WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f15(50,5,0,D,E,F,G,H,I,J,K,L,M) True (1,1)
1. f15(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f19(A,B,C,0,0,F,G,H,I,J,K,L,M) [B >= C] (?,1)
2. f19(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f19(A,B,C,D + N,1 + E,F,G,H,I,J,K,L,M) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f19(A,B,C,D + N,1 + E,F,G,H,I,J,K,L,M) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f19(A,B,C,D + N,1 + C,F,G,H,I,J,K,L,M) [B >= E && C = E] (?,1)
5. f33(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f36(A,B,C,D,E,F,G,1 + G,I,J,K,L,M) [F >= 1 + G] (?,1)
6. f36(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f41(A,B,C,D,E,F,G,H,N,0,K,L,M) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f41(A,B,C,D,E,F,G,H,N,0,K,L,M) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f41(A,B,C,D,E,F,G,H,N,1 + J,K,L,M) [G >= 1 + J] (?,1)
9. f36(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f36(A,B,C,D,E,F,0,1 + H,N,J,K,L,M) [F >= H && G = 0] (?,1)
10. f50(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f54(A,B,C,D,E,F,G,H,N,0,K,L,M) [F >= H] (?,1)
11. f54(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f54(A,B,C,D,E,F,G,H,N,1 + J,K,L,M) [G >= J] (?,1)
12. f66(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f70(A,B,C,D,E,F,G,0,N,J,K,L,M) [F >= G] (?,1)
13. f70(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f70(A,B,C,D,E,F,G,1 + H,N,J,K,L,M) [G >= 1 + H] (?,1)
14. f80(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f84(A,B,C,D,E,F,G,1 + G,N,J,K,L,M) [G >= 0] (?,1)
15. f84(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f84(A,B,C,D,E,F,G,1 + H,N,J,K,L,M) [F >= H] (?,1)
16. f84(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f80(A,B,C,D,E,F,-1 + G,H,I,J,K,L,M) [H >= 1 + F] (?,1)
17. f80(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f96(A,B,C,D,E,F,G,H,I,J,0,0,M) [0 >= 1 + G] (?,1)
18. f70(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f66(A,B,C,D,E,F,1 + G,H,I,J,K,L,M) [H >= G] (?,1)
19. f66(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f80(A,B,C,D,E,F,-1 + F,H,I,J,K,L,M) [G >= 1 + F] (?,1)
20. f54(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f50(A,B,C,D,E,F,G,1 + H,I,J,K,L,M) [J >= 1 + G] (?,1)
21. f50(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f33(A,B,C,D,E,F,1 + G,H,I,J,K,L,M) [H >= 1 + F] (?,1)
22. f41(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f36(A,B,C,D,E,F,G,1 + H,I,J,K,L,M) [J >= G] (?,1)
23. f36(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f50(A,B,C,D,E,F,G,1 + G,I,J,K,L,M) [H >= 1 + F] (?,1)
24. f33(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f66(A,B,C,D,E,F,1,H,I,J,K,L,M) [G >= F] (?,1)
25. f19(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f15(A,B,1 + C,D,E,F,G,H,I,J,K,L,M) [E >= 1 + B] (?,1)
26. f15(A,B,C,D,E,F,G,H,I,J,K,L,M) -> f33(A,B,C,D,E,B,0,H,I,J,K,L,A) [C >= 1 + B] (?,1)
Signature:
{(f0,13)
;(f15,13)
;(f19,13)
;(f33,13)
;(f36,13)
;(f41,13)
;(f50,13)
;(f54,13)
;(f66,13)
;(f70,13)
;(f80,13)
;(f84,13)
;(f96,13)}
Flow Graph:
[0->{1,26},1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8
,22},9->{6,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14,17}
,17->{},18->{12,19},19->{14,17},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26}
,26->{5,24}]
+ Applied Processor:
RestrictVarsProcessor
+ Details:
We removed the arguments [D,I,K,L,M] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
17. f80(A,B,C,E,F,G,H,J) -> f96(A,B,C,E,F,G,H,J) [0 >= 1 + G] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (?,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1,26},1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8
,22},9->{6,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14,17}
,17->{},18->{12,19},19->{14,17},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26}
,26->{5,24}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 0,0,A>, 50, .= 50) (< 0,0,B>, 5, .= 5) (< 0,0,C>, 0, .= 0) (< 0,0,E>, E, .= 0) (< 0,0,F>, F, .= 0) (< 0,0,G>, G, .= 0) (< 0,0,H>, H, .= 0) (< 0,0,J>, J, .= 0)
(< 1,0,A>, A, .= 0) (< 1,0,B>, B, .= 0) (< 1,0,C>, C, .= 0) (< 1,0,E>, 0, .= 0) (< 1,0,F>, F, .= 0) (< 1,0,G>, G, .= 0) (< 1,0,H>, H, .= 0) (< 1,0,J>, J, .= 0)
(< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, C, .= 0) (< 2,0,E>, 1 + E, .+ 1) (< 2,0,F>, F, .= 0) (< 2,0,G>, G, .= 0) (< 2,0,H>, H, .= 0) (< 2,0,J>, J, .= 0)
(< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,E>, 1 + C + E, .* 1) (< 3,0,F>, F, .= 0) (< 3,0,G>, G, .= 0) (< 3,0,H>, H, .= 0) (< 3,0,J>, J, .= 0)
(< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,E>, 1 + C, .+ 1) (< 4,0,F>, F, .= 0) (< 4,0,G>, G, .= 0) (< 4,0,H>, H, .= 0) (< 4,0,J>, J, .= 0)
(< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,E>, E, .= 0) (< 5,0,F>, F, .= 0) (< 5,0,G>, G, .= 0) (< 5,0,H>, 1 + G, .+ 1) (< 5,0,J>, J, .= 0)
(< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0) (< 6,0,E>, E, .= 0) (< 6,0,F>, F, .= 0) (< 6,0,G>, G, .= 0) (< 6,0,H>, H, .= 0) (< 6,0,J>, 0, .= 0)
(< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0) (< 7,0,E>, E, .= 0) (< 7,0,F>, F, .= 0) (< 7,0,G>, G, .= 0) (< 7,0,H>, H, .= 0) (< 7,0,J>, 0, .= 0)
(< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, C, .= 0) (< 8,0,E>, E, .= 0) (< 8,0,F>, F, .= 0) (< 8,0,G>, G, .= 0) (< 8,0,H>, H, .= 0) (< 8,0,J>, 1 + J, .+ 1)
(< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, C, .= 0) (< 9,0,E>, E, .= 0) (< 9,0,F>, F, .= 0) (< 9,0,G>, 0, .= 0) (< 9,0,H>, 1 + H, .+ 1) (< 9,0,J>, J, .= 0)
(<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,E>, E, .= 0) (<10,0,F>, F, .= 0) (<10,0,G>, G, .= 0) (<10,0,H>, H, .= 0) (<10,0,J>, 0, .= 0)
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0) (<11,0,E>, E, .= 0) (<11,0,F>, F, .= 0) (<11,0,G>, G, .= 0) (<11,0,H>, H, .= 0) (<11,0,J>, 1 + J, .+ 1)
(<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, C, .= 0) (<12,0,E>, E, .= 0) (<12,0,F>, F, .= 0) (<12,0,G>, G, .= 0) (<12,0,H>, 0, .= 0) (<12,0,J>, J, .= 0)
(<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,E>, E, .= 0) (<13,0,F>, F, .= 0) (<13,0,G>, G, .= 0) (<13,0,H>, 1 + H, .+ 1) (<13,0,J>, J, .= 0)
(<14,0,A>, A, .= 0) (<14,0,B>, B, .= 0) (<14,0,C>, C, .= 0) (<14,0,E>, E, .= 0) (<14,0,F>, F, .= 0) (<14,0,G>, G, .= 0) (<14,0,H>, 1 + G, .+ 1) (<14,0,J>, J, .= 0)
(<15,0,A>, A, .= 0) (<15,0,B>, B, .= 0) (<15,0,C>, C, .= 0) (<15,0,E>, E, .= 0) (<15,0,F>, F, .= 0) (<15,0,G>, G, .= 0) (<15,0,H>, 1 + H, .+ 1) (<15,0,J>, J, .= 0)
(<16,0,A>, A, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, C, .= 0) (<16,0,E>, E, .= 0) (<16,0,F>, F, .= 0) (<16,0,G>, 1 + G, .+ 1) (<16,0,H>, H, .= 0) (<16,0,J>, J, .= 0)
(<17,0,A>, A, .= 0) (<17,0,B>, B, .= 0) (<17,0,C>, C, .= 0) (<17,0,E>, E, .= 0) (<17,0,F>, F, .= 0) (<17,0,G>, G, .= 0) (<17,0,H>, H, .= 0) (<17,0,J>, J, .= 0)
(<18,0,A>, A, .= 0) (<18,0,B>, B, .= 0) (<18,0,C>, C, .= 0) (<18,0,E>, E, .= 0) (<18,0,F>, F, .= 0) (<18,0,G>, 1 + G, .+ 1) (<18,0,H>, H, .= 0) (<18,0,J>, J, .= 0)
(<19,0,A>, A, .= 0) (<19,0,B>, B, .= 0) (<19,0,C>, C, .= 0) (<19,0,E>, E, .= 0) (<19,0,F>, F, .= 0) (<19,0,G>, 1 + F, .+ 1) (<19,0,H>, H, .= 0) (<19,0,J>, J, .= 0)
(<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,C>, C, .= 0) (<20,0,E>, E, .= 0) (<20,0,F>, F, .= 0) (<20,0,G>, G, .= 0) (<20,0,H>, 1 + H, .+ 1) (<20,0,J>, J, .= 0)
(<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,C>, C, .= 0) (<21,0,E>, E, .= 0) (<21,0,F>, F, .= 0) (<21,0,G>, 1 + G, .+ 1) (<21,0,H>, H, .= 0) (<21,0,J>, J, .= 0)
(<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, C, .= 0) (<22,0,E>, E, .= 0) (<22,0,F>, F, .= 0) (<22,0,G>, G, .= 0) (<22,0,H>, 1 + H, .+ 1) (<22,0,J>, J, .= 0)
(<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,E>, E, .= 0) (<23,0,F>, F, .= 0) (<23,0,G>, G, .= 0) (<23,0,H>, 1 + G, .+ 1) (<23,0,J>, J, .= 0)
(<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,C>, C, .= 0) (<24,0,E>, E, .= 0) (<24,0,F>, F, .= 0) (<24,0,G>, 1, .= 1) (<24,0,H>, H, .= 0) (<24,0,J>, J, .= 0)
(<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,C>, 1 + C, .+ 1) (<25,0,E>, E, .= 0) (<25,0,F>, F, .= 0) (<25,0,G>, G, .= 0) (<25,0,H>, H, .= 0) (<25,0,J>, J, .= 0)
(<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,C>, C, .= 0) (<26,0,E>, E, .= 0) (<26,0,F>, B, .= 0) (<26,0,G>, 0, .= 0) (<26,0,H>, H, .= 0) (<26,0,J>, J, .= 0)
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
17. f80(A,B,C,E,F,G,H,J) -> f96(A,B,C,E,F,G,H,J) [0 >= 1 + G] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (?,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1,26},1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8
,22},9->{6,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14,17}
,17->{},18->{12,19},19->{14,17},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26}
,26->{5,24}]
Sizebounds:
(< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 0,0,E>, ?) (< 0,0,F>, ?) (< 0,0,G>, ?) (< 0,0,H>, ?) (< 0,0,J>, ?)
(< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (< 1,0,E>, ?) (< 1,0,F>, ?) (< 1,0,G>, ?) (< 1,0,H>, ?) (< 1,0,J>, ?)
(< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,E>, ?) (< 2,0,F>, ?) (< 2,0,G>, ?) (< 2,0,H>, ?) (< 2,0,J>, ?)
(< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,E>, ?) (< 3,0,F>, ?) (< 3,0,G>, ?) (< 3,0,H>, ?) (< 3,0,J>, ?)
(< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,E>, ?) (< 4,0,F>, ?) (< 4,0,G>, ?) (< 4,0,H>, ?) (< 4,0,J>, ?)
(< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, ?) (< 5,0,G>, ?) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, ?) (< 6,0,G>, ?) (< 6,0,H>, ?) (< 6,0,J>, ?)
(< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, ?) (< 7,0,G>, ?) (< 7,0,H>, ?) (< 7,0,J>, ?)
(< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, ?) (< 8,0,G>, ?) (< 8,0,H>, ?) (< 8,0,J>, ?)
(< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, ?) (< 9,0,G>, ?) (< 9,0,H>, ?) (< 9,0,J>, ?)
(<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, ?) (<10,0,G>, ?) (<10,0,H>, ?) (<10,0,J>, ?)
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, ?) (<11,0,G>, ?) (<11,0,H>, ?) (<11,0,J>, ?)
(<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, ?) (<12,0,G>, ?) (<12,0,H>, ?) (<12,0,J>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, ?) (<13,0,G>, ?) (<13,0,H>, ?) (<13,0,J>, ?)
(<14,0,A>, ?) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, ?) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, ?) (<15,0,B>, ?) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, ?) (<15,0,G>, ?) (<15,0,H>, ?) (<15,0,J>, ?)
(<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, ?) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<17,0,A>, ?) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,E>, ?) (<17,0,F>, ?) (<17,0,G>, ?) (<17,0,H>, ?) (<17,0,J>, ?)
(<18,0,A>, ?) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, ?) (<18,0,G>, ?) (<18,0,H>, ?) (<18,0,J>, ?)
(<19,0,A>, ?) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, ?) (<19,0,G>, ?) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, ?) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, ?) (<20,0,G>, ?) (<20,0,H>, ?) (<20,0,J>, ?)
(<21,0,A>, ?) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, ?) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, ?) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, ?) (<22,0,G>, ?) (<22,0,H>, ?) (<22,0,J>, ?)
(<23,0,A>, ?) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, ?) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, ?) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, ?) (<24,0,G>, ?) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, ?) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,E>, ?) (<25,0,F>, ?) (<25,0,G>, ?) (<25,0,H>, ?) (<25,0,J>, ?)
(<26,0,A>, ?) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,E>, ?) (<26,0,F>, ?) (<26,0,G>, ?) (<26,0,H>, ?) (<26,0,J>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<17,0,A>, 50) (<17,0,B>, 5) (<17,0,C>, ?) (<17,0,E>, ?) (<17,0,F>, 5) (<17,0,G>, ?) (<17,0,H>, ?) (<17,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 4: UnsatPaths WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
17. f80(A,B,C,E,F,G,H,J) -> f96(A,B,C,E,F,G,H,J) [0 >= 1 + G] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (?,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1,26},1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8
,22},9->{6,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14,17}
,17->{},18->{12,19},19->{14,17},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26}
,26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<17,0,A>, 50) (<17,0,B>, 5) (<17,0,C>, ?) (<17,0,E>, ?) (<17,0,F>, 5) (<17,0,G>, ?) (<17,0,H>, ?) (<17,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(0,26)
,(2,3)
,(2,4)
,(3,2)
,(4,3)
,(4,4)
,(5,23)
,(6,8)
,(7,22)
,(9,6)
,(9,7)]
* Step 5: LeafRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
17. f80(A,B,C,E,F,G,H,J) -> f96(A,B,C,E,F,G,H,J) [0 >= 1 + G] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (?,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14,17},17->{},18->{12,19}
,19->{14,17},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<17,0,A>, 50) (<17,0,B>, 5) (<17,0,C>, ?) (<17,0,E>, ?) (<17,0,F>, 5) (<17,0,G>, ?) (<17,0,H>, ?) (<17,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [17]
* Step 6: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (?,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 1
p(f15) = 1
p(f19) = 1
p(f33) = 0
p(f36) = 0
p(f41) = 0
p(f50) = 0
p(f54) = 0
p(f66) = 0
p(f70) = 0
p(f80) = 0
p(f84) = 0
The following rules are strictly oriented:
[C >= 1 + B] ==>
f15(A,B,C,E,F,G,H,J) = 1
> 0
= f33(A,B,C,E,B,0,H,J)
The following rules are weakly oriented:
True ==>
f0(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(50,5,0,E,F,G,H,J)
[B >= C] ==>
f15(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,0,F,G,H,J)
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + C,F,G,H,J)
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,H,1 + J)
[F >= G] ==>
f66(A,B,C,E,F,G,H,J) = 0
>= 0
= f70(A,B,C,E,F,G,0,J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 0
>= 0
= f70(A,B,C,E,F,G,1 + H,J)
[G >= 0] ==>
f80(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + G,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f80(A,B,C,E,F,-1 + G,H,J)
[H >= G] ==>
f70(A,B,C,E,F,G,H,J) = 0
>= 0
= f66(A,B,C,E,F,1 + G,H,J)
[G >= 1 + F] ==>
f66(A,B,C,E,F,G,H,J) = 0
>= 0
= f80(A,B,C,E,F,-1 + F,H,J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 0
>= 0
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f50(A,B,C,E,F,G,1 + G,J)
[G >= F] ==>
f33(A,B,C,E,F,G,H,J) = 0
>= 0
= f66(A,B,C,E,F,1,H,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(A,B,1 + C,E,F,G,H,J)
* Step 7: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 1
p(f15) = 1
p(f19) = 1
p(f33) = 1
p(f36) = 1
p(f41) = 1
p(f50) = 1
p(f54) = 1
p(f66) = 0
p(f70) = 0
p(f80) = 0
p(f84) = 0
The following rules are strictly oriented:
[G >= F] ==>
f33(A,B,C,E,F,G,H,J) = 1
> 0
= f66(A,B,C,E,F,1,H,J)
The following rules are weakly oriented:
True ==>
f0(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(50,5,0,E,F,G,H,J)
[B >= C] ==>
f15(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,0,F,G,H,J)
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + C,F,G,H,J)
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,1 + J)
[F >= G] ==>
f66(A,B,C,E,F,G,H,J) = 0
>= 0
= f70(A,B,C,E,F,G,0,J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 0
>= 0
= f70(A,B,C,E,F,G,1 + H,J)
[G >= 0] ==>
f80(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + G,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f80(A,B,C,E,F,-1 + G,H,J)
[H >= G] ==>
f70(A,B,C,E,F,G,H,J) = 0
>= 0
= f66(A,B,C,E,F,1 + G,H,J)
[G >= 1 + F] ==>
f66(A,B,C,E,F,G,H,J) = 0
>= 0
= f80(A,B,C,E,F,-1 + F,H,J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1
>= 1
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + G,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(A,B,1 + C,E,F,G,H,J)
[C >= 1 + B] ==>
f15(A,B,C,E,F,G,H,J) = 1
>= 1
= f33(A,B,C,E,B,0,H,J)
* Step 8: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 1
p(f15) = 1
p(f19) = 1
p(f33) = 1
p(f36) = 1
p(f41) = 1
p(f50) = 1
p(f54) = 1
p(f66) = 1
p(f70) = 1
p(f80) = 0
p(f84) = 0
The following rules are strictly oriented:
[G >= 1 + F] ==>
f66(A,B,C,E,F,G,H,J) = 1
> 0
= f80(A,B,C,E,F,-1 + F,H,J)
The following rules are weakly oriented:
True ==>
f0(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(50,5,0,E,F,G,H,J)
[B >= C] ==>
f15(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,0,F,G,H,J)
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + C,F,G,H,J)
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,1 + J)
[F >= G] ==>
f66(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,G,0,J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,G,1 + H,J)
[G >= 0] ==>
f80(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + G,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f80(A,B,C,E,F,-1 + G,H,J)
[H >= G] ==>
f70(A,B,C,E,F,G,H,J) = 1
>= 1
= f66(A,B,C,E,F,1 + G,H,J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1
>= 1
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + G,J)
[G >= F] ==>
f33(A,B,C,E,F,G,H,J) = 1
>= 1
= f66(A,B,C,E,F,1,H,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f15(A,B,1 + C,E,F,G,H,J)
[C >= 1 + B] ==>
f15(A,B,C,E,F,G,H,J) = 1
>= 1
= f33(A,B,C,E,B,0,H,J)
* Step 9: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 6
p(f15) = 1 + x2
p(f19) = 1 + x2
p(f33) = 1 + x5
p(f36) = 1 + x5
p(f41) = 1 + x5
p(f50) = 1 + x5
p(f54) = 1 + x5
p(f66) = 1 + x5
p(f70) = 1 + x5
p(f80) = 2 + x6
p(f84) = 1 + x6
The following rules are strictly oriented:
[G >= 0] ==>
f80(A,B,C,E,F,G,H,J) = 2 + G
> 1 + G
= f84(A,B,C,E,F,G,1 + G,J)
The following rules are weakly oriented:
True ==>
f0(A,B,C,E,F,G,H,J) = 6
>= 6
= f15(50,5,0,E,F,G,H,J)
[B >= C] ==>
f15(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f19(A,B,C,0,F,G,H,J)
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f19(A,B,C,1 + C,F,G,H,J)
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f54(A,B,C,E,F,G,H,1 + J)
[F >= G] ==>
f66(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f70(A,B,C,E,F,G,0,J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f70(A,B,C,E,F,G,1 + H,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 1 + G
>= 1 + G
= f84(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f84(A,B,C,E,F,G,H,J) = 1 + G
>= 1 + G
= f80(A,B,C,E,F,-1 + G,H,J)
[H >= G] ==>
f70(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f66(A,B,C,E,F,1 + G,H,J)
[G >= 1 + F] ==>
f66(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f80(A,B,C,E,F,-1 + F,H,J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f50(A,B,C,E,F,G,1 + G,J)
[G >= F] ==>
f33(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f66(A,B,C,E,F,1,H,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f15(A,B,1 + C,E,F,G,H,J)
[C >= 1 + B] ==>
f15(A,B,C,E,F,G,H,J) = 1 + B
>= 1 + B
= f33(A,B,C,E,B,0,H,J)
* Step 10: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (?,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 7
p(f15) = 2 + x2 + -1*x3
p(f19) = 1 + x2 + -1*x3
p(f33) = 1 + x2 + -1*x3
p(f36) = 1 + x2 + -1*x3
p(f41) = 1 + x2 + -1*x3
p(f50) = 1 + x2 + -1*x3
p(f54) = 1 + x2 + -1*x3
p(f66) = 1 + x2 + -1*x3
p(f70) = 1 + x2 + -1*x3
p(f80) = 1 + x2 + -1*x3
p(f84) = 1 + x2 + -1*x3
The following rules are strictly oriented:
[B >= C] ==>
f15(A,B,C,E,F,G,H,J) = 2 + B + -1*C
> 1 + B + -1*C
= f19(A,B,C,0,F,G,H,J)
The following rules are weakly oriented:
True ==>
f0(A,B,C,E,F,G,H,J) = 7
>= 7
= f15(50,5,0,E,F,G,H,J)
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f19(A,B,C,1 + C,F,G,H,J)
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f54(A,B,C,E,F,G,H,1 + J)
[F >= G] ==>
f66(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f70(A,B,C,E,F,G,0,J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f70(A,B,C,E,F,G,1 + H,J)
[G >= 0] ==>
f80(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f84(A,B,C,E,F,G,1 + G,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f84(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f84(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f80(A,B,C,E,F,-1 + G,H,J)
[H >= G] ==>
f70(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f66(A,B,C,E,F,1 + G,H,J)
[G >= 1 + F] ==>
f66(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f80(A,B,C,E,F,-1 + F,H,J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f50(A,B,C,E,F,G,1 + G,J)
[G >= F] ==>
f33(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f66(A,B,C,E,F,1,H,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*C
>= 1 + B + -1*C
= f15(A,B,1 + C,E,F,G,H,J)
[C >= 1 + B] ==>
f15(A,B,C,E,F,G,H,J) = 2 + B + -1*C
>= 1 + B + -1*C
= f33(A,B,C,E,B,0,H,J)
* Step 11: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (?,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [2,4,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f19) = 1 + x3 + -1*x4
The following rules are strictly oriented:
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + C + -1*E
> 0
= f19(A,B,C,1 + C,F,G,H,J)
The following rules are weakly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1 + C + -1*E
>= C + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + C + -1*E
>= C + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 12: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [25,2,4,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f15) = 0
p(f19) = 1
The following rules are strictly oriented:
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1
> 0
= f15(A,B,1 + C,E,F,G,H,J)
The following rules are weakly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + C,F,G,H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 13: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (?,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [25,2,4,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f15) = 1 + x2 + -1*x4
p(f19) = 1 + x2 + -1*x4
The following rules are strictly oriented:
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
> B + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
> B + -1*C
= f19(A,B,C,1 + C,F,G,H,J)
The following rules are weakly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
>= B + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
>= 1 + B + -1*E
= f15(A,B,1 + C,E,F,G,H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 14: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (?,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [25,2,4,3], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f15) = 1 + x2 + -1*x4
p(f19) = 1 + x2 + -1*x4
The following rules are strictly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
> B + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
> B + -1*E
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
> B + -1*C
= f19(A,B,C,1 + C,F,G,H,J)
The following rules are weakly oriented:
[E >= 1 + B] ==>
f19(A,B,C,E,F,G,H,J) = 1 + B + -1*E
>= 1 + B + -1*E
= f15(A,B,1 + C,E,F,G,H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 15: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (?,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,21,20,10,23,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 2 + x5 + -1*x6
p(f36) = 1 + x5 + -1*x6
p(f41) = 1 + x5 + -1*x6
p(f50) = 1 + x5 + -1*x6
p(f54) = 1 + x5 + -1*x6
The following rules are strictly oriented:
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 2 + F + -1*G
> 1 + F + -1*G
= f36(A,B,C,E,F,G,1 + G,J)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f50(A,B,C,E,F,G,1 + G,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 16: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [21,20,10,23,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 0
p(f36) = 1
p(f41) = 1
p(f50) = 0
p(f54) = 0
The following rules are strictly oriented:
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1
> 0
= f50(A,B,C,E,F,G,1 + G,J)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 0
>= 0
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 17: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [21,20,10,23,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 0
p(f36) = 1
p(f41) = 1
p(f50) = 1
p(f54) = 1
The following rules are strictly oriented:
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1
> 0
= f33(A,B,C,E,F,1 + G,H,J)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,0,1 + H,J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f50(A,B,C,E,F,G,1 + G,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 18: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (?,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (?,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,21,20,10,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 1 + x5
p(f36) = 2 + x5 + x6 + -1*x7
p(f41) = 1 + x5 + x6 + -1*x7
p(f50) = 1 + x5
p(f54) = 1 + x5
The following rules are strictly oriented:
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + G + -1*H
> 1 + F + G + -1*H
= f41(A,B,C,E,F,G,H,0)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + G + -1*H
> 1 + F + -1*H
= f36(A,B,C,E,F,0,1 + H,J)
The following rules are weakly oriented:
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + G + -1*H
>= 1 + F + G + -1*H
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + G + -1*H
>= 1 + F + G + -1*H
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f54(A,B,C,E,F,G,H,0)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 1 + F
>= 1 + F
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + G + -1*H
>= 1 + F + G + -1*H
= f36(A,B,C,E,F,G,1 + H,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 19: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (?,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [21,20,10,23,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 2 + x5 + -1*x7
p(f36) = 1 + x5 + -1*x6
p(f41) = 1 + x5 + -1*x6
p(f50) = 2 + x5 + -1*x7
p(f54) = 1 + x5 + -1*x7
The following rules are strictly oriented:
[F >= H] ==>
f50(A,B,C,E,F,G,H,J) = 2 + F + -1*H
> 1 + F + -1*H
= f54(A,B,C,E,F,G,H,0)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*H
>= 1 + F + -1*H
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*H
>= 1 + F + -1*H
= f50(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 2 + F + -1*H
>= 2 + F + -1*H
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f50(A,B,C,E,F,G,1 + G,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 20: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [5,21,20,23,9,22,6,8,7,11], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f33) = 0
p(f36) = 0
p(f41) = 0
p(f50) = 0
p(f54) = 1
The following rules are strictly oriented:
[J >= 1 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1
> 0
= f50(A,B,C,E,F,G,1 + H,J)
The following rules are weakly oriented:
[F >= 1 + G] ==>
f33(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,G,1 + G,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 0
>= 0
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,1 + J)
[H >= 1 + F] ==>
f50(A,B,C,E,F,G,H,J) = 0
>= 0
= f33(A,B,C,E,F,1 + G,H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f50(A,B,C,E,F,G,1 + G,J)
We use the following global sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
* Step 21: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
0. f0(A,B,C,E,F,G,H,J) -> f15(50,5,0,E,F,G,H,J) True (1,1)
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (77,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[0->{1},1->{2,3,4,25},2->{2,25},3->{3,4,25},4->{2,25},5->{6,7,9},6->{22},7->{8},8->{8,22},9->{9,23}
,10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24}]
Sizebounds:
(< 0,0,A>, 50) (< 0,0,B>, 5) (< 0,0,C>, 0) (< 0,0,E>, E) (< 0,0,F>, F) (< 0,0,G>, G) (< 0,0,H>, H) (< 0,0,J>, J)
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
+ Applied Processor:
ChainProcessor False [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26]
+ Details:
We chained rule 0 to obtain the rules [27] .
* Step 22: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
16. f84(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + G,H,J) [H >= 1 + F] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (77,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,16},15->{15,16},16->{14},18->{12,19}
,19->{14},20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24},27->{2,3,4
,25}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<16,0,A>, 50) (<16,0,B>, 5) (<16,0,C>, ?) (<16,0,E>, ?) (<16,0,F>, 5) (<16,0,G>, ?) (<16,0,H>, ?) (<16,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27]
+ Details:
We chained rule 16 to obtain the rules [28] .
* Step 23: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
18. f70(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1 + G,H,J) [H >= G] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (77,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,20},11->{11,20},12->{13,18},13->{13,18},14->{15,28},15->{15,28},18->{12,19},19->{14}
,20->{10,21},21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15
,28}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<18,0,A>, 50) (<18,0,B>, 5) (<18,0,C>, ?) (<18,0,E>, ?) (<18,0,F>, 5) (<18,0,G>, 5) (<18,0,H>, 5) (<18,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,19,20,21,22,23,24,25,26,27,28]
+ Details:
We chained rule 18 to obtain the rules [29,30] .
* Step 24: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
19. f66(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [G >= 1 + F] (1,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (77,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,20},11->{11,20},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},19->{14},20->{10,21}
,21->{5,24},22->{6,7,9,23},23->{10,21},24->{12,19},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13
,29,30},30->{14}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<19,0,A>, 50) (<19,0,B>, 5) (<19,0,C>, ?) (<19,0,E>, ?) (<19,0,F>, 5) (<19,0,G>, 6) (<19,0,H>, ?) (<19,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,19,20,21,22,23,24,25,26,27,28,29,30]
+ Details:
We chained rule 19 to obtain the rules [31] .
* Step 25: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
20. f54(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + H,J) [J >= 1 + G] (77,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,20},11->{11,20},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},20->{10,21},21->{5
,24},22->{6,7,9,23},23->{10,21},24->{12,31},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13,29,30}
,30->{14},31->{15,28}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<20,0,A>, 50) (<20,0,B>, 5) (<20,0,C>, ?) (<20,0,E>, ?) (<20,0,F>, 5) (<20,0,G>, ?) (<20,0,H>, 5) (<20,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,20,21,22,23,24,25,26,27,28,29,30,31]
+ Details:
We chained rule 20 to obtain the rules [32,33] .
* Step 26: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
21. f50(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,H,J) [H >= 1 + F] (7,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,32,33},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},21->{5,24}
,22->{6,7,9,23},23->{10,21},24->{12,31},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13,29,30}
,30->{14},31->{15,28},32->{11,32,33},33->{5,24}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<21,0,A>, 50) (<21,0,B>, 5) (<21,0,C>, ?) (<21,0,E>, ?) (<21,0,F>, 5) (<21,0,G>, ?) (<21,0,H>, ?) (<21,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,21,22,23,24,25,26,27,28,29,30,31,32,33]
+ Details:
We chained rule 21 to obtain the rules [34,35] .
* Step 27: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
23. f36(A,B,C,E,F,G,H,J) -> f50(A,B,C,E,F,G,1 + G,J) [H >= 1 + F] (7,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
34. f50(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && F >= 2 + G] (7,2)
35. f50(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [H >= 1 + F && 1 + G >= F] (7,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,23},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,23},10->{11,32,33},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},22->{6,7,9,23}
,23->{10,34,35},24->{12,31},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13,29,30},30->{14},31->{15
,28},32->{11,32,33},33->{5,24},34->{6,7,9,23},35->{12,31}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<23,0,A>, 50) (<23,0,B>, 5) (<23,0,C>, ?) (<23,0,E>, ?) (<23,0,F>, 5) (<23,0,G>, ?) (<23,0,H>, ?) (<23,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<34,0,A>, 50) (<34,0,B>, 5) (<34,0,C>, ?) (<34,0,E>, ?) (<34,0,F>, 5) (<34,0,G>, 5) (<34,0,H>, ?) (<34,0,J>, ?)
(<35,0,A>, 50) (<35,0,B>, 5) (<35,0,C>, ?) (<35,0,E>, ?) (<35,0,F>, 5) (<35,0,G>, 1) (<35,0,H>, ?) (<35,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,22,23,24,25,26,27,28,29,30,31,32,33,34,35]
+ Details:
We chained rule 23 to obtain the rules [36,37,38] .
* Step 28: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
10. f50(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,0) [F >= H] (77,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
34. f50(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && F >= 2 + G] (7,2)
35. f50(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [H >= 1 + F && 1 + G >= F] (7,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},10->{11,32,33},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28}
,22->{6,7,9,36,37,38},24->{12,31},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13,29,30},30->{14}
,31->{15,28},32->{11,32,33},33->{5,24},34->{6,7,9,36,37,38},35->{12,31},36->{11,32,33},37->{6,7,9,36,37,38}
,38->{12,31}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<10,0,A>, 50) (<10,0,B>, 5) (<10,0,C>, ?) (<10,0,E>, ?) (<10,0,F>, 5) (<10,0,G>, ?) (<10,0,H>, 5) (<10,0,J>, 0)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<34,0,A>, 50) (<34,0,B>, 5) (<34,0,C>, ?) (<34,0,E>, ?) (<34,0,F>, 5) (<34,0,G>, 5) (<34,0,H>, ?) (<34,0,J>, ?)
(<35,0,A>, 50) (<35,0,B>, 5) (<35,0,C>, ?) (<35,0,E>, ?) (<35,0,F>, 5) (<35,0,G>, 1) (<35,0,H>, ?) (<35,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [10,34,35]
* Step 29: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
24. f33(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,H,J) [G >= F] (1,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},22->{6,7,9,36,37
,38},24->{12,31},25->{1,26},26->{5,24},27->{2,3,4,25},28->{15,28},29->{13,29,30},30->{14},31->{15,28}
,32->{11,32,33},33->{5,24},36->{11,32,33},37->{6,7,9,36,37,38},38->{12,31}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<24,0,A>, 50) (<24,0,B>, 5) (<24,0,C>, ?) (<24,0,E>, ?) (<24,0,F>, 5) (<24,0,G>, 1) (<24,0,H>, ?) (<24,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,11,12,13,14,15,22,24,25,26,27,28,29,30,31,32,33,36,37,38]
+ Details:
We chained rule 24 to obtain the rules [39,40] .
* Step 30: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
25. f19(A,B,C,E,F,G,H,J) -> f15(A,B,1 + C,E,F,G,H,J) [E >= 1 + B] (7,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,25},2->{2,3,4,25},3->{2,3,4,25},4->{2,3,4,25},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},22->{6,7,9,36,37
,38},25->{1,26},26->{5,39,40},27->{2,3,4,25},28->{15,28},29->{13,29,30},30->{14},31->{15,28},32->{11,32,33}
,33->{5,39,40},36->{11,32,33},37->{6,7,9,36,37,38},38->{12,31},39->{13,29,30},40->{15,28}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<25,0,A>, 50) (<25,0,B>, 5) (<25,0,C>, 5) (<25,0,E>, 6) (<25,0,F>, F) (<25,0,G>, G) (<25,0,H>, H) (<25,0,J>, J)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
+ Applied Processor:
ChainProcessor False [1,2,3,4,5,6,7,8,9,11,12,13,14,15,22,25,26,27,28,29,30,31,32,33,36,37,38,39,40]
+ Details:
We chained rule 25 to obtain the rules [41,42] .
* Step 31: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
1. f15(A,B,C,E,F,G,H,J) -> f19(A,B,C,0,F,G,H,J) [B >= C] (7,1)
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
26. f15(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,B,0,H,J) [C >= 1 + B] (1,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[1->{2,3,4,41,42},2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,38},6->{8,22},7->{8
,22},8->{8,22},9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28}
,22->{6,7,9,36,37,38},26->{5,39,40},27->{2,3,4,41,42},28->{15,28},29->{13,29,30},30->{14},31->{15,28}
,32->{11,32,33},33->{5,39,40},36->{11,32,33},37->{6,7,9,36,37,38},38->{12,31},39->{13,29,30},40->{15,28}
,41->{2,3,4,41,42},42->{5,39,40}]
Sizebounds:
(< 1,0,A>, 50) (< 1,0,B>, 5) (< 1,0,C>, 5) (< 1,0,E>, 0) (< 1,0,F>, F) (< 1,0,G>, G) (< 1,0,H>, H) (< 1,0,J>, J)
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<26,0,A>, 50) (<26,0,B>, 5) (<26,0,C>, 5) (<26,0,E>, 6 + E) (<26,0,F>, 5) (<26,0,G>, 0) (<26,0,H>, H) (<26,0,J>, J)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [1,26]
* Step 32: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
30. f70(A,B,C,E,F,G,H,J) -> f80(A,B,C,E,F,-1 + F,H,J) [H >= G && 1 + G >= 1 + F] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,30},13->{13,29,30},14->{15,28},15->{15,28},22->{6,7,9,36,37
,38},27->{2,3,4,41,42},28->{15,28},29->{13,29,30},30->{14},31->{15,28},32->{11,32,33},33->{5,39,40},36->{11
,32,33},37->{6,7,9,36,37,38},38->{12,31},39->{13,29,30},40->{15,28},41->{2,3,4,41,42},42->{5,39,40}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<30,0,A>, 50) (<30,0,B>, 5) (<30,0,C>, ?) (<30,0,E>, ?) (<30,0,F>, 5) (<30,0,G>, 6) (<30,0,H>, ?) (<30,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
+ Applied Processor:
ChainProcessor False [2,3,4,5,6,7,8,9,11,12,13,14,15,22,27,28,29,30,31,32,33,36,37,38,39,40,41,42]
+ Details:
We chained rule 30 to obtain the rules [43] .
* Step 33: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
14. f80(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + G,J) [G >= 0] (6,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,43},13->{13,29,43},14->{15,28},15->{15,28},22->{6,7,9,36,37
,38},27->{2,3,4,41,42},28->{15,28},29->{13,29,43},31->{15,28},32->{11,32,33},33->{5,39,40},36->{11,32,33}
,37->{6,7,9,36,37,38},38->{12,31},39->{13,29,43},40->{15,28},41->{2,3,4,41,42},42->{5,39,40},43->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<14,0,A>, 50) (<14,0,B>, 5) (<14,0,C>, ?) (<14,0,E>, ?) (<14,0,F>, 5) (<14,0,G>, ?) (<14,0,H>, ?) (<14,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [14]
* Step 34: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
33. f54(A,B,C,E,F,G,H,J) -> f33(A,B,C,E,F,1 + G,1 + H,J) [J >= 1 + G && 1 + H >= 1 + F] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,33},12->{13,29,43},13->{13,29,43},15->{15,28},22->{6,7,9,36,37,38},27->{2,3
,4,41,42},28->{15,28},29->{13,29,43},31->{15,28},32->{11,32,33},33->{5,39,40},36->{11,32,33},37->{6,7,9,36
,37,38},38->{12,31},39->{13,29,43},40->{15,28},41->{2,3,4,41,42},42->{5,39,40},43->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<33,0,A>, 50) (<33,0,B>, 5) (<33,0,C>, ?) (<33,0,E>, ?) (<33,0,F>, 5) (<33,0,G>, ?) (<33,0,H>, ?) (<33,0,J>, ?)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
+ Applied Processor:
ChainProcessor False [2,3,4,5,6,7,8,9,11,12,13,15,22,27,28,29,31,32,33,36,37,38,39,40,41,42,43]
+ Details:
We chained rule 33 to obtain the rules [44,45,46] .
* Step 35: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
38. f36(A,B,C,E,F,G,H,J) -> f66(A,B,C,E,F,1,1 + G,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,38},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,38},11->{11,32,44,45,46},12->{13,29,43},13->{13,29,43},15->{15,28},22->{6,7,9,36,37,38}
,27->{2,3,4,41,42},28->{15,28},29->{13,29,43},31->{15,28},32->{11,32,44,45,46},36->{11,32,44,45,46},37->{6,7
,9,36,37,38},38->{12,31},39->{13,29,43},40->{15,28},41->{2,3,4,41,42},42->{5,39,40},43->{15,28},44->{6,7,9
,36,37,38},45->{13,29,43},46->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<38,0,A>, 50) (<38,0,B>, 5) (<38,0,C>, ?) (<38,0,E>, ?) (<38,0,F>, 5) (<38,0,G>, 1) (<38,0,H>, ?) (<38,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
+ Applied Processor:
ChainProcessor False [2,3,4,5,6,7,8,9,11,12,13,15,22,27,28,29,31,32,36,37,38,39,40,41,42,43,44,45,46]
+ Details:
We chained rule 38 to obtain the rules [47,48] .
* Step 36: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
12. f66(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,0,J) [F >= G] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
31. f66(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= 1 + F && -1 + F >= 0] (1,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
48. f36(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (7,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,47,48},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,47,48},11->{11,32,44,45,46},12->{13,29,43},13->{13,29,43},15->{15,28},22->{6,7,9,36,37,47
,48},27->{2,3,4,41,42},28->{15,28},29->{13,29,43},31->{15,28},32->{11,32,44,45,46},36->{11,32,44,45,46}
,37->{6,7,9,36,37,47,48},39->{13,29,43},40->{15,28},41->{2,3,4,41,42},42->{5,39,40},43->{15,28},44->{6,7,9
,36,37,47,48},45->{13,29,43},46->{15,28},47->{13,29,43},48->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<12,0,A>, 50) (<12,0,B>, 5) (<12,0,C>, ?) (<12,0,E>, ?) (<12,0,F>, 5) (<12,0,G>, 5) (<12,0,H>, 0) (<12,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<31,0,A>, 50) (<31,0,B>, 5) (<31,0,C>, ?) (<31,0,E>, ?) (<31,0,F>, 5) (<31,0,G>, ?) (<31,0,H>, ?) (<31,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<48,0,A>, 50) (<48,0,B>, 5) (<48,0,C>, ?) (<48,0,E>, ?) (<48,0,F>, 5) (<48,0,G>, ?) (<48,0,H>, ?) (<48,0,J>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [12,31]
* Step 37: ChainProcessor WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
42. f19(A,B,C,E,F,G,H,J) -> f33(A,B,1 + C,E,B,0,H,J) [E >= 1 + B && 1 + C >= 1 + B] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
48. f36(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (7,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,42},3->{2,3,4,41,42},4->{2,3,4,41,42},5->{6,7,9,36,37,47,48},6->{8,22},7->{8,22},8->{8,22}
,9->{6,7,9,36,37,47,48},11->{11,32,44,45,46},13->{13,29,43},15->{15,28},22->{6,7,9,36,37,47,48},27->{2,3,4
,41,42},28->{15,28},29->{13,29,43},32->{11,32,44,45,46},36->{11,32,44,45,46},37->{6,7,9,36,37,47,48},39->{13
,29,43},40->{15,28},41->{2,3,4,41,42},42->{5,39,40},43->{15,28},44->{6,7,9,36,37,47,48},45->{13,29,43}
,46->{15,28},47->{13,29,43},48->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<42,0,A>, 50) (<42,0,B>, 5) (<42,0,C>, 5) (<42,0,E>, 6 + E) (<42,0,F>, 5) (<42,0,G>, 0) (<42,0,H>, H) (<42,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<48,0,A>, 50) (<48,0,B>, 5) (<48,0,C>, ?) (<48,0,E>, ?) (<48,0,F>, 5) (<48,0,G>, ?) (<48,0,H>, ?) (<48,0,J>, ?)
+ Applied Processor:
ChainProcessor False [2,3,4,5,6,7,8,9,11,13,15,22,27,28,29,32,36,37,39,40,41,42,43,44,45,46,47,48]
+ Details:
We chained rule 42 to obtain the rules [49,50,51] .
* Step 38: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
5. f33(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + G,J) [F >= 1 + G] (7,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
39. f33(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [G >= F && F >= 1] (1,2)
40. f33(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [G >= F && 1 >= 1 + F && -1 + F >= 0] (1,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
48. f36(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (7,5)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
50. f19(A,B,C,E,F,G,H,J) -> f70(A,B,1 + C,E,B,1,0,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && B >= 1] (7,4)
51. f19(A,B,C,E,F,G,H,J) -> f84(A,B,1 + C,E,B,-1 + B,B,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && 1 >= 1 + B && -1 + B >= 0] (7,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,49,50,51},3->{2,3,4,41,49,50,51},4->{2,3,4,41,49,50,51},5->{6,7,9,36,37,47,48},6->{8,22}
,7->{8,22},8->{8,22},9->{6,7,9,36,37,47,48},11->{11,32,44,45,46},13->{13,29,43},15->{15,28},22->{6,7,9,36,37
,47,48},27->{2,3,4,41,49,50,51},28->{15,28},29->{13,29,43},32->{11,32,44,45,46},36->{11,32,44,45,46},37->{6
,7,9,36,37,47,48},39->{13,29,43},40->{15,28},41->{2,3,4,41,49,50,51},43->{15,28},44->{6,7,9,36,37,47,48}
,45->{13,29,43},46->{15,28},47->{13,29,43},48->{15,28},49->{6,7,9,36,37,47,48},50->{13,29,43},51->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 5,0,A>, 50) (< 5,0,B>, 5) (< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,F>, 5) (< 5,0,G>, 5) (< 5,0,H>, ?) (< 5,0,J>, ?)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<39,0,A>, 50) (<39,0,B>, 5) (<39,0,C>, ?) (<39,0,E>, ?) (<39,0,F>, 5) (<39,0,G>, 5) (<39,0,H>, 0) (<39,0,J>, ?)
(<40,0,A>, 50) (<40,0,B>, 5) (<40,0,C>, ?) (<40,0,E>, ?) (<40,0,F>, 5) (<40,0,G>, ?) (<40,0,H>, ?) (<40,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<48,0,A>, 50) (<48,0,B>, 5) (<48,0,C>, ?) (<48,0,E>, ?) (<48,0,F>, 5) (<48,0,G>, ?) (<48,0,H>, ?) (<48,0,J>, ?)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, ?) (<49,0,E>, ?) (<49,0,F>, 5) (<49,0,G>, 5) (<49,0,H>, ?) (<49,0,J>, ?)
(<50,0,A>, 50) (<50,0,B>, 5) (<50,0,C>, ?) (<50,0,E>, ?) (<50,0,F>, 5) (<50,0,G>, 5) (<50,0,H>, 0) (<50,0,J>, ?)
(<51,0,A>, 50) (<51,0,B>, 5) (<51,0,C>, ?) (<51,0,E>, ?) (<51,0,F>, 5) (<51,0,G>, ?) (<51,0,H>, ?) (<51,0,J>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [5,39,40]
* Step 39: UnsatPaths WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
48. f36(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (7,5)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
50. f19(A,B,C,E,F,G,H,J) -> f70(A,B,1 + C,E,B,1,0,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && B >= 1] (7,4)
51. f19(A,B,C,E,F,G,H,J) -> f84(A,B,1 + C,E,B,-1 + B,B,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && 1 >= 1 + B && -1 + B >= 0] (7,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,3,4,41,49,50,51},3->{2,3,4,41,49,50,51},4->{2,3,4,41,49,50,51},6->{8,22},7->{8,22},8->{8,22},9->{6
,7,9,36,37,47,48},11->{11,32,44,45,46},13->{13,29,43},15->{15,28},22->{6,7,9,36,37,47,48},27->{2,3,4,41,49
,50,51},28->{15,28},29->{13,29,43},32->{11,32,44,45,46},36->{11,32,44,45,46},37->{6,7,9,36,37,47,48},41->{2
,3,4,41,49,50,51},43->{15,28},44->{6,7,9,36,37,47,48},45->{13,29,43},46->{15,28},47->{13,29,43},48->{15,28}
,49->{6,7,9,36,37,47,48},50->{13,29,43},51->{15,28}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<48,0,A>, 50) (<48,0,B>, 5) (<48,0,C>, ?) (<48,0,E>, ?) (<48,0,F>, 5) (<48,0,G>, ?) (<48,0,H>, ?) (<48,0,J>, ?)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, ?) (<49,0,E>, ?) (<49,0,F>, 5) (<49,0,G>, 5) (<49,0,H>, ?) (<49,0,J>, ?)
(<50,0,A>, 50) (<50,0,B>, 5) (<50,0,C>, ?) (<50,0,E>, ?) (<50,0,F>, 5) (<50,0,G>, 5) (<50,0,H>, 0) (<50,0,J>, ?)
(<51,0,A>, 50) (<51,0,B>, 5) (<51,0,C>, ?) (<51,0,E>, ?) (<51,0,F>, 5) (<51,0,G>, ?) (<51,0,H>, ?) (<51,0,J>, ?)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(2,3)
,(2,4)
,(2,49)
,(2,50)
,(2,51)
,(3,2)
,(3,41)
,(3,50)
,(3,51)
,(4,3)
,(4,4)
,(4,41)
,(4,50)
,(4,51)
,(6,8)
,(7,22)
,(9,6)
,(9,7)
,(9,37)
,(9,47)
,(9,48)
,(11,46)
,(22,37)
,(22,48)
,(27,2)
,(27,3)
,(27,41)
,(27,49)
,(27,50)
,(27,51)
,(29,43)
,(32,45)
,(32,46)
,(36,44)
,(36,45)
,(36,46)
,(37,6)
,(37,7)
,(37,9)
,(37,36)
,(37,37)
,(37,47)
,(37,48)
,(41,49)
,(41,50)
,(41,51)
,(43,28)
,(44,36)
,(44,37)
,(44,47)
,(44,48)
,(45,29)
,(45,43)
,(46,15)
,(46,28)
,(47,29)
,(47,43)
,(48,15)
,(48,28)
,(49,6)
,(49,7)
,(49,36)
,(49,37)
,(49,47)
,(49,48)
,(50,13)
,(50,29)
,(50,43)
,(51,15)
,(51,28)]
* Step 40: UnreachableRules WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
37. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [H >= 1 + F && 1 + G >= 1 + F && F >= 2 + G] (7,3)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
46. f54(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (77,5)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
48. f36(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && 1 >= 1 + F && -1 + F >= 0] (7,5)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
50. f19(A,B,C,E,F,G,H,J) -> f70(A,B,1 + C,E,B,1,0,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && B >= 1] (7,4)
51. f19(A,B,C,E,F,G,H,J) -> f84(A,B,1 + C,E,B,-1 + B,B,J) [E >= 1 + B && 1 + C >= 1 + B && 0 >= B && 1 >= 1 + B && -1 + B >= 0] (7,5)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},37->{},41->{2,3,4
,41},43->{15},44->{6,7,9},45->{13},46->{},47->{13},48->{},49->{9},50->{},51->{}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<37,0,A>, 50) (<37,0,B>, 5) (<37,0,C>, ?) (<37,0,E>, ?) (<37,0,F>, 5) (<37,0,G>, 5) (<37,0,H>, ?) (<37,0,J>, ?)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<46,0,A>, 50) (<46,0,B>, 5) (<46,0,C>, ?) (<46,0,E>, ?) (<46,0,F>, 5) (<46,0,G>, ?) (<46,0,H>, ?) (<46,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<48,0,A>, 50) (<48,0,B>, 5) (<48,0,C>, ?) (<48,0,E>, ?) (<48,0,F>, 5) (<48,0,G>, ?) (<48,0,H>, ?) (<48,0,J>, ?)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, ?) (<49,0,E>, ?) (<49,0,F>, 5) (<49,0,G>, 5) (<49,0,H>, ?) (<49,0,J>, ?)
(<50,0,A>, 50) (<50,0,B>, 5) (<50,0,C>, ?) (<50,0,E>, ?) (<50,0,F>, 5) (<50,0,G>, 5) (<50,0,H>, 0) (<50,0,J>, ?)
(<51,0,A>, 50) (<51,0,B>, 5) (<51,0,C>, ?) (<51,0,E>, ?) (<51,0,F>, 5) (<51,0,G>, ?) (<51,0,H>, ?) (<51,0,J>, ?)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [37,46,48,50,51]
* Step 41: LocalSizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 5) (< 2,0,E>, 6) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 5) (< 3,0,E>, 6) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 5) (< 4,0,E>, 5) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, 5) (< 6,0,G>, 0) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, 5) (< 7,0,G>, ?) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, 5) (< 8,0,G>, ?) (< 8,0,H>, 5) (< 8,0,J>, ?)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, ?)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, 5) (<11,0,G>, ?) (<11,0,H>, 5) (<11,0,J>, ?)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, 5) (<22,0,G>, ?) (<22,0,H>, 5) (<22,0,J>, ?)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 5) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, 5) (<32,0,G>, ?) (<32,0,H>, 5) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, 5) (<36,0,G>, ?) (<36,0,H>, 5) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 5) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, 5) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, 5) (<44,0,G>, 5) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, 5) (<45,0,G>, 5) (<45,0,H>, 0) (<45,0,J>, ?)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, 5) (<47,0,G>, 5) (<47,0,H>, 0) (<47,0,J>, ?)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, ?) (<49,0,E>, ?) (<49,0,F>, 5) (<49,0,G>, 5) (<49,0,H>, ?) (<49,0,J>, ?)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, C, .= 0) (< 2,0,E>, 1 + E, .+ 1) (< 2,0,F>, F, .= 0) (< 2,0,G>, G, .= 0) (< 2,0,H>, H, .= 0) (< 2,0,J>, J, .= 0)
(< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,E>, 1 + C + E, .* 1) (< 3,0,F>, F, .= 0) (< 3,0,G>, G, .= 0) (< 3,0,H>, H, .= 0) (< 3,0,J>, J, .= 0)
(< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,E>, 1 + C, .+ 1) (< 4,0,F>, F, .= 0) (< 4,0,G>, G, .= 0) (< 4,0,H>, H, .= 0) (< 4,0,J>, J, .= 0)
(< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0) (< 6,0,E>, E, .= 0) (< 6,0,F>, F, .= 0) (< 6,0,G>, G, .= 0) (< 6,0,H>, H, .= 0) (< 6,0,J>, 0, .= 0)
(< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0) (< 7,0,E>, E, .= 0) (< 7,0,F>, F, .= 0) (< 7,0,G>, G, .= 0) (< 7,0,H>, H, .= 0) (< 7,0,J>, 0, .= 0)
(< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, C, .= 0) (< 8,0,E>, E, .= 0) (< 8,0,F>, F, .= 0) (< 8,0,G>, G, .= 0) (< 8,0,H>, H, .= 0) (< 8,0,J>, 1 + J, .+ 1)
(< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, C, .= 0) (< 9,0,E>, E, .= 0) (< 9,0,F>, F, .= 0) (< 9,0,G>, 0, .= 0) (< 9,0,H>, 1 + H, .+ 1) (< 9,0,J>, J, .= 0)
(<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0) (<11,0,E>, E, .= 0) (<11,0,F>, F, .= 0) (<11,0,G>, G, .= 0) (<11,0,H>, H, .= 0) (<11,0,J>, 1 + J, .+ 1)
(<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,E>, E, .= 0) (<13,0,F>, F, .= 0) (<13,0,G>, G, .= 0) (<13,0,H>, 1 + H, .+ 1) (<13,0,J>, J, .= 0)
(<15,0,A>, A, .= 0) (<15,0,B>, B, .= 0) (<15,0,C>, C, .= 0) (<15,0,E>, E, .= 0) (<15,0,F>, F, .= 0) (<15,0,G>, G, .= 0) (<15,0,H>, 1 + H, .+ 1) (<15,0,J>, J, .= 0)
(<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, C, .= 0) (<22,0,E>, E, .= 0) (<22,0,F>, F, .= 0) (<22,0,G>, G, .= 0) (<22,0,H>, 1 + H, .+ 1) (<22,0,J>, J, .= 0)
(<27,0,A>, 50, .= 50) (<27,0,B>, 5, .= 5) (<27,0,C>, 0, .= 0) (<27,0,E>, 0, .= 0) (<27,0,F>, F, .= 0) (<27,0,G>, G, .= 0) (<27,0,H>, H, .= 0) (<27,0,J>, J, .= 0)
(<28,0,A>, A, .= 0) (<28,0,B>, B, .= 0) (<28,0,C>, C, .= 0) (<28,0,E>, E, .= 0) (<28,0,F>, F, .= 0) (<28,0,G>, 1 + G, .+ 1) (<28,0,H>, G, .= 0) (<28,0,J>, J, .= 0)
(<29,0,A>, A, .= 0) (<29,0,B>, B, .= 0) (<29,0,C>, C, .= 0) (<29,0,E>, E, .= 0) (<29,0,F>, F, .= 0) (<29,0,G>, 1 + G + H, .* 1) (<29,0,H>, 0, .= 0) (<29,0,J>, J, .= 0)
(<32,0,A>, A, .= 0) (<32,0,B>, B, .= 0) (<32,0,C>, C, .= 0) (<32,0,E>, E, .= 0) (<32,0,F>, F, .= 0) (<32,0,G>, G, .= 0) (<32,0,H>, 1 + H, .+ 1) (<32,0,J>, 0, .= 0)
(<36,0,A>, A, .= 0) (<36,0,B>, B, .= 0) (<36,0,C>, C, .= 0) (<36,0,E>, E, .= 0) (<36,0,F>, F, .= 0) (<36,0,G>, G, .= 0) (<36,0,H>, 1 + G, .+ 1) (<36,0,J>, 0, .= 0)
(<41,0,A>, A, .= 0) (<41,0,B>, B, .= 0) (<41,0,C>, 1 + C, .+ 1) (<41,0,E>, 0, .= 0) (<41,0,F>, F, .= 0) (<41,0,G>, G, .= 0) (<41,0,H>, H, .= 0) (<41,0,J>, J, .= 0)
(<43,0,A>, A, .= 0) (<43,0,B>, B, .= 0) (<43,0,C>, C, .= 0) (<43,0,E>, E, .= 0) (<43,0,F>, F, .= 0) (<43,0,G>, 1 + F, .+ 1) (<43,0,H>, F, .= 0) (<43,0,J>, J, .= 0)
(<44,0,A>, A, .= 0) (<44,0,B>, B, .= 0) (<44,0,C>, C, .= 0) (<44,0,E>, E, .= 0) (<44,0,F>, F, .= 0) (<44,0,G>, 1 + G, .+ 1) (<44,0,H>, 2 + G, .+ 2) (<44,0,J>, J, .= 0)
(<45,0,A>, A, .= 0) (<45,0,B>, B, .= 0) (<45,0,C>, C, .= 0) (<45,0,E>, E, .= 0) (<45,0,F>, F, .= 0) (<45,0,G>, 1, .= 1) (<45,0,H>, 0, .= 0) (<45,0,J>, J, .= 0)
(<47,0,A>, A, .= 0) (<47,0,B>, B, .= 0) (<47,0,C>, C, .= 0) (<47,0,E>, E, .= 0) (<47,0,F>, F, .= 0) (<47,0,G>, 1, .= 1) (<47,0,H>, 0, .= 0) (<47,0,J>, J, .= 0)
(<49,0,A>, A, .= 0) (<49,0,B>, B, .= 0) (<49,0,C>, 1 + C, .+ 1) (<49,0,E>, E, .= 0) (<49,0,F>, B, .= 0) (<49,0,G>, 0, .= 0) (<49,0,H>, 1, .= 1) (<49,0,J>, J, .= 0)
* Step 42: SizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,E>, ?) (< 2,0,F>, ?) (< 2,0,G>, ?) (< 2,0,H>, ?) (< 2,0,J>, ?)
(< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,E>, ?) (< 3,0,F>, ?) (< 3,0,G>, ?) (< 3,0,H>, ?) (< 3,0,J>, ?)
(< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,E>, ?) (< 4,0,F>, ?) (< 4,0,G>, ?) (< 4,0,H>, ?) (< 4,0,J>, ?)
(< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,F>, ?) (< 6,0,G>, ?) (< 6,0,H>, ?) (< 6,0,J>, ?)
(< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,F>, ?) (< 7,0,G>, ?) (< 7,0,H>, ?) (< 7,0,J>, ?)
(< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,F>, ?) (< 8,0,G>, ?) (< 8,0,H>, ?) (< 8,0,J>, ?)
(< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,F>, ?) (< 9,0,G>, ?) (< 9,0,H>, ?) (< 9,0,J>, ?)
(<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,E>, ?) (<11,0,F>, ?) (<11,0,G>, ?) (<11,0,H>, ?) (<11,0,J>, ?)
(<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,E>, ?) (<13,0,F>, ?) (<13,0,G>, ?) (<13,0,H>, ?) (<13,0,J>, ?)
(<15,0,A>, ?) (<15,0,B>, ?) (<15,0,C>, ?) (<15,0,E>, ?) (<15,0,F>, ?) (<15,0,G>, ?) (<15,0,H>, ?) (<15,0,J>, ?)
(<22,0,A>, ?) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,E>, ?) (<22,0,F>, ?) (<22,0,G>, ?) (<22,0,H>, ?) (<22,0,J>, ?)
(<27,0,A>, ?) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,E>, ?) (<27,0,F>, ?) (<27,0,G>, ?) (<27,0,H>, ?) (<27,0,J>, ?)
(<28,0,A>, ?) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,E>, ?) (<28,0,F>, ?) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, ?) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,E>, ?) (<29,0,F>, ?) (<29,0,G>, ?) (<29,0,H>, ?) (<29,0,J>, ?)
(<32,0,A>, ?) (<32,0,B>, ?) (<32,0,C>, ?) (<32,0,E>, ?) (<32,0,F>, ?) (<32,0,G>, ?) (<32,0,H>, ?) (<32,0,J>, ?)
(<36,0,A>, ?) (<36,0,B>, ?) (<36,0,C>, ?) (<36,0,E>, ?) (<36,0,F>, ?) (<36,0,G>, ?) (<36,0,H>, ?) (<36,0,J>, ?)
(<41,0,A>, ?) (<41,0,B>, ?) (<41,0,C>, ?) (<41,0,E>, ?) (<41,0,F>, ?) (<41,0,G>, ?) (<41,0,H>, ?) (<41,0,J>, ?)
(<43,0,A>, ?) (<43,0,B>, ?) (<43,0,C>, ?) (<43,0,E>, ?) (<43,0,F>, ?) (<43,0,G>, ?) (<43,0,H>, ?) (<43,0,J>, ?)
(<44,0,A>, ?) (<44,0,B>, ?) (<44,0,C>, ?) (<44,0,E>, ?) (<44,0,F>, ?) (<44,0,G>, ?) (<44,0,H>, ?) (<44,0,J>, ?)
(<45,0,A>, ?) (<45,0,B>, ?) (<45,0,C>, ?) (<45,0,E>, ?) (<45,0,F>, ?) (<45,0,G>, ?) (<45,0,H>, ?) (<45,0,J>, ?)
(<47,0,A>, ?) (<47,0,B>, ?) (<47,0,C>, ?) (<47,0,E>, ?) (<47,0,F>, ?) (<47,0,G>, ?) (<47,0,H>, ?) (<47,0,J>, ?)
(<49,0,A>, ?) (<49,0,B>, ?) (<49,0,C>, ?) (<49,0,E>, ?) (<49,0,F>, ?) (<49,0,G>, ?) (<49,0,H>, ?) (<49,0,J>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 43: LocationConstraintsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 2 : True 3 : [False] 4 : True 6 : [J >= G] 7 : [J >= G] 8 : [G >= 1] 9 : True 11 : True 13 : True 15 : True 22 : True 27 : True 28 : [False] 29 : [False] 32 : True 36 : True 41 : [False] 43 : [False] 44 : True 45 : [False] 47 : [J >= G] 49 : True .
* Step 44: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (?,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Constant}
+ Details:
We apply a polynomial interpretation of shape constant:
p(f0) = 1
p(f19) = 1
p(f36) = 1
p(f41) = 1
p(f54) = 1
p(f70) = 1
p(f84) = 0
The following rules are strictly oriented:
[H >= G && 1 + G >= 1 + F && -1 + F >= 0] ==>
f70(A,B,C,E,F,G,H,J) = 1
> 0
= f84(A,B,C,E,F,-1 + F,F,J)
The following rules are weakly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,C,1 + C,F,G,H,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,H,1 + J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,G,1 + H,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,G,1 + H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,G,1 + H,J)
[5 >= 0] ==>
f0(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(50,5,0,0,F,G,H,J)
[H >= 1 + F && -1 + G >= 0] ==>
f84(A,B,C,E,F,G,H,J) = 0
>= 0
= f84(A,B,C,E,F,-1 + G,G,J)
[H >= G && F >= 1 + G] ==>
f70(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,1 + G,0,J)
[J >= 1 + G && F >= 1 + H] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,1 + H,0)
[H >= 1 + F && F >= 1 + G] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f54(A,B,C,E,F,G,1 + G,0)
[E >= 1 + B && B >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f19(A,B,1 + C,0,F,G,H,J)
[J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,C,E,F,1 + G,2 + G,J)
[J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] ==>
f54(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,1,0,J)
[H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] ==>
f36(A,B,C,E,F,G,H,J) = 1
>= 1
= f70(A,B,C,E,F,1,0,J)
[E >= 1 + B && 1 + C >= 1 + B && B >= 1] ==>
f19(A,B,C,E,F,G,H,J) = 1
>= 1
= f36(A,B,1 + C,E,B,0,1,J)
* Step 45: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (?,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f0) = 5
p(f19) = x2
p(f36) = x5
p(f41) = x5
p(f54) = x5
p(f70) = x5
p(f84) = x6
The following rules are strictly oriented:
[H >= 1 + F && -1 + G >= 0] ==>
f84(A,B,C,E,F,G,H,J) = G
> -1 + G
= f84(A,B,C,E,F,-1 + G,G,J)
[H >= G && 1 + G >= 1 + F && -1 + F >= 0] ==>
f70(A,B,C,E,F,G,H,J) = F
> -1 + F
= f84(A,B,C,E,F,-1 + F,F,J)
The following rules are weakly oriented:
[B >= E && E >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = B
>= B
= f19(A,B,C,1 + E,F,G,H,J)
[C >= 1 + E && B >= E] ==>
f19(A,B,C,E,F,G,H,J) = B
>= B
= f19(A,B,C,1 + E,F,G,H,J)
[B >= E && C = E] ==>
f19(A,B,C,E,F,G,H,J) = B
>= B
= f19(A,B,C,1 + C,F,G,H,J)
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = F
>= F
= f54(A,B,C,E,F,G,H,1 + J)
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = F
>= F
= f70(A,B,C,E,F,G,1 + H,J)
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = G
>= G
= f84(A,B,C,E,F,G,1 + H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = F
>= F
= f36(A,B,C,E,F,G,1 + H,J)
[5 >= 0] ==>
f0(A,B,C,E,F,G,H,J) = 5
>= 5
= f19(50,5,0,0,F,G,H,J)
[H >= G && F >= 1 + G] ==>
f70(A,B,C,E,F,G,H,J) = F
>= F
= f70(A,B,C,E,F,1 + G,0,J)
[J >= 1 + G && F >= 1 + H] ==>
f54(A,B,C,E,F,G,H,J) = F
>= F
= f54(A,B,C,E,F,G,1 + H,0)
[H >= 1 + F && F >= 1 + G] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f54(A,B,C,E,F,G,1 + G,0)
[E >= 1 + B && B >= 1 + C] ==>
f19(A,B,C,E,F,G,H,J) = B
>= B
= f19(A,B,1 + C,0,F,G,H,J)
[J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] ==>
f54(A,B,C,E,F,G,H,J) = F
>= F
= f36(A,B,C,E,F,1 + G,2 + G,J)
[J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] ==>
f54(A,B,C,E,F,G,H,J) = F
>= F
= f70(A,B,C,E,F,1,0,J)
[H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f70(A,B,C,E,F,1,0,J)
[E >= 1 + B && 1 + C >= 1 + B && B >= 1] ==>
f19(A,B,C,E,F,G,H,J) = B
>= B
= f36(A,B,1 + C,E,B,0,1,J)
* Step 46: SizeboundsProc WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, ?)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, ?) (<15,0,H>, 6) (<15,0,J>, ?)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, ?) (<28,0,H>, ?) (<28,0,J>, ?)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, ?)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, ?)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 47: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (?,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [9,22,6,44,11,32,8,7], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = 2 + x5 + -1*x7
p(f41) = 1 + x5 + -1*x7
p(f54) = 1 + x5 + -1*x6
The following rules are strictly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + -1*H
> 1 + F + -1*H
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + -1*H
> 1 + F + -1*H
= f41(A,B,C,E,F,G,H,0)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 2 + F + -1*H
> 1 + F + -1*H
= f36(A,B,C,E,F,0,1 + H,J)
[J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*G
> F + -1*G
= f36(A,B,C,E,F,1 + G,2 + G,J)
The following rules are weakly oriented:
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*H
>= 1 + F + -1*H
= f41(A,B,C,E,F,G,H,1 + J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f54(A,B,C,E,F,G,H,1 + J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1 + F + -1*H
>= 1 + F + -1*H
= f36(A,B,C,E,F,G,1 + H,J)
[J >= 1 + G && F >= 1 + H] ==>
f54(A,B,C,E,F,G,H,J) = 1 + F + -1*G
>= 1 + F + -1*G
= f54(A,B,C,E,F,G,1 + H,0)
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 48: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (?,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [9,22,6,11,36,8,7], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = x5
p(f41) = x5
p(f54) = 1 + x6 + -1*x8
The following rules are strictly oriented:
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 1 + G + -1*J
> G + -1*J
= f54(A,B,C,E,F,G,H,1 + J)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,0)
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = F
>= F
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = F
>= F
= f36(A,B,C,E,F,0,1 + H,J)
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = F
>= F
= f36(A,B,C,E,F,G,1 + H,J)
[H >= 1 + F && F >= 1 + G] ==>
f36(A,B,C,E,F,G,H,J) = F
>= 1 + G
= f54(A,B,C,E,F,G,1 + G,0)
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 49: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (?,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [9,22,44,11,32,36,8], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = 0
p(f41) = 1
p(f54) = 0
The following rules are strictly oriented:
[J >= G] ==>
f41(A,B,C,E,F,G,H,J) = 1
> 0
= f36(A,B,C,E,F,G,1 + H,J)
The following rules are weakly oriented:
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = 1
>= 1
= f41(A,B,C,E,F,G,H,1 + J)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G && F >= 1 + H] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,1 + H,0)
[H >= 1 + F && F >= 1 + G] ==>
f36(A,B,C,E,F,G,H,J) = 0
>= 0
= f54(A,B,C,E,F,G,1 + G,0)
[J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] ==>
f54(A,B,C,E,F,G,H,J) = 0
>= 0
= f36(A,B,C,E,F,1 + G,2 + G,J)
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 50: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (?,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (685,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [9,6,11,32,36,8,7], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f36) = x6
p(f41) = x6 + -1*x8
p(f54) = x6
The following rules are strictly oriented:
[G >= 1 + J] ==>
f41(A,B,C,E,F,G,H,J) = G + -1*J
> -1 + G + -1*J
= f41(A,B,C,E,F,G,H,1 + J)
The following rules are weakly oriented:
[0 >= 1 + G && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = G
>= G
= f41(A,B,C,E,F,G,H,0)
[G >= 1 && F >= H] ==>
f36(A,B,C,E,F,G,H,J) = G
>= G
= f41(A,B,C,E,F,G,H,0)
[F >= H && G = 0] ==>
f36(A,B,C,E,F,G,H,J) = G
>= 0
= f36(A,B,C,E,F,0,1 + H,J)
[G >= J] ==>
f54(A,B,C,E,F,G,H,J) = G
>= G
= f54(A,B,C,E,F,G,H,1 + J)
[J >= 1 + G && F >= 1 + H] ==>
f54(A,B,C,E,F,G,H,J) = G
>= G
= f54(A,B,C,E,F,G,1 + H,0)
[H >= 1 + F && F >= 1 + G] ==>
f36(A,B,C,E,F,G,H,J) = G
>= G
= f54(A,B,C,E,F,G,1 + G,0)
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 51: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (58674,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (685,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (?,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [13,29], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f70) = x5 + -1*x6
The following rules are strictly oriented:
[H >= G && F >= 1 + G] ==>
f70(A,B,C,E,F,G,H,J) = F + -1*G
> -1 + F + -1*G
= f70(A,B,C,E,F,1 + G,0,J)
The following rules are weakly oriented:
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = F + -1*G
>= F + -1*G
= f70(A,B,C,E,F,G,1 + H,J)
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 52: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (58674,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (?,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (685,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (504,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [13], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f70) = x6 + -1*x7
The following rules are strictly oriented:
[G >= 1 + H] ==>
f70(A,B,C,E,F,G,H,J) = G + -1*H
> -1 + G + -1*H
= f70(A,B,C,E,F,G,1 + H,J)
The following rules are weakly oriented:
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 53: PolyRank WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (58674,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (2604,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (?,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (685,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (504,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [15], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f84) = 1 + x5 + -1*x7
The following rules are strictly oriented:
[F >= H] ==>
f84(A,B,C,E,F,G,H,J) = 1 + F + -1*H
> F + -1*H
= f84(A,B,C,E,F,G,1 + H,J)
The following rules are weakly oriented:
We use the following global sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
* Step 54: KnowledgePropagation WORST_CASE(?,O(1))
+ Considered Problem:
Rules:
2. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [B >= E && E >= 1 + C] (42,1)
3. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + E,F,G,H,J) [C >= 1 + E && B >= E] (42,1)
4. f19(A,B,C,E,F,G,H,J) -> f19(A,B,C,1 + C,F,G,H,J) [B >= E && C = E] (42,1)
6. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [0 >= 1 + G && F >= H] (637,1)
7. f36(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,0) [G >= 1 && F >= H] (48,1)
8. f41(A,B,C,E,F,G,H,J) -> f41(A,B,C,E,F,G,H,1 + J) [G >= 1 + J] (58674,1)
9. f36(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,0,1 + H,J) [F >= H && G = 0] (48,1)
11. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,H,1 + J) [G >= J] (6426,1)
13. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,G,1 + H,J) [G >= 1 + H] (2604,1)
15. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,G,1 + H,J) [F >= H] (96,1)
22. f41(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,G,1 + H,J) [J >= G] (685,1)
27. f0(A,B,C,E,F,G,H,J) -> f19(50,5,0,0,F,G,H,J) [5 >= 0] (1,2)
28. f84(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + G,G,J) [H >= 1 + F && -1 + G >= 0] (5,2)
29. f70(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1 + G,0,J) [H >= G && F >= 1 + G] (504,2)
32. f54(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + H,0) [J >= 1 + G && F >= 1 + H] (77,2)
36. f36(A,B,C,E,F,G,H,J) -> f54(A,B,C,E,F,G,1 + G,0) [H >= 1 + F && F >= 1 + G] (7,2)
41. f19(A,B,C,E,F,G,H,J) -> f19(A,B,1 + C,0,F,G,H,J) [E >= 1 + B && B >= 1 + C] (7,2)
43. f70(A,B,C,E,F,G,H,J) -> f84(A,B,C,E,F,-1 + F,F,J) [H >= G && 1 + G >= 1 + F && -1 + F >= 0] (1,3)
44. f54(A,B,C,E,F,G,H,J) -> f36(A,B,C,E,F,1 + G,2 + G,J) [J >= 1 + G && 1 + H >= 1 + F && F >= 2 + G] (77,3)
45. f54(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [J >= 1 + G && 1 + H >= 1 + F && 1 + G >= F && F >= 1] (77,4)
47. f36(A,B,C,E,F,G,H,J) -> f70(A,B,C,E,F,1,0,J) [H >= 1 + F && 1 + G >= 1 + F && 1 + G >= F && F >= 1] (7,4)
49. f19(A,B,C,E,F,G,H,J) -> f36(A,B,1 + C,E,B,0,1,J) [E >= 1 + B && 1 + C >= 1 + B && B >= 1] (7,3)
Signature:
{(f0,8);(f15,8);(f19,8);(f33,8);(f36,8);(f41,8);(f50,8);(f54,8);(f66,8);(f70,8);(f80,8);(f84,8);(f96,8)}
Flow Graph:
[2->{2,41},3->{3,4,49},4->{2,49},6->{22},7->{8},8->{8,22},9->{9,36},11->{11,32,44,45},13->{13,29,43}
,15->{15,28},22->{6,7,9,36,47},27->{4},28->{15,28},29->{13,29},32->{11,32,44},36->{11,32},41->{2,3,4,41}
,43->{15},44->{6,7,9},45->{13},47->{13},49->{9}]
Sizebounds:
(< 2,0,A>, 50) (< 2,0,B>, 5) (< 2,0,C>, 7) (< 2,0,E>, 50) (< 2,0,F>, F) (< 2,0,G>, G) (< 2,0,H>, H) (< 2,0,J>, J)
(< 3,0,A>, 50) (< 3,0,B>, 5) (< 3,0,C>, 7) (< 3,0,E>, 343) (< 3,0,F>, F) (< 3,0,G>, G) (< 3,0,H>, H) (< 3,0,J>, J)
(< 4,0,A>, 50) (< 4,0,B>, 5) (< 4,0,C>, 7) (< 4,0,E>, 8) (< 4,0,F>, F) (< 4,0,G>, G) (< 4,0,H>, H) (< 4,0,J>, J)
(< 6,0,A>, 50) (< 6,0,B>, 5) (< 6,0,C>, 8) (< 6,0,E>, 343) (< 6,0,F>, 5) (< 6,0,G>, 77) (< 6,0,H>, 5) (< 6,0,J>, 0)
(< 7,0,A>, 50) (< 7,0,B>, 5) (< 7,0,C>, 8) (< 7,0,E>, 343) (< 7,0,F>, 5) (< 7,0,G>, 77) (< 7,0,H>, 5) (< 7,0,J>, 0)
(< 8,0,A>, 50) (< 8,0,B>, 5) (< 8,0,C>, 8) (< 8,0,E>, 343) (< 8,0,F>, 5) (< 8,0,G>, 77) (< 8,0,H>, 5) (< 8,0,J>, 77)
(< 9,0,A>, 50) (< 9,0,B>, 5) (< 9,0,C>, 8) (< 9,0,E>, 343) (< 9,0,F>, 5) (< 9,0,G>, 0) (< 9,0,H>, 6) (< 9,0,J>, 78 + J)
(<11,0,A>, 50) (<11,0,B>, 5) (<11,0,C>, 8) (<11,0,E>, 343) (<11,0,F>, 5) (<11,0,G>, 77) (<11,0,H>, 155) (<11,0,J>, 78)
(<13,0,A>, 50) (<13,0,B>, 5) (<13,0,C>, 8) (<13,0,E>, 343) (<13,0,F>, 5) (<13,0,G>, 5) (<13,0,H>, 5) (<13,0,J>, 78)
(<15,0,A>, 50) (<15,0,B>, 5) (<15,0,C>, 8) (<15,0,E>, 343) (<15,0,F>, 5) (<15,0,G>, 11) (<15,0,H>, 6) (<15,0,J>, 78)
(<22,0,A>, 50) (<22,0,B>, 5) (<22,0,C>, 8) (<22,0,E>, 343) (<22,0,F>, 5) (<22,0,G>, 77) (<22,0,H>, 5) (<22,0,J>, 77)
(<27,0,A>, 50) (<27,0,B>, 5) (<27,0,C>, 0) (<27,0,E>, 0) (<27,0,F>, F) (<27,0,G>, G) (<27,0,H>, H) (<27,0,J>, J)
(<28,0,A>, 50) (<28,0,B>, 5) (<28,0,C>, 8) (<28,0,E>, 343) (<28,0,F>, 5) (<28,0,G>, 11) (<28,0,H>, 11) (<28,0,J>, 78)
(<29,0,A>, 50) (<29,0,B>, 5) (<29,0,C>, 8) (<29,0,E>, 343) (<29,0,F>, 5) (<29,0,G>, 5) (<29,0,H>, 0) (<29,0,J>, 78)
(<32,0,A>, 50) (<32,0,B>, 5) (<32,0,C>, 8) (<32,0,E>, 343) (<32,0,F>, 5) (<32,0,G>, 77) (<32,0,H>, 155) (<32,0,J>, 0)
(<36,0,A>, 50) (<36,0,B>, 5) (<36,0,C>, 8) (<36,0,E>, 343) (<36,0,F>, 5) (<36,0,G>, 77) (<36,0,H>, 78) (<36,0,J>, 0)
(<41,0,A>, 50) (<41,0,B>, 5) (<41,0,C>, 7) (<41,0,E>, 0) (<41,0,F>, F) (<41,0,G>, G) (<41,0,H>, H) (<41,0,J>, J)
(<43,0,A>, 50) (<43,0,B>, 5) (<43,0,C>, 8) (<43,0,E>, 343) (<43,0,F>, 5) (<43,0,G>, 6) (<43,0,H>, 5) (<43,0,J>, 78)
(<44,0,A>, 50) (<44,0,B>, 5) (<44,0,C>, 8) (<44,0,E>, 343) (<44,0,F>, 5) (<44,0,G>, 77) (<44,0,H>, 79) (<44,0,J>, 78)
(<45,0,A>, 50) (<45,0,B>, 5) (<45,0,C>, 8) (<45,0,E>, 343) (<45,0,F>, 5) (<45,0,G>, 1) (<45,0,H>, 0) (<45,0,J>, 78)
(<47,0,A>, 50) (<47,0,B>, 5) (<47,0,C>, 8) (<47,0,E>, 343) (<47,0,F>, 5) (<47,0,G>, 1) (<47,0,H>, 0) (<47,0,J>, 77)
(<49,0,A>, 50) (<49,0,B>, 5) (<49,0,C>, 8) (<49,0,E>, 343) (<49,0,F>, 5) (<49,0,G>, 0) (<49,0,H>, 1) (<49,0,J>, J)
+ Applied Processor:
KnowledgePropagation
+ Details:
The problem is already solved.
WORST_CASE(?,O(1))