WORST_CASE(?,O(n^9))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
14. 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)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{14},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{2,3},14->{}]
+ 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>, B, .= 0) (< 1,0,B>, A, .= 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>, B, .= 0) (< 4,0,E>, E, .= 0)
(< 5,0,A>, A, .= 0) (< 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>, 1 + B, .+ 1) (<13,0,C>, C, .= 0) (<13,0,D>, D, .= 0) (<13,0,E>, E, .= 0)
(<14,0,A>, A, .= 0) (<14,0,B>, B, .= 0) (<14,0,C>, C, .= 0) (<14,0,D>, D, .= 0) (<14,0,E>, E, .= 0)
* Step 2: SizeboundsProc WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
14. 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)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{14},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{2,3},14->{}]
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>, ?)
(<14,0,A>, ?) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 3,0,A>, B) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
* Step 3: LeafRules WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1)
3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= B] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
14. 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)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2,3},2->{4,5},3->{14},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7}
,12->{4,5},13->{2,3},14->{}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 3,0,A>, B) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [3,14]
* Step 4: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (?,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 2 + x2
p(evalfbb3in) = 1 + x2
p(evalfbb4in) = 1 + x2
p(evalfbb5in) = 1 + x2
p(evalfbb6in) = 1 + x2
p(evalfbb7in) = 1 + x2
p(evalfbb8in) = 1 + x2
p(evalfbb9in) = 1 + x2
p(evalfentryin) = 2 + x1
p(evalfstart) = 2 + x1
The following rules are strictly oriented:
[B >= 1] ==>
evalfbb10in(A,B,C,D,E) = 2 + B
> 1 + B
= evalfbb8in(A,B,1,D,E)
The following rules are weakly oriented:
True ==>
evalfstart(A,B,C,D,E) = 2 + A
>= 2 + A
= evalfentryin(A,B,C,D,E)
True ==>
evalfentryin(A,B,C,D,E) = 2 + A
>= 2 + A
= evalfbb10in(B,A,C,D,E)
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb6in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb9in(A,B,C,D,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb8in(A,B,1 + C,D,E)
True ==>
evalfbb9in(A,B,C,D,E) = 1 + B
>= 1 + B
= evalfbb10in(A,-1 + B,C,D,E)
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (?,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 6: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (?,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [13,5,12,7,4,11,9,6,10,8], 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
p(evalfbb9in) = 1
The following rules are strictly oriented:
True ==>
evalfbb9in(A,B,C,D,E) = 1
> 0
= evalfbb10in(A,-1 + B,C,D,E)
The following rules are weakly oriented:
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb9in(A,B,C,D,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 7: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (?,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [13,5,12,7,4,11,9,6,10,8], 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
p(evalfbb9in) = 0
The following rules are strictly oriented:
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1
> 0
= evalfbb9in(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,B,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
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)
True ==>
evalfbb9in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 8: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (?,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,12,7,4,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = x1
p(evalfbb3in) = x1 + -1*x3
p(evalfbb4in) = x1 + -1*x3
p(evalfbb5in) = x1 + -1*x3
p(evalfbb6in) = x1 + -1*x3
p(evalfbb7in) = x1 + -1*x3
p(evalfbb8in) = 1 + x1 + -1*x3
p(evalfbb9in) = x1
The following rules are strictly oriented:
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1 + A + -1*C
> A + -1*C
= evalfbb6in(A,B,C,B,E)
The following rules are weakly oriented:
[B >= 1] ==>
evalfbb10in(A,B,C,D,E) = A
>= A
= evalfbb8in(A,B,1,D,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb7in(A,B,C,D,E) = A + -1*C
>= A + -1*C
= evalfbb8in(A,B,1 + C,D,E)
True ==>
evalfbb9in(A,B,C,D,E) = A
>= A
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 9: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,5,12,7,11,9,6,10,8], 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
p(evalfbb9in) = 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 >= 1] ==>
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
= evalfbb9in(A,B,C,D,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
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 ==>
evalfbb9in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 10: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (?,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 (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,5,12,7,11,9,6,10,8], 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
p(evalfbb9in) = 0
The following rules are strictly oriented:
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = 1
> 0
= evalfbb7in(A,B,C,D,E)
The following rules are weakly oriented:
[B >= 1] ==>
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
= evalfbb9in(A,B,C,D,E)
[B + C >= 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)
True ==>
evalfbb9in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 11: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (?,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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 (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,5,7,4,11,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1 + x1
p(evalfbb3in) = x2 + x3 + -1*x4
p(evalfbb4in) = x2 + x3 + -1*x4
p(evalfbb5in) = x2 + x3 + -1*x4
p(evalfbb6in) = 1 + x2 + x3 + -1*x4
p(evalfbb7in) = 1 + x2 + x3 + -1*x4
p(evalfbb8in) = 1 + x1
p(evalfbb9in) = 1 + x1
The following rules are strictly oriented:
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1 + B + C + -1*D
> B + C + -1*D
= evalfbb4in(A,B,C,D,1)
The following rules are weakly oriented:
[B >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1 + A
>= 1 + A
= evalfbb8in(A,B,1,D,E)
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1 + A
>= 1 + C
= evalfbb6in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1 + A
>= 1 + A
= evalfbb9in(A,B,C,D,E)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = 1 + B + C + -1*D
>= 1 + B + C + -1*D
= evalfbb7in(A,B,C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = B + C + -1*D
>= B + C + -1*D
= evalfbb3in(A,B,C,D,E)
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = B + C + -1*D
>= B + C + -1*D
= evalfbb5in(A,B,C,D,E)
True ==>
evalfbb3in(A,B,C,D,E) = B + C + -1*D
>= B + C + -1*D
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb5in(A,B,C,D,E) = B + C + -1*D
>= B + C + -1*D
= evalfbb6in(A,B,C,1 + D,E)
True ==>
evalfbb9in(A,B,C,D,E) = 1 + A
>= 1 + A
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 12: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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 (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,5,12,7,4,11,9,10,8], 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) = 0
p(evalfbb7in) = 0
p(evalfbb8in) = 0
p(evalfbb9in) = 0
The following rules are strictly oriented:
True ==>
evalfbb5in(A,B,C,D,E) = 1
> 0
= evalfbb6in(A,B,C,1 + D,E)
The following rules are weakly oriented:
[B >= 1] ==>
evalfbb10in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1,D,E)
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb6in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 0
>= 0
= evalfbb9in(A,B,C,D,E)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = 0
>= 0
= 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 ==>
evalfbb7in(A,B,C,D,E) = 0
>= 0
= evalfbb8in(A,B,1 + C,D,E)
True ==>
evalfbb9in(A,B,C,D,E) = 0
>= 0
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 13: PolyRank WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,13,5,12,7,4,9,6,10,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1
p(evalfbb3in) = 1
p(evalfbb4in) = 1
p(evalfbb5in) = 0
p(evalfbb6in) = 1
p(evalfbb7in) = 1
p(evalfbb8in) = 1
p(evalfbb9in) = 1
The following rules are strictly oriented:
[E >= 1 + D] ==>
evalfbb4in(A,B,C,D,E) = 1
> 0
= evalfbb5in(A,B,C,D,E)
The following rules are weakly oriented:
[B >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1
>= 1
= evalfbb8in(A,B,1,D,E)
[A >= C] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb9in(A,B,C,D,E)
[B + C >= D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1)
[D >= 1 + B + C] ==>
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)
True ==>
evalfbb3in(A,B,C,D,E) = 1
>= 1
= evalfbb4in(A,B,C,D,1 + E)
True ==>
evalfbb7in(A,B,C,D,E) = 1
>= 1
= evalfbb8in(A,B,1 + C,D,E)
True ==>
evalfbb9in(A,B,C,D,E) = 1
>= 1
= evalfbb10in(A,-1 + B,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>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
* Step 14: ChainProcessor WORST_CASE(?,O(n^9))
+ 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(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[0->{1},1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5}
,13->{2}]
Sizebounds:
(< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E)
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
+ Applied Processor:
ChainProcessor False [0,1,2,4,5,6,7,8,9,10,11,12,13]
+ Details:
We chained rule 0 to obtain the rules [14] .
* Step 15: UnreachableRules WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
1. evalfentryin(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,1)
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[1->{2},2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{2}
,14->{2}]
Sizebounds:
(< 1,0,A>, B) (< 1,0,B>, A) (< 1,0,C>, C) (< 1,0,D>, D) (< 1,0,E>, E)
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [1]
* Step 16: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [B >= 1] (2 + A,1)
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[2->{4,5},4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{2},14->{2}]
Sizebounds:
(< 2,0,A>, B) (< 2,0,B>, ?) (< 2,0,C>, 1) (< 2,0,D>, ?) (< 2,0,E>, ?)
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
+ Applied Processor:
ChainProcessor False [2,4,5,6,7,8,9,10,11,12,13,14]
+ Details:
We chained rule 2 to obtain the rules [15,16] .
* Step 17: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,B,E) [A >= C] (A*B + 3*B,1)
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[4->{6,7},5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{4,5},13->{15,16},14->{15,16}
,15->{6,7},16->{13}]
Sizebounds:
(< 4,0,A>, B) (< 4,0,B>, ?) (< 4,0,C>, B) (< 4,0,D>, ?) (< 4,0,E>, ?)
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
+ Applied Processor:
ChainProcessor False [4,5,6,7,8,9,10,11,12,13,14,15,16]
+ Details:
We chained rule 4 to obtain the rules [17,18] .
* Step 18: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
5. evalfbb8in(A,B,C,D,E) -> evalfbb9in(A,B,C,D,E) [C >= 1 + A] (2 + A,1)
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[5->{13},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{5,17,18},13->{15,16},14->{15,16},15->{6
,7},16->{13},17->{8,9},18->{12}]
Sizebounds:
(< 5,0,A>, B) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?)
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
+ Applied Processor:
ChainProcessor False [5,6,7,8,9,10,11,12,13,14,15,16,17,18]
+ Details:
We chained rule 5 to obtain the rules [19] .
* Step 19: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [B + C >= D] (1 + A*B + A*B^2 + 4*B + 3*B^2,1)
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7},12->{17,18,19},13->{15,16},14->{15,16},15->{6,7}
,16->{13},17->{8,9},18->{12},19->{15,16}]
Sizebounds:
(< 6,0,A>, B) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, 1)
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
+ Applied Processor:
ChainProcessor False [6,7,8,9,10,11,12,13,14,15,16,17,18,19]
+ Details:
We chained rule 6 to obtain the rules [20,21] .
* Step 20: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [D >= 1 + B + C] (A*B + 3*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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[7->{12},8->{10},9->{11},10->{8,9},11->{7,20,21},12->{17,18,19},13->{15,16},14->{15,16},15->{7,20,21}
,16->{13},17->{8,9},18->{12},19->{15,16},20->{10},21->{11}]
Sizebounds:
(< 7,0,A>, B) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?)
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
+ Applied Processor:
ChainProcessor False [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
+ Details:
We chained rule 7 to obtain the rules [22] .
* Step 21: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
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] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[8->{10},9->{11},10->{8,9},11->{20,21,22},12->{17,18,19},13->{15,16},14->{15,16},15->{20,21,22},16->{13}
,17->{8,9},18->{12},19->{15,16},20->{10},21->{11},22->{17,18,19}]
Sizebounds:
(< 8,0,A>, B) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?)
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
+ Applied Processor:
ChainProcessor False [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]
+ Details:
We chained rule 8 to obtain the rules [23] .
* Step 22: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,1)
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. 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)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[9->{11},10->{9,23},11->{20,21,22},12->{17,18,19},13->{15,16},14->{15,16},15->{20,21,22},16->{13},17->{9
,23},18->{12},19->{15,16},20->{10},21->{11},22->{17,18,19},23->{9,23}]
Sizebounds:
(< 9,0,A>, B) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?)
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, B) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
+ Applied Processor:
ChainProcessor False [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
+ Details:
We chained rule 9 to obtain the rules [24] .
* Step 23: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
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 + A*B + A*B^2 + 4*B + 3*B^2,1)
12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) True (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},11->{20,21,22},12->{17,18,19},13->{15,16},14->{15,16},15->{20,21,22},16->{13},17->{23,24}
,18->{12},19->{15,16},20->{10},21->{11},22->{17,18,19},23->{23,24},24->{20,21,22}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<11,0,A>, B) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, B) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, B) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
+ Applied Processor:
ChainProcessor False [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]
+ Details:
We chained rule 11 to obtain the rules [25,26,27] .
* Step 24: ChainProcessor WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
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 (A*B + 3*B,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},12->{17,18,19},13->{15,16},14->{15,16},15->{20,21,22},16->{13},17->{23,24},18->{12},19->{15
,16},20->{10},21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18
,19}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<12,0,A>, B) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, B) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, B) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, B) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, B) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, B) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,E>, ?)
+ Applied Processor:
ChainProcessor False [10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]
+ Details:
We chained rule 12 to obtain the rules [28,29,30] .
* Step 25: UnsatPaths WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20,21,22},16->{13},17->{23,24},18->{28,29,30},19->{15,16}
,20->{10},21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19}
,28->{23,24},29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, B) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, B) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, B) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, B) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, B) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,E>, ?)
(<28,0,A>, B) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<30,0,A>, B) (<30,0,B>, ?) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(15,21),(15,22)]
* Step 26: LocalSizeboundsProc WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?)
(<13,0,A>, B) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, ?) (<15,0,C>, B) (<15,0,D>, ?) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?)
(<19,0,A>, B) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?)
(<20,0,A>, B) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?)
(<21,0,A>, B) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?)
(<22,0,A>, B) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?)
(<23,0,A>, B) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?)
(<24,0,A>, B) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?)
(<25,0,A>, B) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?)
(<26,0,A>, B) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?)
(<27,0,A>, B) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,E>, ?)
(<28,0,A>, B) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?)
(<30,0,A>, B) (<30,0,B>, ?) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(<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>, A, .= 0) (<13,0,B>, 1 + B, .+ 1) (<13,0,C>, C, .= 0) (<13,0,D>, D, .= 0) (<13,0,E>, E, .= 0)
(<14,0,A>, B, .= 0) (<14,0,B>, A, .= 0) (<14,0,C>, C, .= 0) (<14,0,D>, D, .= 0) (<14,0,E>, E, .= 0)
(<15,0,A>, A, .= 0) (<15,0,B>, B, .= 0) (<15,0,C>, 1, .= 1) (<15,0,D>, B, .= 0) (<15,0,E>, E, .= 0)
(<16,0,A>, A, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, 1, .= 1) (<16,0,D>, D, .= 0) (<16,0,E>, E, .= 0)
(<17,0,A>, A, .= 0) (<17,0,B>, B, .= 0) (<17,0,C>, C, .= 0) (<17,0,D>, B, .= 0) (<17,0,E>, 1, .= 1)
(<18,0,A>, A, .= 0) (<18,0,B>, B, .= 0) (<18,0,C>, C, .= 0) (<18,0,D>, B, .= 0) (<18,0,E>, E, .= 0)
(<19,0,A>, A, .= 0) (<19,0,B>, 1 + B, .+ 1) (<19,0,C>, C, .= 0) (<19,0,D>, D, .= 0) (<19,0,E>, E, .= 0)
(<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,C>, C, .= 0) (<20,0,D>, D, .= 0) (<20,0,E>, 1, .= 1)
(<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,C>, C, .= 0) (<21,0,D>, D, .= 0) (<21,0,E>, 1, .= 1)
(<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, 1 + C, .+ 1) (<22,0,D>, D, .= 0) (<22,0,E>, E, .= 0)
(<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,D>, D, .= 0) (<23,0,E>, 1 + E, .+ 1)
(<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,C>, C, .= 0) (<24,0,D>, 1 + D, .+ 1) (<24,0,E>, E, .= 0)
(<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,C>, C, .= 0) (<25,0,D>, 1 + B + C + D, .* 1) (<25,0,E>, 1, .= 1)
(<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,C>, C, .= 0) (<26,0,D>, 1 + B + C + D, .* 1) (<26,0,E>, 1, .= 1)
(<27,0,A>, A, .= 0) (<27,0,B>, B, .= 0) (<27,0,C>, 1 + C, .+ 1) (<27,0,D>, 1 + D, .+ 1) (<27,0,E>, E, .= 0)
(<28,0,A>, A, .= 0) (<28,0,B>, B, .= 0) (<28,0,C>, 1 + A + C, .* 1) (<28,0,D>, B, .= 0) (<28,0,E>, 1, .= 1)
(<29,0,A>, A, .= 0) (<29,0,B>, B, .= 0) (<29,0,C>, 1 + A + C, .* 1) (<29,0,D>, B, .= 0) (<29,0,E>, E, .= 0)
(<30,0,A>, A, .= 0) (<30,0,B>, 1 + B, .+ 1) (<30,0,C>, 1 + C, .+ 1) (<30,0,D>, D, .= 0) (<30,0,E>, E, .= 0)
* Step 27: SizeboundsProc WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<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>, ?)
(<14,0,A>, ?) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,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>, ?)
(<27,0,A>, ?) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,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>, ?)
(<30,0,A>, ?) (<30,0,B>, ?) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
* Step 28: LocationConstraintsProc WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 10 : [B + C >= D] 13 : [B >= 1] 14 : True 15 : True 16 : True 17 : True 18 : True 19 : True 20 : True 21 : [False] 22 : [False] 23 : True 24 : True 25 : [B + C >= D] 26 : [B + C >= D] 27 : [B + C >= D] 28 : [A >= C] 29 : [A >= C] 30 : [A >= C] .
* Step 29: SizeboundsProc WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, ?)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, ?)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, ?)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
* Step 30: PolyRank WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (?,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [10,20,15,13,16,19,22,17,27,21,26,23,28,18,29,30,25], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = 1
p(evalfbb3in) = 1
p(evalfbb4in) = 0
p(evalfbb5in) = 1
p(evalfbb6in) = 1
p(evalfbb7in) = 1
p(evalfbb8in) = 1
p(evalfbb9in) = 1
The following rules are strictly oriented:
True ==>
evalfbb3in(A,B,C,D,E) = 1
> 0
= evalfbb4in(A,B,C,D,1 + E)
[A >= 1 + C && 1 + B + C >= B] ==>
evalfbb7in(A,B,C,D,E) = 1
> 0
= evalfbb4in(A,B,1 + C,B,1)
The following rules are weakly oriented:
True ==>
evalfbb9in(A,B,C,D,E) = 1
>= 1
= evalfbb10in(A,-1 + B,C,D,E)
[B >= 1 && A >= 1] ==>
evalfbb10in(A,B,C,D,E) = 1
>= 1
= evalfbb6in(A,B,1,B,E)
[B >= 1 && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = 1
>= 1
= evalfbb9in(A,B,1,D,E)
[A >= C && B + C >= B] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 0
= evalfbb4in(A,B,C,B,1)
[A >= C && B >= 1 + B + C] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb7in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = 1
>= 1
= evalfbb10in(A,-1 + B,C,D,E)
[B + C >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb3in(A,B,C,D,1)
[B + C >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,D,1)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = 1
>= 1
= evalfbb8in(A,B,1 + C,D,E)
[D >= E] ==>
evalfbb4in(A,B,C,D,E) = 0
>= 0
= evalfbb4in(A,B,C,D,1 + E)
[B + C >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb3in(A,B,C,1 + D,1)
[B + C >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb5in(A,B,C,1 + D,1)
[1 + D >= 1 + B + C] ==>
evalfbb5in(A,B,C,D,E) = 1
>= 1
= evalfbb8in(A,B,1 + C,1 + D,E)
[A >= 1 + C && B >= 2 + B + C] ==>
evalfbb7in(A,B,C,D,E) = 1
>= 1
= evalfbb7in(A,B,1 + C,B,E)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = 1
>= 1
= evalfbb10in(A,-1 + B,1 + C,D,E)
We use the following global sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
* Step 31: PolyRank WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (3 + A*B + A*B^2 + 4*B + 3*B^2,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (?,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [20,15,13,16,19,22,17,27,21,26,23,28,18,29,30,25], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(evalfbb10in) = x2
p(evalfbb3in) = x2
p(evalfbb4in) = 1 + x4 + -1*x5
p(evalfbb5in) = x2
p(evalfbb6in) = x2
p(evalfbb7in) = x2
p(evalfbb8in) = x2
p(evalfbb9in) = -1 + x2
The following rules are strictly oriented:
[B >= 1 && 1 >= 1 + A] ==>
evalfbb10in(A,B,C,D,E) = B
> -1 + B
= evalfbb9in(A,B,1,D,E)
[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:
True ==>
evalfbb9in(A,B,C,D,E) = -1 + B
>= -1 + B
= evalfbb10in(A,-1 + B,C,D,E)
[B >= 1 && A >= 1] ==>
evalfbb10in(A,B,C,D,E) = B
>= B
= evalfbb6in(A,B,1,B,E)
[A >= C && B + C >= B] ==>
evalfbb8in(A,B,C,D,E) = B
>= B
= evalfbb4in(A,B,C,B,1)
[A >= C && B >= 1 + B + C] ==>
evalfbb8in(A,B,C,D,E) = B
>= B
= evalfbb7in(A,B,C,B,E)
[C >= 1 + A] ==>
evalfbb8in(A,B,C,D,E) = B
>= -1 + B
= evalfbb10in(A,-1 + B,C,D,E)
[B + C >= D && D >= 1] ==>
evalfbb6in(A,B,C,D,E) = B
>= B
= evalfbb3in(A,B,C,D,1)
[B + C >= D && 1 >= 1 + D] ==>
evalfbb6in(A,B,C,D,E) = B
>= B
= evalfbb5in(A,B,C,D,1)
[D >= 1 + B + C] ==>
evalfbb6in(A,B,C,D,E) = B
>= B
= evalfbb8in(A,B,1 + C,D,E)
[B + C >= 1 + D && 1 + D >= 1] ==>
evalfbb5in(A,B,C,D,E) = B
>= B
= evalfbb3in(A,B,C,1 + D,1)
[B + C >= 1 + D && 1 >= 2 + D] ==>
evalfbb5in(A,B,C,D,E) = B
>= B
= evalfbb5in(A,B,C,1 + D,1)
[1 + D >= 1 + B + C] ==>
evalfbb5in(A,B,C,D,E) = B
>= B
= evalfbb8in(A,B,1 + C,1 + D,E)
[A >= 1 + C && 1 + B + C >= B] ==>
evalfbb7in(A,B,C,D,E) = B
>= B
= evalfbb4in(A,B,1 + C,B,1)
[A >= 1 + C && B >= 2 + B + C] ==>
evalfbb7in(A,B,C,D,E) = B
>= B
= evalfbb7in(A,B,1 + C,B,E)
[1 + C >= 1 + A] ==>
evalfbb7in(A,B,C,D,E) = B
>= -1 + B
= evalfbb10in(A,-1 + B,1 + C,D,E)
We use the following global sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
* Step 32: KnowledgePropagation WORST_CASE(?,O(n^9))
+ Considered Problem:
Rules:
10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) True (3 + A*B + A*B^2 + 4*B + 3*B^2,1)
13. evalfbb9in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) True (2 + A,1)
14. evalfstart(A,B,C,D,E) -> evalfbb10in(B,A,C,D,E) True (1,2)
15. evalfbb10in(A,B,C,D,E) -> evalfbb6in(A,B,1,B,E) [B >= 1 && A >= 1] (2 + A,2)
16. evalfbb10in(A,B,C,D,E) -> evalfbb9in(A,B,1,D,E) [B >= 1 && 1 >= 1 + A] (2 + A,2)
17. evalfbb8in(A,B,C,D,E) -> evalfbb4in(A,B,C,B,1) [A >= C && B + C >= B] (A*B + 3*B,2)
18. evalfbb8in(A,B,C,D,E) -> evalfbb7in(A,B,C,B,E) [A >= C && B >= 1 + B + C] (A*B + 3*B,2)
19. evalfbb8in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,C,D,E) [C >= 1 + A] (2 + A,2)
20. evalfbb6in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,1) [B + C >= D && D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
21. evalfbb6in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,1) [B + C >= D && 1 >= 1 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,2)
22. evalfbb6in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [D >= 1 + B + C] (A*B + 3*B,2)
23. evalfbb4in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D >= E] (77 + 34*A + 236*A*B + 738*A*B^2 + 1263*A*B^3 + 1262*A*B^4 + 690*A*B^5 + 162*A*B^6 + 30*A^2*B + 138*A^2*B^2 + 300*A^2*B^3 + 352*A^2*B^4 + 214*A^2*B^5 + 54*A^2*B^6 + 6*A^3*B^2 + 22*A^3*B^3 + 32*A^3*B^4 + 22*A^3*B^5 + 6*A^3*B^6 + 438*B + 1149*B^2 + 1687*B^3 + 1482*B^4 + 738*B^5 + 162*B^6
,2)
24. evalfbb4in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [E >= 1 + D] (2 + A*B + A*B^2 + 4*B + 3*B^2,2)
25. evalfbb5in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 + D >= 1] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
26. evalfbb5in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,1) [B + C >= 1 + D && 1 >= 2 + D] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
27. evalfbb5in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,1 + D,E) [1 + D >= 1 + B + C] (1 + A*B + A*B^2 + 4*B + 3*B^2,3)
28. evalfbb7in(A,B,C,D,E) -> evalfbb4in(A,B,1 + C,B,1) [A >= 1 + C && 1 + B + C >= B] (A*B + 3*B,3)
29. evalfbb7in(A,B,C,D,E) -> evalfbb7in(A,B,1 + C,B,E) [A >= 1 + C && B >= 2 + B + C] (A*B + 3*B,3)
30. evalfbb7in(A,B,C,D,E) -> evalfbb10in(A,-1 + B,1 + C,D,E) [1 + C >= 1 + A] (A*B + 3*B,3)
Signature:
{(evalfbb10in,5)
;(evalfbb3in,5)
;(evalfbb4in,5)
;(evalfbb5in,5)
;(evalfbb6in,5)
;(evalfbb7in,5)
;(evalfbb8in,5)
;(evalfbb9in,5)
;(evalfentryin,5)
;(evalfreturnin,5)
;(evalfstart,5)
;(evalfstop,5)}
Flow Graph:
[10->{23,24},13->{15,16},14->{15,16},15->{20},16->{13},17->{23,24},18->{28,29,30},19->{15,16},20->{10}
,21->{25,26,27},22->{17,18,19},23->{23,24},24->{20,21,22},25->{10},26->{25,26,27},27->{17,18,19},28->{23,24}
,29->{28,29,30},30->{15,16}]
Sizebounds:
(<10,0,A>, B) (<10,0,B>, 4 + 3*A + A*B + 3*B) (<10,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<10,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<10,0,E>, 2)
(<13,0,A>, B) (<13,0,B>, 4 + 3*A + A*B + 3*B) (<13,0,C>, 1) (<13,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<13,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<14,0,A>, B) (<14,0,B>, A) (<14,0,C>, C) (<14,0,D>, D) (<14,0,E>, E)
(<15,0,A>, B) (<15,0,B>, 4 + 3*A + A*B + 3*B) (<15,0,C>, 1) (<15,0,D>, 4 + 3*A + A*B + 3*B) (<15,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<16,0,A>, B) (<16,0,B>, 4 + 3*A + A*B + 3*B) (<16,0,C>, 1) (<16,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + D) (<16,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4 + E)
(<17,0,A>, B) (<17,0,B>, 4 + 3*A + A*B + 3*B) (<17,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<17,0,D>, 4 + 3*A + A*B + 3*B) (<17,0,E>, 1)
(<18,0,A>, B) (<18,0,B>, 4 + 3*A + A*B + 3*B) (<18,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<18,0,D>, 4 + 3*A + A*B + 3*B) (<18,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<19,0,A>, B) (<19,0,B>, 4 + 3*A + A*B + 3*B) (<19,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<19,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<19,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<20,0,A>, B) (<20,0,B>, 4 + 3*A + A*B + 3*B) (<20,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<20,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<20,0,E>, 1)
(<21,0,A>, B) (<21,0,B>, 4 + 3*A + A*B + 3*B) (<21,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<21,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<21,0,E>, 1)
(<22,0,A>, B) (<22,0,B>, 4 + 3*A + A*B + 3*B) (<22,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<22,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<22,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<23,0,A>, B) (<23,0,B>, 4 + 3*A + A*B + 3*B) (<23,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<23,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<23,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<24,0,A>, B) (<24,0,B>, 4 + 3*A + A*B + 3*B) (<24,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<24,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<24,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<25,0,A>, B) (<25,0,B>, 4 + 3*A + A*B + 3*B) (<25,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<25,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<25,0,E>, 1)
(<26,0,A>, B) (<26,0,B>, 4 + 3*A + A*B + 3*B) (<26,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<26,0,D>, 20 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<26,0,E>, 1)
(<27,0,A>, B) (<27,0,B>, 4 + 3*A + A*B + 3*B) (<27,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<27,0,D>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4) (<27,0,E>, 1)
(<28,0,A>, B) (<28,0,B>, 4 + 3*A + A*B + 3*B) (<28,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<28,0,D>, 4 + 3*A + A*B + 3*B) (<28,0,E>, 1)
(<29,0,A>, B) (<29,0,B>, 4 + 3*A + A*B + 3*B) (<29,0,C>, 2 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<29,0,D>, 4 + 3*A + A*B + 3*B) (<29,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
(<30,0,A>, B) (<30,0,B>, 4 + 3*A + A*B + 3*B) (<30,0,C>, 3 + 4*A*B + 3*A*B^2 + 14*B + 9*B^2) (<30,0,D>, 4 + 3*A + A*B + 3*B) (<30,0,E>, 21 + 9*A + 53*A*B + 116*A*B^2 + 106*A*B^3 + 36*A*B^4 + 6*A^2*B + 16*A^2*B^2 + 16*A^2*B^3 + 6*A^2*B^4 + 108*B + 208*B^2 + 174*B^3 + 54*B^4)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^9))