}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,9,10,11,12,13,14,15,16,17,18,19,20,21]
+ Details:
We chained rule 9 to obtain the rules [22] .
* Step 18: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},10->{21,22},11->{18,19,20},12->{5,16,17},13->{14,15},14->{18,19,20},15->{14,15},16->{21,22}
,17->{12},18->{10},19->{11},20->{5,16,17},21->{21,22},22->{18,19,20}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,10,11,12,13,14,15,16,17,18,19,20,21,22]
+ Details:
We chained rule 11 to obtain the rules [23,24,25] .
* Step 19: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (3 + 4*B + B^2,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},10->{21,22},12->{5,16,17},13->{14,15},14->{18,19,20},15->{14,15},16->{21,22},17->{12},18->{10}
,19->{23,24,25},20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25]
+ Details:
We chained rule 12 to obtain the rules [26,27,28] .
* Step 20: ChainProcessor WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
14. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,1 + A,E) [B >= A && A >= 1] (1 + B,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
27. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,1 + A,1) [A >= 1 + C && B >= 1 + A] (3 + 4*B + B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{14,15},10->{21,22},13->{14,15},14->{18,19,20},15->{14,15},16->{21,22},17->{26,27,28},18->{10},19->{23
,24,25},20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{14,15},27->{21
,22},28->{26,27,28}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, 1)
(<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,10,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]
+ Details:
We chained rule 14 to obtain the rules [29,30,31] .
* Step 21: UnsatPaths WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
27. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,1 + A,1) [A >= 1 + C && B >= 1 + A] (3 + 4*B + B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
30. evalfbb10in(A,B,C,D,E) -> evalfbb5in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 >= 2 + A] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,30,31},10->{21,22},13->{15,29,30,31},15->{15,29,30,31},16->{21,22},17->{26,27,28},18->{10}
,19->{23,24,25},20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,30
,31},27->{21,22},28->{26,27,28},29->{10},30->{23,24,25},31->{5,16,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, 1)
(<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?)
(<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?)
(<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(5,30)
,(13,15)
,(13,30)
,(15,30)
,(17,27)
,(26,30)
,(28,27)
,(30,23)
,(30,24)
,(30,25)
,(31,16)]
* Step 22: UnreachableRules WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
27. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,1 + A,1) [A >= 1 + C && B >= 1 + A] (3 + 4*B + B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
30. evalfbb10in(A,B,C,D,E) -> evalfbb5in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 >= 2 + A] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},27->{21,22}
,28->{26,28},29->{10},30->{},31->{5,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, 1)
(<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?)
(<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?)
(<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [27,30]
* Step 23: LocalSizeboundsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, B) (<16,0,E>, 1)
(<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?)
(<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 5,0,A>, 1 + A, .+ 1) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,D>, D, .= 0) (< 5,0,E>, E, .= 0)
(<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,D>, D, .= 0) (<10,0,E>, 1 + E, .+ 1)
(<13,0,A>, 1, .= 1) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,D>, D, .= 0) (<13,0,E>, E, .= 0)
(<15,0,A>, 1 + A + B, .* 1) (<15,0,B>, B, .= 0) (<15,0,C>, 1, .= 1) (<15,0,D>, D, .= 0) (<15,0,E>, E, .= 0)
(<16,0,A>, A, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, C, .= 0) (<16,0,D>, 1 + A, .+ 1) (<16,0,E>, 1, .= 1)
(<17,0,A>, A, .= 0) (<17,0,B>, B, .= 0) (<17,0,C>, C, .= 0) (<17,0,D>, 1 + A + B, .* 1) (<17,0,E>, E, .= 0)
(<18,0,A>, A, .= 0) (<18,0,B>, B, .= 0) (<18,0,C>, C, .= 0) (<18,0,D>, D, .= 0) (<18,0,E>, 1, .= 1)
(<19,0,A>, A, .= 0) (<19,0,B>, B, .= 0) (<19,0,C>, C, .= 0) (<19,0,D>, D, .= 0) (<19,0,E>, 1, .= 1)
(<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,C>, 1 + C, .+ 1) (<20,0,D>, D, .= 0) (<20,0,E>, E, .= 0)
(<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,C>, C, .= 0) (<21,0,D>, D, .= 0) (<21,0,E>, 1 + E, .+ 1)
(<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, C, .= 0) (<22,0,D>, 1 + D, .+ 1) (<22,0,E>, E, .= 0)
(<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,D>, 1 + B + D, .* 1) (<23,0,E>, 1, .= 1)
(<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,C>, C, .= 0) (<24,0,D>, 1 + B + D, .* 1) (<24,0,E>, 1, .= 1)
(<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,C>, 1 + C, .+ 1) (<25,0,D>, 1 + D, .+ 1) (<25,0,E>, E, .= 0)
(<26,0,A>, 1 + A, .+ 1) (<26,0,B>, B, .= 0) (<26,0,C>, 1 + C, .+ 1) (<26,0,D>, D, .= 0) (<26,0,E>, E, .= 0)
(<28,0,A>, A, .= 0) (<28,0,B>, B, .= 0) (<28,0,C>, 1 + C, .+ 1) (<28,0,D>, 1 + A + B, .* 1) (<28,0,E>, E, .= 0)
(<29,0,A>, A, .= 0) (<29,0,B>, B, .= 0) (<29,0,C>, 1, .= 1) (<29,0,D>, 1 + A, .+ 1) (<29,0,E>, 1, .= 1)
(<31,0,A>, A, .= 0) (<31,0,B>, B, .= 0) (<31,0,C>, 2, .= 2) (<31,0,D>, 1 + A, .+ 1) (<31,0,E>, E, .= 0)
* Step 24: SizeboundsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<15,0,A>, ?) (<15,0,B>, ?) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, ?) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?)
(<18,0,A>, ?) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, ?) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, ?) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, ?) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, ?) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, ?) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, ?) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, ?) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, ?) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<28,0,A>, ?) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?)
(<29,0,A>, ?) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<31,0,A>, ?) (<31,0,B>, ?) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, ?)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, ?)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, ?)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, ?)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, ?)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, ?)
* Step 25: LocationConstraintsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, ?)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, ?)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, ?)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, ?)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, ?)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, ?)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 5 : True 10 : True 13 : True 15 : True 16 : True 17 : True 18 : [False] 19 : [False] 20 : [False] 21 : True 22 : True 23 : [B >= D] 24 : [B >= D] 25 : [B >= D] 26 : [A >= C] 28 : [A >= C] 29 : True 31 : True .
* Step 26: SizeboundsProc WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, ?)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, ?)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, ?)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, ?)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, ?)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 27: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (?,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [20,22,10,18,23,19,24,29,15,26,17,25,31,28,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + -1*x1 + x2
p(evalfbb3in) = 2
p(evalfbb4in) = 2
p(evalfbb5in) = 2
p(evalfbb6in) = 2
p(evalfbb7in) = -1*x1 + x2
p(evalfbb8in) = 1
The following rules are strictly oriented:
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = 1
> -1*A + B
= evalfbb7in(A,B,C,1 + A,E)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 2
> 1
= evalfbb8in(A,B,1 + C,D,E)
[1 + D >= 1 + B] ==>
evalfbb5in(A,B,C,D,E) = 2
> 1
= evalfbb8in(A,B,1 + C,1 + D,E)
The following rules are weakly oriented:
True ==>
evalfbb3in(A,B,C,D,E) = 2
>= 2
= evalfbb4in(A,B,C,D,1 + E)
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
>= -1*A + B
= evalfbb10in(1 + A,B,1,D,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 2
>= 2
= evalfbb3in(A,B,C,D,1)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 2
>= 2
= evalfbb5in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 2
>= 2
= evalfbb4in(A,B,C,D,1 + E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 2
>= 2
= evalfbb6in(A,B,C,1 + D,E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 2
>= 2
= evalfbb3in(A,B,C,1 + D,1)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 2
>= 2
= evalfbb5in(A,B,C,1 + D,1)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
>= 2
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
>= 1
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 28: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (?,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,22,10,18,23,19,24,29,15,26,17,31,28,16,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + -1*x1
p(evalfbb3in) = -1*x4
p(evalfbb4in) = -1*x4
p(evalfbb5in) = -1*x4
p(evalfbb6in) = -1*x4
p(evalfbb7in) = -1*x1
p(evalfbb8in) = -1*x1
The following rules are strictly oriented:
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
> -1*A
= evalfbb10in(1 + A,B,1,D,E)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = -1*D
> -1 + -1*D
= evalfbb5in(A,B,C,1 + D,1)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = -1*D
>= -1*D
= evalfbb4in(A,B,C,D,1 + E)
[A >= C && B >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1 + -1*A
= evalfbb4in(A,B,C,1 + A,1)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,C,1 + A,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = -1*D
>= -1*D
= evalfbb3in(A,B,C,D,1)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = -1*D
>= -1*D
= evalfbb5in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = -1*D
>= -1*D
= evalfbb4in(A,B,C,D,1 + E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = -1*D
>= -1 + -1*D
= evalfbb6in(A,B,C,1 + D,E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = -1*D
>= -1 + -1*D
= evalfbb3in(A,B,C,1 + D,1)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= -1 + -1*A
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= -1*A
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 29: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (?,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,22,10,18,23,19,24,29,15,26,17,31,28,16,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + -1*x1
p(evalfbb3in) = 2 + -1*x4
p(evalfbb4in) = 1 + -1*x4
p(evalfbb5in) = 2
p(evalfbb6in) = 2 + -1*x4
p(evalfbb7in) = -1*x1
p(evalfbb8in) = -1*x1
The following rules are strictly oriented:
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
> -1*A
= evalfbb10in(1 + A,B,1,D,E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 2
> 1 + -1*D
= evalfbb3in(A,B,C,1 + D,1)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 2 + -1*D
>= 1 + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[A >= C && B >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb4in(A,B,C,1 + A,1)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,C,1 + A,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 2 + -1*D
>= 2 + -1*D
= evalfbb3in(A,B,C,D,1)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 2 + -1*D
>= 2
= evalfbb5in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*D
>= 1 + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*D
>= 1 + -1*D
= evalfbb6in(A,B,C,1 + D,E)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 2
>= 2
= evalfbb5in(A,B,C,1 + D,1)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= 1 + -1*A
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= -1*A
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 30: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (?,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,22,10,18,23,19,24,29,15,26,17,31,28,16,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + -1*x1
p(evalfbb3in) = 2 + -1*x4
p(evalfbb4in) = 1 + -1*x4
p(evalfbb5in) = 1
p(evalfbb6in) = 2 + -1*x4
p(evalfbb7in) = -1*x1
p(evalfbb8in) = -1*x1
The following rules are strictly oriented:
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
> -1*A
= evalfbb10in(1 + A,B,1,D,E)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 2 + -1*D
> 1
= evalfbb5in(A,B,C,D,1)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 2 + -1*D
>= 1 + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[A >= C && B >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb4in(A,B,C,1 + A,1)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,C,1 + A,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 2 + -1*D
>= 2 + -1*D
= evalfbb3in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*D
>= 1 + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + -1*D
>= 1 + -1*D
= evalfbb6in(A,B,C,1 + D,E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1 + -1*D
= evalfbb3in(A,B,C,1 + D,1)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,1 + D,1)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = -1*A
>= -1*A
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= 1 + -1*A
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A
>= -1*A
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 31: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (?,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,22,10,18,23,19,24,29,15,26,17,31,28,16,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + -1*x1 + x2
p(evalfbb3in) = 1 + x2 + -1*x4
p(evalfbb4in) = 1 + x2 + -1*x4
p(evalfbb5in) = 1 + x2 + -1*x4
p(evalfbb6in) = 2 + x2 + -1*x4
p(evalfbb7in) = -1*x1 + x2
p(evalfbb8in) = -1*x1 + x2
The following rules are strictly oriented:
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
> -1*A + B
= evalfbb10in(1 + A,B,1,D,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 2 + B + -1*D
> 1 + B + -1*D
= evalfbb3in(A,B,C,D,1)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 2 + B + -1*D
> 1 + B + -1*D
= evalfbb5in(A,B,C,D,1)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 1 + B + -1*D
> B + -1*D
= evalfbb3in(A,B,C,1 + D,1)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 1 + B + -1*D
> B + -1*D
= evalfbb5in(A,B,C,1 + D,1)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
> -1*A + B
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 1 + -1*A + B
> -1*A + B
= evalfbb8in(A,B,2,1 + A,E)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb10in(1 + A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1 + B + -1*D
>= 1 + B + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[A >= C && B >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb4in(A,B,C,1 + A,1)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb7in(A,B,C,1 + A,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + B + -1*D
>= 1 + B + -1*D
= evalfbb4in(A,B,C,D,1 + E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + B + -1*D
>= 1 + B + -1*D
= evalfbb6in(A,B,C,1 + D,E)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = -1*A + B
>= -1*A + B
= evalfbb7in(A,B,1 + C,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 32: KnowledgePropagation WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (110 + 337*B + 381*B^2 + 196*B^3 + 46*B^4 + 4*B^5,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 33: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (221 + 656*B + 733*B^2 + 378*B^3 + 90*B^4 + 8*B^5,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (110 + 337*B + 381*B^2 + 196*B^3 + 46*B^4 + 4*B^5,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (?,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,20,22,18,23,19,24,29,15,26,17,25,31,28,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 0
p(evalfbb3in) = 0
p(evalfbb4in) = 1
p(evalfbb5in) = 0
p(evalfbb6in) = 0
p(evalfbb7in) = 0
p(evalfbb8in) = 0
The following rules are strictly oriented:
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1
> 0
= evalfbb6in(A,B,C,1 + D,E)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(1 + A,B,C,D,E)
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(1 + A,B,1,D,E)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb7in(A,B,C,1 + A,E)
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 0
>= 0
= evalfbb3in(A,B,C,D,1)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 0
>= 0
= evalfbb5in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1 + C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1 + E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 0
>= 0
= evalfbb3in(A,B,C,1 + D,1)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 0
>= 0
= evalfbb5in(A,B,C,1 + D,1)
[1 + D >= 1 + B] ==>
evalfbb5in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1 + C,1 + D,E)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = 0
>= 0
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 34: PolyRank WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (221 + 656*B + 733*B^2 + 378*B^3 + 90*B^4 + 8*B^5,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (110 + 337*B + 381*B^2 + 196*B^3 + 46*B^4 + 4*B^5,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (224 + 660*B + 734*B^2 + 378*B^3 + 90*B^4 + 8*B^5,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,20,10,18,23,19,24,29,15,26,17,25,31,28,16,21], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = x2
p(evalfbb3in) = x4 + -1*x5
p(evalfbb4in) = 1 + x4 + -1*x5
p(evalfbb5in) = x2
p(evalfbb6in) = x2
p(evalfbb7in) = x2
p(evalfbb8in) = x2
The following rules are strictly oriented:
[B >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = B
> -1 + D
= evalfbb3in(A,B,C,D,1)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + D + -1*E
> D + -1*E
= evalfbb4in(A,B,C,D,1 + E)
The following rules are weakly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = B
>= B
= evalfbb10in(1 + A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = D + -1*E
>= D + -1*E
= evalfbb4in(A,B,C,D,1 + E)
[B >= A && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = B
>= B
= evalfbb10in(1 + A,B,1,D,E)
[A >= C && B >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = B
>= 1 + A
= evalfbb4in(A,B,C,1 + A,1)
[A >= C && 1 + A >= 1 + B] ==>
evalfbb8in(A,B,C,D,E) = B
>= B
= evalfbb7in(A,B,C,1 + A,E)
[B >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = B
>= B
= evalfbb5in(A,B,C,D,1)
[D >= 1 + B] ==>
evalfbb6in(A,B,C,D,E) = B
>= B
= evalfbb8in(A,B,1 + C,D,E)
[B >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = B
>= D
= evalfbb3in(A,B,C,1 + D,1)
[B >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = B
>= B
= evalfbb5in(A,B,C,1 + D,1)
[1 + D >= 1 + B] ==>
evalfbb5in(A,B,C,D,E) = B
>= B
= evalfbb8in(A,B,1 + C,1 + D,E)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = B
>= B
= evalfbb10in(1 + A,B,1 + C,D,E)
[A >= 1 + C && 1 + A >= 1 + B] ==>
evalfbb7in(A,B,C,D,E) = B
>= B
= evalfbb7in(A,B,1 + C,1 + A,E)
[B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] ==>
evalfbb10in(A,B,C,D,E) = B
>= A
= evalfbb3in(A,B,1,1 + A,1)
[B >= A && A >= 1 && 1 + A >= 1 + B] ==>
evalfbb10in(A,B,C,D,E) = B
>= B
= evalfbb8in(A,B,2,1 + A,E)
We use the following global sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
* Step 35: KnowledgePropagation WORST_CASE(?,O(n^6))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [C >= 1 + A] (1 + B,1)
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (221 + 656*B + 733*B^2 + 378*B^3 + 90*B^4 + 8*B^5,1)
13. evalfstart(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1,D,E) [B >= A && 1 >= 1 + A] (1 + B,2)
16. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,1 + A,1) [A >= C && B >= 1 + A] (3 + 4*B + B^2,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,1 + A,E) [A >= C && 1 + A >= 1 + B] (3 + 4*B + B^2,2)
18. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B >= D && D >= 1] (110 + 337*B + 381*B^2 + 196*B^3 + 46*B^4 + 4*B^5,2)
19. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B >= D && 1 >= 1 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B] (3 + 4*B + B^2,2)
21. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (225*B + 660*B^2 + 734*B^3 + 378*B^4 + 90*B^5 + 8*B^6,2)
22. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (224 + 660*B + 734*B^2 + 378*B^3 + 90*B^4 + 8*B^5,2)
23. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B >= 1 + D && 1 + D >= 1] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
24. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B >= 1 + D && 1 >= 2 + D] (110 + 318*B + 352*B^2 + 182*B^3 + 44*B^4 + 4*B^5,3)
25. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B] (15 + 25*B + 13*B^2 + 2*B^3,3)
26. evalfbb7in(A,B,C,D,E) -> evalfbb10in(1 + A,B,1 + C,D,E) [1 + C >= 1 + A] (3 + 4*B + B^2,2)
28. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,1 + A,E) [A >= 1 + C && 1 + A >= 1 + B] (3 + 4*B + B^2,3)
29. evalfbb10in(A,B,C,D,E) -> evalfbb3in(A,B,1,1 + A,1) [B >= A && A >= 1 && B >= 1 + A && 1 + A >= 1] (1 + B,4)
31. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,2,1 + A,E) [B >= A && A >= 1 && 1 + A >= 1 + B] (1 + B,4)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{15,29,31},10->{21,22},13->{29,31},15->{15,29,31},16->{21,22},17->{26,28},18->{10},19->{23,24,25}
,20->{5,16,17},21->{21,22},22->{18,19,20},23->{10},24->{23,24,25},25->{5,16,17},26->{15,29,31},28->{26,28}
,29->{10},31->{5,17}]
Sizebounds:
(< 5,0,A>, 6 + 8*B + 2*B^2) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, 7 + 8*B + 2*B^2) (< 5,0,E>, 8 + 8*B + 2*B^2 + E)
(<10,0,A>, 6 + 8*B + 2*B^2) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, 7 + 8*B + 2*B^2) (<10,0,E>, 2)
(<13,0,A>, 1) (<13,0,B>, B) (<13,0,C>, C) (<13,0,D>, D) (<13,0,E>, E)
(<15,0,A>, 6 + 8*B + 2*B^2) (<15,0,B>, B) (<15,0,C>, 1) (<15,0,D>, 7 + 9*B + 2*B^2) (<15,0,E>, 8 + 8*B + 2*B^2 + E)
(<16,0,A>, 6 + 8*B + 2*B^2) (<16,0,B>, B) (<16,0,C>, 6 + 8*B + 2*B^2) (<16,0,D>, 7 + 8*B + 2*B^2) (<16,0,E>, 1)
(<17,0,A>, 6 + 8*B + 2*B^2) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, 7 + 9*B + 2*B^2) (<17,0,E>, 8 + 8*B + 2*B^2 + E)
(<18,0,A>, 6 + 8*B + 2*B^2) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, B) (<18,0,E>, 1)
(<19,0,A>, 6 + 8*B + 2*B^2) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, B) (<19,0,E>, 1)
(<20,0,A>, 6 + 8*B + 2*B^2) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, 7 + 8*B + 2*B^2) (<20,0,E>, 8 + 8*B + 2*B^2)
(<21,0,A>, 6 + 8*B + 2*B^2) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, 7 + 8*B + 2*B^2) (<21,0,E>, 8 + 8*B + 2*B^2)
(<22,0,A>, 6 + 8*B + 2*B^2) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, 7 + 8*B + 2*B^2) (<22,0,E>, 8 + 8*B + 2*B^2)
(<23,0,A>, 6 + 8*B + 2*B^2) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, 1)
(<24,0,A>, 6 + 8*B + 2*B^2) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, B) (<24,0,E>, 1)
(<25,0,A>, 6 + 8*B + 2*B^2) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, 1 + B) (<25,0,E>, 1)
(<26,0,A>, 6 + 8*B + 2*B^2) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, 7 + 9*B + 2*B^2) (<26,0,E>, 8 + 8*B + 2*B^2 + E)
(<28,0,A>, 6 + 8*B + 2*B^2) (<28,0,B>, B) (<28,0,C>, 6 + 8*B + 2*B^2) (<28,0,D>, 7 + 9*B + 2*B^2) (<28,0,E>, 8 + 8*B + 2*B^2 + E)
(<29,0,A>, 6 + 8*B + 2*B^2) (<29,0,B>, B) (<29,0,C>, 1) (<29,0,D>, 7 + 8*B + 2*B^2) (<29,0,E>, 1)
(<31,0,A>, 6 + 8*B + 2*B^2) (<31,0,B>, B) (<31,0,C>, 2) (<31,0,D>, 7 + 8*B + 2*B^2) (<31,0,E>, 8 + 8*B + 2*B^2 + E)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^6))