WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) True (1,1)
1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,0,1,P,O,7,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
2. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,0,1,P,O,7,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
3. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,1 + C,1 + C,1 + E,1 + E,P,4,1,1,P,4,7,M,N) [7 >= P && P >= 1] (?,1)
4. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,C,C,E,E,3,P,0,0,3,P,2,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,C,C,E,E,3,P,0,0,3,P,2,M,N) [7 >= P && P >= 5] (?,1)
6. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,1 + C,1 + C,1 + E,1 + E,3,4,1,0,3,4,2,M,N) True (?,1)
7. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,H,1,P,O,7,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
8. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,H,1,P,O,7,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
9. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,1 + C,1 + C,1 + E,1 + E,P,4,1,1,P,4,7,M,N) [7 >= P && P >= 1] (?,1)
10. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f3(0,C,C,E,E,P,O,H,0,P,O,3,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f3(0,C,C,E,E,P,O,H,0,P,O,3,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f3(0,1 + C,1 + C,1 + E,1 + E,P,4,1,0,P,4,3,M,N) [7 >= P && P >= 1] (?,1)
13. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f6(1,C,C,E,E,P,O,H,1,P,O,6,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f6(1,C,C,E,E,P,O,H,1,P,O,6,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f6(1,1 + C,1 + C,1 + E,1 + E,P,4,1,1,P,4,6,M,N) [7 >= P && P >= 1] (?,1)
16. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,C,C,E,E,O,2,0,P,O,2,4,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,C,C,E,E,O,7,1,P,O,7,4,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,C,C,E,E,P,O,0,0,P,O,2,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,C,C,E,E,P,O,0,0,P,O,2,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f2(0,1 + C,1 + C,1 + E,1 + E,P,4,0,0,P,4,2,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
21. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(0,C,C,E,E,P,O,H,0,P,O,7,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
22. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(0,C,C,E,E,P,O,H,0,P,O,7,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
23. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(0,1 + C,1 + C,1 + E,1 + E,P,4,1,0,P,4,7,M,N) [1 + E >= M && 1 + C >= N && 7 >= P && P >= 1] (?,1)
24. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,H,1,P,O,7,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
25. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,C,C,E,E,P,O,H,1,P,O,7,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
26. f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f7(1,1 + C,1 + C,1 + E,1 + E,P,4,1,1,P,4,7,M,N) [7 >= P && P >= 1] (?,1)
Signature:
{(f1,14);(f2,14);(f3,14);(f4,14);(f6,14);(f7,14);(f8,14)}
Flow Graph:
[0->{1,2,3,4,5,6},1->{},2->{},3->{},4->{7,8,9,10,11,12},5->{7,8,9,10,11,12},6->{7,8,9,10,11,12},7->{}
,8->{},9->{},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20
,21,22,23,24,25,26},17->{18,19,20,21,22,23,24,25,26},18->{7,8,9,10,11,12},19->{7,8,9,10,11,12},20->{7,8,9,10
,11,12},21->{},22->{},23->{},24->{},25->{},26->{}]
+ Applied Processor:
RestrictVarsProcessor
+ Details:
We removed the arguments [A,B,D,F,G,I,J,K,L] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
1. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
2. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
3. f1(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
7. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
8. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
9. f2(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
21. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
22. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
23. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [1 + E >= M && 1 + C >= N && 7 >= P && P >= 1] (?,1)
24. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
25. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
26. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{1,2,3,4,5,6},1->{},2->{},3->{},4->{7,8,9,10,11,12},5->{7,8,9,10,11,12},6->{7,8,9,10,11,12},7->{}
,8->{},9->{},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20
,21,22,23,24,25,26},17->{18,19,20,21,22,23,24,25,26},18->{7,8,9,10,11,12},19->{7,8,9,10,11,12},20->{7,8,9,10
,11,12},21->{},22->{},23->{},24->{},25->{},26->{}]
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 0,0,C>, C, .= 0) (< 0,0,E>, E, .= 0) (< 0,0,H>, H, .= 0) (< 0,0,M>, M, .= 0) (< 0,0,N>, N, .= 0)
(< 1,0,C>, C, .= 0) (< 1,0,E>, E, .= 0) (< 1,0,H>, 0, .= 0) (< 1,0,M>, M, .= 0) (< 1,0,N>, N, .= 0)
(< 2,0,C>, C, .= 0) (< 2,0,E>, E, .= 0) (< 2,0,H>, 0, .= 0) (< 2,0,M>, M, .= 0) (< 2,0,N>, N, .= 0)
(< 3,0,C>, 1 + C, .+ 1) (< 3,0,E>, 1 + E, .+ 1) (< 3,0,H>, 1, .= 1) (< 3,0,M>, M, .= 0) (< 3,0,N>, N, .= 0)
(< 4,0,C>, C, .= 0) (< 4,0,E>, E, .= 0) (< 4,0,H>, 0, .= 0) (< 4,0,M>, M, .= 0) (< 4,0,N>, N, .= 0)
(< 5,0,C>, C, .= 0) (< 5,0,E>, E, .= 0) (< 5,0,H>, 0, .= 0) (< 5,0,M>, M, .= 0) (< 5,0,N>, N, .= 0)
(< 6,0,C>, 1 + C, .+ 1) (< 6,0,E>, 1 + E, .+ 1) (< 6,0,H>, 1, .= 1) (< 6,0,M>, M, .= 0) (< 6,0,N>, N, .= 0)
(< 7,0,C>, C, .= 0) (< 7,0,E>, E, .= 0) (< 7,0,H>, H, .= 0) (< 7,0,M>, M, .= 0) (< 7,0,N>, N, .= 0)
(< 8,0,C>, C, .= 0) (< 8,0,E>, E, .= 0) (< 8,0,H>, H, .= 0) (< 8,0,M>, M, .= 0) (< 8,0,N>, N, .= 0)
(< 9,0,C>, 1 + C, .+ 1) (< 9,0,E>, 1 + E, .+ 1) (< 9,0,H>, 1, .= 1) (< 9,0,M>, M, .= 0) (< 9,0,N>, N, .= 0)
(<10,0,C>, C, .= 0) (<10,0,E>, E, .= 0) (<10,0,H>, H, .= 0) (<10,0,M>, M, .= 0) (<10,0,N>, N, .= 0)
(<11,0,C>, C, .= 0) (<11,0,E>, E, .= 0) (<11,0,H>, H, .= 0) (<11,0,M>, M, .= 0) (<11,0,N>, N, .= 0)
(<12,0,C>, 1 + C, .+ 1) (<12,0,E>, 1 + E, .+ 1) (<12,0,H>, 1, .= 1) (<12,0,M>, M, .= 0) (<12,0,N>, N, .= 0)
(<13,0,C>, C, .= 0) (<13,0,E>, E, .= 0) (<13,0,H>, H, .= 0) (<13,0,M>, M, .= 0) (<13,0,N>, N, .= 0)
(<14,0,C>, C, .= 0) (<14,0,E>, E, .= 0) (<14,0,H>, H, .= 0) (<14,0,M>, M, .= 0) (<14,0,N>, N, .= 0)
(<15,0,C>, 1 + C, .+ 1) (<15,0,E>, 1 + E, .+ 1) (<15,0,H>, 1, .= 1) (<15,0,M>, M, .= 0) (<15,0,N>, N, .= 0)
(<16,0,C>, C, .= 0) (<16,0,E>, E, .= 0) (<16,0,H>, 0, .= 0) (<16,0,M>, M, .= 0) (<16,0,N>, N, .= 0)
(<17,0,C>, C, .= 0) (<17,0,E>, E, .= 0) (<17,0,H>, 1, .= 1) (<17,0,M>, M, .= 0) (<17,0,N>, N, .= 0)
(<18,0,C>, C, .= 0) (<18,0,E>, E, .= 0) (<18,0,H>, 0, .= 0) (<18,0,M>, M, .= 0) (<18,0,N>, N, .= 0)
(<19,0,C>, C, .= 0) (<19,0,E>, E, .= 0) (<19,0,H>, 0, .= 0) (<19,0,M>, M, .= 0) (<19,0,N>, N, .= 0)
(<20,0,C>, 1 + C, .+ 1) (<20,0,E>, 1 + E, .+ 1) (<20,0,H>, 0, .= 0) (<20,0,M>, M, .= 0) (<20,0,N>, N, .= 0)
(<21,0,C>, C, .= 0) (<21,0,E>, E, .= 0) (<21,0,H>, H, .= 0) (<21,0,M>, M, .= 0) (<21,0,N>, N, .= 0)
(<22,0,C>, C, .= 0) (<22,0,E>, E, .= 0) (<22,0,H>, H, .= 0) (<22,0,M>, M, .= 0) (<22,0,N>, N, .= 0)
(<23,0,C>, 1 + C, .+ 1) (<23,0,E>, 1 + E, .+ 1) (<23,0,H>, 1, .= 1) (<23,0,M>, M, .= 0) (<23,0,N>, N, .= 0)
(<24,0,C>, C, .= 0) (<24,0,E>, E, .= 0) (<24,0,H>, H, .= 0) (<24,0,M>, M, .= 0) (<24,0,N>, N, .= 0)
(<25,0,C>, C, .= 0) (<25,0,E>, E, .= 0) (<25,0,H>, H, .= 0) (<25,0,M>, M, .= 0) (<25,0,N>, N, .= 0)
(<26,0,C>, 1 + C, .+ 1) (<26,0,E>, 1 + E, .+ 1) (<26,0,H>, 1, .= 1) (<26,0,M>, M, .= 0) (<26,0,N>, N, .= 0)
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
1. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
2. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
3. f1(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
7. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
8. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
9. f2(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
21. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
22. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
23. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [1 + E >= M && 1 + C >= N && 7 >= P && P >= 1] (?,1)
24. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
25. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
26. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{1,2,3,4,5,6},1->{},2->{},3->{},4->{7,8,9,10,11,12},5->{7,8,9,10,11,12},6->{7,8,9,10,11,12},7->{}
,8->{},9->{},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20
,21,22,23,24,25,26},17->{18,19,20,21,22,23,24,25,26},18->{7,8,9,10,11,12},19->{7,8,9,10,11,12},20->{7,8,9,10
,11,12},21->{},22->{},23->{},24->{},25->{},26->{}]
Sizebounds:
(< 0,0,C>, ?) (< 0,0,E>, ?) (< 0,0,H>, ?) (< 0,0,M>, ?) (< 0,0,N>, ?)
(< 1,0,C>, ?) (< 1,0,E>, ?) (< 1,0,H>, ?) (< 1,0,M>, ?) (< 1,0,N>, ?)
(< 2,0,C>, ?) (< 2,0,E>, ?) (< 2,0,H>, ?) (< 2,0,M>, ?) (< 2,0,N>, ?)
(< 3,0,C>, ?) (< 3,0,E>, ?) (< 3,0,H>, ?) (< 3,0,M>, ?) (< 3,0,N>, ?)
(< 4,0,C>, ?) (< 4,0,E>, ?) (< 4,0,H>, ?) (< 4,0,M>, ?) (< 4,0,N>, ?)
(< 5,0,C>, ?) (< 5,0,E>, ?) (< 5,0,H>, ?) (< 5,0,M>, ?) (< 5,0,N>, ?)
(< 6,0,C>, ?) (< 6,0,E>, ?) (< 6,0,H>, ?) (< 6,0,M>, ?) (< 6,0,N>, ?)
(< 7,0,C>, ?) (< 7,0,E>, ?) (< 7,0,H>, ?) (< 7,0,M>, ?) (< 7,0,N>, ?)
(< 8,0,C>, ?) (< 8,0,E>, ?) (< 8,0,H>, ?) (< 8,0,M>, ?) (< 8,0,N>, ?)
(< 9,0,C>, ?) (< 9,0,E>, ?) (< 9,0,H>, ?) (< 9,0,M>, ?) (< 9,0,N>, ?)
(<10,0,C>, ?) (<10,0,E>, ?) (<10,0,H>, ?) (<10,0,M>, ?) (<10,0,N>, ?)
(<11,0,C>, ?) (<11,0,E>, ?) (<11,0,H>, ?) (<11,0,M>, ?) (<11,0,N>, ?)
(<12,0,C>, ?) (<12,0,E>, ?) (<12,0,H>, ?) (<12,0,M>, ?) (<12,0,N>, ?)
(<13,0,C>, ?) (<13,0,E>, ?) (<13,0,H>, ?) (<13,0,M>, ?) (<13,0,N>, ?)
(<14,0,C>, ?) (<14,0,E>, ?) (<14,0,H>, ?) (<14,0,M>, ?) (<14,0,N>, ?)
(<15,0,C>, ?) (<15,0,E>, ?) (<15,0,H>, ?) (<15,0,M>, ?) (<15,0,N>, ?)
(<16,0,C>, ?) (<16,0,E>, ?) (<16,0,H>, ?) (<16,0,M>, ?) (<16,0,N>, ?)
(<17,0,C>, ?) (<17,0,E>, ?) (<17,0,H>, ?) (<17,0,M>, ?) (<17,0,N>, ?)
(<18,0,C>, ?) (<18,0,E>, ?) (<18,0,H>, ?) (<18,0,M>, ?) (<18,0,N>, ?)
(<19,0,C>, ?) (<19,0,E>, ?) (<19,0,H>, ?) (<19,0,M>, ?) (<19,0,N>, ?)
(<20,0,C>, ?) (<20,0,E>, ?) (<20,0,H>, ?) (<20,0,M>, ?) (<20,0,N>, ?)
(<21,0,C>, ?) (<21,0,E>, ?) (<21,0,H>, ?) (<21,0,M>, ?) (<21,0,N>, ?)
(<22,0,C>, ?) (<22,0,E>, ?) (<22,0,H>, ?) (<22,0,M>, ?) (<22,0,N>, ?)
(<23,0,C>, ?) (<23,0,E>, ?) (<23,0,H>, ?) (<23,0,M>, ?) (<23,0,N>, ?)
(<24,0,C>, ?) (<24,0,E>, ?) (<24,0,H>, ?) (<24,0,M>, ?) (<24,0,N>, ?)
(<25,0,C>, ?) (<25,0,E>, ?) (<25,0,H>, ?) (<25,0,M>, ?) (<25,0,N>, ?)
(<26,0,C>, ?) (<26,0,E>, ?) (<26,0,H>, ?) (<26,0,M>, ?) (<26,0,N>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 1,0,C>, C) (< 1,0,E>, E) (< 1,0,H>, 0) (< 1,0,M>, M) (< 1,0,N>, N)
(< 2,0,C>, C) (< 2,0,E>, E) (< 2,0,H>, 0) (< 2,0,M>, M) (< 2,0,N>, N)
(< 3,0,C>, 1 + C) (< 3,0,E>, 1 + E) (< 3,0,H>, 1) (< 3,0,M>, M) (< 3,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(< 7,0,C>, 1 + C + N) (< 7,0,E>, 1 + E + M) (< 7,0,H>, 1) (< 7,0,M>, M) (< 7,0,N>, N)
(< 8,0,C>, 1 + C + N) (< 8,0,E>, 1 + E + M) (< 8,0,H>, 1) (< 8,0,M>, M) (< 8,0,N>, N)
(< 9,0,C>, 2 + C + N) (< 9,0,E>, 2 + E + M) (< 9,0,H>, 1) (< 9,0,M>, M) (< 9,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, 1 + C + N) (<21,0,E>, 1 + E + M) (<21,0,H>, 1) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, 1 + C + N) (<22,0,E>, 1 + E + M) (<22,0,H>, 1) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C + N) (<23,0,E>, 1 + E + M) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
* Step 4: UnsatPaths WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
1. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
2. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
3. f1(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
7. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
8. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
9. f2(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
21. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
22. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
23. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [1 + E >= M && 1 + C >= N && 7 >= P && P >= 1] (?,1)
24. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
25. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
26. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{1,2,3,4,5,6},1->{},2->{},3->{},4->{7,8,9,10,11,12},5->{7,8,9,10,11,12},6->{7,8,9,10,11,12},7->{}
,8->{},9->{},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20
,21,22,23,24,25,26},17->{18,19,20,21,22,23,24,25,26},18->{7,8,9,10,11,12},19->{7,8,9,10,11,12},20->{7,8,9,10
,11,12},21->{},22->{},23->{},24->{},25->{},26->{}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 1,0,C>, C) (< 1,0,E>, E) (< 1,0,H>, 0) (< 1,0,M>, M) (< 1,0,N>, N)
(< 2,0,C>, C) (< 2,0,E>, E) (< 2,0,H>, 0) (< 2,0,M>, M) (< 2,0,N>, N)
(< 3,0,C>, 1 + C) (< 3,0,E>, 1 + E) (< 3,0,H>, 1) (< 3,0,M>, M) (< 3,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(< 7,0,C>, 1 + C + N) (< 7,0,E>, 1 + E + M) (< 7,0,H>, 1) (< 7,0,M>, M) (< 7,0,N>, N)
(< 8,0,C>, 1 + C + N) (< 8,0,E>, 1 + E + M) (< 8,0,H>, 1) (< 8,0,M>, M) (< 8,0,N>, N)
(< 9,0,C>, 2 + C + N) (< 9,0,E>, 2 + E + M) (< 9,0,H>, 1) (< 9,0,M>, M) (< 9,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, 1 + C + N) (<21,0,E>, 1 + E + M) (<21,0,H>, 1) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, 1 + C + N) (<22,0,E>, 1 + E + M) (<22,0,H>, 1) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C + N) (<23,0,E>, 1 + E + M) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(16,18),(16,19)]
* Step 5: LeafRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
1. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
2. f1(C,E,H,M,N) -> f7(C,E,0,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
3. f1(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
7. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
8. f2(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
9. f2(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
21. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
22. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [E >= M && C >= N && 7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
23. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [1 + E >= M && 1 + C >= N && 7 >= P && P >= 1] (?,1)
24. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
25. f4(C,E,H,M,N) -> f7(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
26. f4(C,E,H,M,N) -> f7(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{1,2,3,4,5,6},1->{},2->{},3->{},4->{7,8,9,10,11,12},5->{7,8,9,10,11,12},6->{7,8,9,10,11,12},7->{}
,8->{},9->{},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{20,21,22
,23,24,25,26},17->{18,19,20,21,22,23,24,25,26},18->{7,8,9,10,11,12},19->{7,8,9,10,11,12},20->{7,8,9,10,11
,12},21->{},22->{},23->{},24->{},25->{},26->{}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 1,0,C>, C) (< 1,0,E>, E) (< 1,0,H>, 0) (< 1,0,M>, M) (< 1,0,N>, N)
(< 2,0,C>, C) (< 2,0,E>, E) (< 2,0,H>, 0) (< 2,0,M>, M) (< 2,0,N>, N)
(< 3,0,C>, 1 + C) (< 3,0,E>, 1 + E) (< 3,0,H>, 1) (< 3,0,M>, M) (< 3,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(< 7,0,C>, 1 + C + N) (< 7,0,E>, 1 + E + M) (< 7,0,H>, 1) (< 7,0,M>, M) (< 7,0,N>, N)
(< 8,0,C>, 1 + C + N) (< 8,0,E>, 1 + E + M) (< 8,0,H>, 1) (< 8,0,M>, M) (< 8,0,N>, N)
(< 9,0,C>, 2 + C + N) (< 9,0,E>, 2 + E + M) (< 9,0,H>, 1) (< 9,0,M>, M) (< 9,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, 1 + C + N) (<21,0,E>, 1 + E + M) (<21,0,H>, 1) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, 1 + C + N) (<22,0,E>, 1 + E + M) (<22,0,H>, 1) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C + N) (<23,0,E>, 1 + E + M) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
+ Applied Processor:
LeafRules
+ Details:
The following transitions are estimated by its predecessors and are removed [1,2,3,7,8,9,21,22,23,24,25,26]
* Step 6: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (?,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{4,5,6},4->{10,11,12},5->{10,11,12},6->{10,11,12},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16
,17},14->{16,17},15->{16,17},16->{20},17->{18,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f1) = -13*x1 + 13*x5
p(f2) = -13*x1 + 13*x5
p(f3) = -13*x1 + 13*x5
p(f4) = -13*x1 + 13*x5
p(f6) = -13*x1 + 13*x5
p(f8) = -13*x1 + 13*x5
The following rules are strictly oriented:
[M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] ==>
f4(C,E,H,M,N) = -13*C + 13*N
> -13 + -13*C + 13*N
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
True ==>
f8(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f1(C,E,H,M,N)
[7 >= P && 3 >= P && P >= 1] ==>
f1(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f2(C,E,0,M,N)
[7 >= P && P >= 5] ==>
f1(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f2(C,E,0,M,N)
True ==>
f1(C,E,H,M,N) = -13*C + 13*N
>= -13 + -13*C + 13*N
= f2(1 + C,1 + E,1,M,N)
[7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] ==>
f2(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f3(C,E,H,M,N)
[7 >= O && 7 >= P && O >= 5 && P >= 1] ==>
f2(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f3(C,E,H,M,N)
[7 >= P && P >= 1] ==>
f2(C,E,H,M,N) = -13*C + 13*N
>= -13 + -13*C + 13*N
= f3(1 + C,1 + E,1,M,N)
[7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] ==>
f3(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f6(C,E,H,M,N)
[7 >= O && 7 >= P && O >= 5 && P >= 1] ==>
f3(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f6(C,E,H,M,N)
[7 >= P && P >= 1] ==>
f3(C,E,H,M,N) = -13*C + 13*N
>= -13 + -13*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1] ==>
f6(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f4(C,E,0,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] ==>
f6(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f4(C,E,1,M,N)
[M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] ==>
f4(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f2(C,E,0,M,N)
[M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] ==>
f4(C,E,H,M,N) = -13*C + 13*N
>= -13*C + 13*N
= f2(C,E,0,M,N)
* Step 7: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (?,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (?,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (?,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{4,5,6},4->{10,11,12},5->{10,11,12},6->{10,11,12},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16
,17},14->{16,17},15->{16,17},16->{20},17->{18,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 8: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (1,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (1,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (?,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{4,5,6},4->{10,11,12},5->{10,11,12},6->{10,11,12},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16
,17},14->{16,17},15->{16,17},16->{20},17->{18,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [10,18,17,13,11,19,16,14,12,15], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = 1
p(f3) = 1
p(f4) = x3
p(f6) = 1
The following rules are strictly oriented:
[7 >= O && 1 >= P && P >= 0 && O >= 1] ==>
f6(C,E,H,M,N) = 1
> 0
= f4(C,E,0,M,N)
The following rules are weakly oriented:
[7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] ==>
f2(C,E,H,M,N) = 1
>= 1
= f3(C,E,H,M,N)
[7 >= O && 7 >= P && O >= 5 && P >= 1] ==>
f2(C,E,H,M,N) = 1
>= 1
= f3(C,E,H,M,N)
[7 >= P && P >= 1] ==>
f2(C,E,H,M,N) = 1
>= 1
= f3(1 + C,1 + E,1,M,N)
[7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] ==>
f3(C,E,H,M,N) = 1
>= 1
= f6(C,E,H,M,N)
[7 >= O && 7 >= P && O >= 5 && P >= 1] ==>
f3(C,E,H,M,N) = 1
>= 1
= f6(C,E,H,M,N)
[7 >= P && P >= 1] ==>
f3(C,E,H,M,N) = 1
>= 1
= f6(1 + C,1 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] ==>
f6(C,E,H,M,N) = 1
>= 1
= f4(C,E,1,M,N)
[M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] ==>
f4(C,E,H,M,N) = H
>= 1
= f2(C,E,0,M,N)
[M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] ==>
f4(C,E,H,M,N) = H
>= 1
= f2(C,E,0,M,N)
We use the following global sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
* Step 9: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
0. f8(C,E,H,M,N) -> f1(C,E,H,M,N) True (1,1)
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (1,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (1,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[0->{4,5,6},4->{10,11,12},5->{10,11,12},6->{10,11,12},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16
,17},14->{16,17},15->{16,17},16->{20},17->{18,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12}]
Sizebounds:
(< 0,0,C>, C) (< 0,0,E>, E) (< 0,0,H>, H) (< 0,0,M>, M) (< 0,0,N>, N)
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
+ Applied Processor:
ChainProcessor False [0,4,5,6,10,11,12,13,14,15,16,17,18,19,20]
+ Details:
We chained rule 0 to obtain the rules [21,22,23] .
* Step 10: UnreachableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
4. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && 3 >= P && P >= 1] (1,1)
5. f1(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P && P >= 5] (1,1)
6. f1(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,1)
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[4->{10,11,12},5->{10,11,12},6->{10,11,12},10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17}
,14->{16,17},15->{16,17},16->{18,19,20},17->{18,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12},21->{10
,11,12},22->{10,11,12},23->{10,11,12}]
Sizebounds:
(< 4,0,C>, C) (< 4,0,E>, E) (< 4,0,H>, 0) (< 4,0,M>, M) (< 4,0,N>, N)
(< 5,0,C>, C) (< 5,0,E>, E) (< 5,0,H>, 0) (< 5,0,M>, M) (< 5,0,N>, N)
(< 6,0,C>, 1 + C) (< 6,0,E>, 1 + E) (< 6,0,H>, 1) (< 6,0,M>, M) (< 6,0,N>, N)
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [4,5,6]
* Step 11: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
10. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[10->{13,14,15},11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20},17->{18
,19,20},18->{10,11,12},19->{10,11,12},20->{10,11,12},21->{10,11,12},22->{10,11,12},23->{10,11,12}]
Sizebounds:
(<10,0,C>, 1 + C + N) (<10,0,E>, 1 + E + M) (<10,0,H>, 1) (<10,0,M>, M) (<10,0,N>, N)
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
+ Applied Processor:
ChainProcessor False [10,11,12,13,14,15,16,17,18,19,20,21,22,23]
+ Details:
We chained rule 10 to obtain the rules [24,25,26] .
* Step 12: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
11. f2(C,E,H,M,N) -> f3(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[11->{13,14,15},12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20},17->{18,19,20},18->{11
,12,24,25,26},19->{11,12,24,25,26},20->{11,12,24,25,26},21->{11,12,24,25,26},22->{11,12,24,25,26},23->{11,12
,24,25,26},24->{16,17},25->{16,17},26->{16,17}]
Sizebounds:
(<11,0,C>, 1 + C + N) (<11,0,E>, 1 + E + M) (<11,0,H>, 1) (<11,0,M>, M) (<11,0,N>, N)
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
+ Applied Processor:
ChainProcessor False [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]
+ Details:
We chained rule 11 to obtain the rules [27,28,29] .
* Step 13: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
12. f2(C,E,H,M,N) -> f3(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[12->{13,14,15},13->{16,17},14->{16,17},15->{16,17},16->{18,19,20},17->{18,19,20},18->{12,24,25,26,27,28
,29},19->{12,24,25,26,27,28,29},20->{12,24,25,26,27,28,29},21->{12,24,25,26,27,28,29},22->{12,24,25,26,27,28
,29},23->{12,24,25,26,27,28,29},24->{16,17},25->{16,17},26->{16,17},27->{16,17},28->{16,17},29->{16,17}]
Sizebounds:
(<12,0,C>, 1 + C + N) (<12,0,E>, 1 + E + M) (<12,0,H>, 1) (<12,0,M>, M) (<12,0,N>, N)
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
+ Applied Processor:
ChainProcessor False [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]
+ Details:
We chained rule 12 to obtain the rules [30,31,32] .
* Step 14: UnreachableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
13. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1] (?,1)
14. f3(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1] (?,1)
15. f3(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1] (?,1)
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[13->{16,17},14->{16,17},15->{16,17},16->{18,19,20},17->{18,19,20},18->{24,25,26,27,28,29,30,31,32}
,19->{24,25,26,27,28,29,30,31,32},20->{24,25,26,27,28,29,30,31,32},21->{24,25,26,27,28,29,30,31,32},22->{24
,25,26,27,28,29,30,31,32},23->{24,25,26,27,28,29,30,31,32},24->{16,17},25->{16,17},26->{16,17},27->{16,17}
,28->{16,17},29->{16,17},30->{16,17},31->{16,17},32->{16,17}]
Sizebounds:
(<13,0,C>, 1 + C + N) (<13,0,E>, 1 + E + M) (<13,0,H>, 1) (<13,0,M>, M) (<13,0,N>, N)
(<14,0,C>, 1 + C + N) (<14,0,E>, 1 + E + M) (<14,0,H>, 1) (<14,0,M>, M) (<14,0,N>, N)
(<15,0,C>, 1 + C + N) (<15,0,E>, 1 + E + M) (<15,0,H>, 1) (<15,0,M>, M) (<15,0,N>, N)
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [13,14,15]
* Step 15: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
16. f6(C,E,H,M,N) -> f4(C,E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1] (3 + 13*C + 13*N,1)
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[16->{18,19,20},17->{18,19,20},18->{24,25,26,27,28,29,30,31,32},19->{24,25,26,27,28,29,30,31,32},20->{24
,25,26,27,28,29,30,31,32},21->{24,25,26,27,28,29,30,31,32},22->{24,25,26,27,28,29,30,31,32},23->{24,25,26,27
,28,29,30,31,32},24->{16,17},25->{16,17},26->{16,17},27->{16,17},28->{16,17},29->{16,17},30->{16,17},31->{16
,17},32->{16,17}]
Sizebounds:
(<16,0,C>, 1 + C + N) (<16,0,E>, 1 + E + M) (<16,0,H>, 0) (<16,0,M>, M) (<16,0,N>, N)
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
+ Applied Processor:
ChainProcessor False [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]
+ Details:
We chained rule 16 to obtain the rules [33,34,35] .
* Step 16: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
17. f6(C,E,H,M,N) -> f4(C,E,1,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && H = 1] (?,1)
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[17->{18,19,20},18->{24,25,26,27,28,29,30,31,32},19->{24,25,26,27,28,29,30,31,32},20->{24,25,26,27,28,29
,30,31,32},21->{24,25,26,27,28,29,30,31,32},22->{24,25,26,27,28,29,30,31,32},23->{24,25,26,27,28,29,30,31
,32},24->{17,33,34,35},25->{17,33,34,35},26->{17,33,34,35},27->{17,33,34,35},28->{17,33,34,35},29->{17,33,34
,35},30->{17,33,34,35},31->{17,33,34,35},32->{17,33,34,35},33->{24,25,26,27,28,29,30,31,32},34->{24,25,26,27
,28,29,30,31,32},35->{24,25,26,27,28,29,30,31,32}]
Sizebounds:
(<17,0,C>, 1 + C + N) (<17,0,E>, 1 + E + M) (<17,0,H>, 1) (<17,0,M>, M) (<17,0,N>, N)
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
+ Applied Processor:
ChainProcessor False [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]
+ Details:
We chained rule 17 to obtain the rules [36,37,38] .
* Step 17: UnreachableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
18. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && H = 1] (?,1)
19. f4(C,E,H,M,N) -> f2(C,E,0,M,N) [M >= 1 && M >= 1 + E && N >= 1 && N >= 1 + C && 7 >= O && 7 >= P && O >= 5 && P >= 1 && H = 1] (?,1)
20. f4(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P && P >= 1] (13*C + 13*N,1)
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[18->{24,25,26,27,28,29,30,31,32},19->{24,25,26,27,28,29,30,31,32},20->{24,25,26,27,28,29,30,31,32}
,21->{24,25,26,27,28,29,30,31,32},22->{24,25,26,27,28,29,30,31,32},23->{24,25,26,27,28,29,30,31,32},24->{33
,34,35,36,37,38},25->{33,34,35,36,37,38},26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33,34,35,36,37
,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{24
,25,26,27,28,29,30,31,32},34->{24,25,26,27,28,29,30,31,32},35->{24,25,26,27,28,29,30,31,32},36->{24,25,26,27
,28,29,30,31,32},37->{24,25,26,27,28,29,30,31,32},38->{24,25,26,27,28,29,30,31,32}]
Sizebounds:
(<18,0,C>, N) (<18,0,E>, M) (<18,0,H>, 0) (<18,0,M>, M) (<18,0,N>, N)
(<19,0,C>, N) (<19,0,E>, M) (<19,0,H>, 0) (<19,0,M>, M) (<19,0,N>, N)
(<20,0,C>, N) (<20,0,E>, M) (<20,0,H>, 0) (<20,0,M>, M) (<20,0,N>, N)
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [18,19,20]
* Step 18: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
21. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1] (1,2)
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[21->{24,25,26,27,28,29,30,31,32},22->{24,25,26,27,28,29,30,31,32},23->{24,25,26,27,28,29,30,31,32}
,24->{33,34,35,36,37,38},25->{33,34,35,36,37,38},26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33,34
,35,36,37,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37
,38},33->{24,25,26,27,28,29,30,31,32},34->{24,25,26,27,28,29,30,31,32},35->{24,25,26,27,28,29,30,31,32}
,36->{24,25,26,27,28,29,30,31,32},37->{24,25,26,27,28,29,30,31,32},38->{24,25,26,27,28,29,30,31,32}]
Sizebounds:
(<21,0,C>, C) (<21,0,E>, E) (<21,0,H>, 0) (<21,0,M>, M) (<21,0,N>, N)
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
+ Applied Processor:
ChainProcessor False [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]
+ Details:
We chained rule 21 to obtain the rules [39,40,41,42,43,44,45,46,47] .
* Step 19: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
22. f8(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= P$ && P$ >= 5] (1,2)
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[22->{24,25,26,27,28,29,30,31,32},23->{24,25,26,27,28,29,30,31,32},24->{33,34,35,36,37,38},25->{33,34,35
,36,37,38},26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33,34,35,36,37,38},29->{33,34,35,36,37,38}
,30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{24,25,26,27,28,29,30,31,32}
,34->{24,25,26,27,28,29,30,31,32},35->{24,25,26,27,28,29,30,31,32},36->{24,25,26,27,28,29,30,31,32},37->{24
,25,26,27,28,29,30,31,32},38->{24,25,26,27,28,29,30,31,32},39->{33,34,35,36,37,38},40->{33,34,35,36,37,38}
,41->{33,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34,35,36,37,38},45->{33,34
,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38}]
Sizebounds:
(<22,0,C>, C) (<22,0,E>, E) (<22,0,H>, 0) (<22,0,M>, M) (<22,0,N>, N)
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
+ Applied Processor:
ChainProcessor False [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]
+ Details:
We chained rule 22 to obtain the rules [48,49,50,51,52,53,54,55,56] .
* Step 20: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
23. f8(C,E,H,M,N) -> f2(1 + C,1 + E,1,M,N) True (1,2)
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[23->{24,25,26,27,28,29,30,31,32},24->{33,34,35,36,37,38},25->{33,34,35,36,37,38},26->{33,34,35,36,37,38}
,27->{33,34,35,36,37,38},28->{33,34,35,36,37,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34
,35,36,37,38},32->{33,34,35,36,37,38},33->{24,25,26,27,28,29,30,31,32},34->{24,25,26,27,28,29,30,31,32}
,35->{24,25,26,27,28,29,30,31,32},36->{24,25,26,27,28,29,30,31,32},37->{24,25,26,27,28,29,30,31,32},38->{24
,25,26,27,28,29,30,31,32},39->{33,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34
,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37
,38},47->{33,34,35,36,37,38},48->{33,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33
,34,35,36,37,38},52->{33,34,35,36,37,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37
,38},56->{33,34,35,36,37,38}]
Sizebounds:
(<23,0,C>, 1 + C) (<23,0,E>, 1 + E) (<23,0,H>, 1) (<23,0,M>, M) (<23,0,N>, N)
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
+ Applied Processor:
ChainProcessor False [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]
+ Details:
We chained rule 23 to obtain the rules [57,58,59,60,61,62,63,64,65] .
* Step 21: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
24. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[24->{33,34,35,36,37,38},25->{33,34,35,36,37,38},26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33
,34,35,36,37,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37
,38},33->{24,25,26,27,28,29,30,31,32},34->{24,25,26,27,28,29,30,31,32},35->{24,25,26,27,28,29,30,31,32}
,36->{24,25,26,27,28,29,30,31,32},37->{24,25,26,27,28,29,30,31,32},38->{24,25,26,27,28,29,30,31,32},39->{33
,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37
,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33
,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37
,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33
,34,35,36,37,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37
,38},62->{33,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33,34,35,36,37,38},65->{33,34,35,36,37,38}]
Sizebounds:
(<24,0,C>, 1 + C + N) (<24,0,E>, 1 + E + M) (<24,0,H>, 1) (<24,0,M>, M) (<24,0,N>, N)
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
+ Applied Processor:
ChainProcessor False [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 24 to obtain the rules [66,67,68,69,70,71] .
* Step 22: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
25. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[25->{33,34,35,36,37,38},26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33,34,35,36,37,38},29->{33
,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{25,26,27,28,29
,30,31,32,66,67,68,69,70,71},34->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},35->{25,26,27,28,29,30,31,32,66
,67,68,69,70,71},36->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},37->{25,26,27,28,29,30,31,32,66,67,68,69,70
,71},38->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},39->{33,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33
,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37
,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33
,34,35,36,37,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37
,38},55->{33,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33,34,35,36,37,38},58->{33,34,35,36,37,38},59->{33
,34,35,36,37,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37,38},62->{33,34,35,36,37,38},63->{33,34,35,36,37
,38},64->{33,34,35,36,37,38},65->{33,34,35,36,37,38},66->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},67->{25
,26,27,28,29,30,31,32,66,67,68,69,70,71},68->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},69->{25,26,27,28,29
,30,31,32,66,67,68,69,70,71},70->{25,26,27,28,29,30,31,32,66,67,68,69,70,71},71->{25,26,27,28,29,30,31,32,66
,67,68,69,70,71}]
Sizebounds:
(<25,0,C>, 1 + C + N) (<25,0,E>, 1 + E + M) (<25,0,H>, 1) (<25,0,M>, M) (<25,0,N>, N)
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
(<66,0,C>, N) (<66,0,E>, M) (<66,0,H>, 0) (<66,0,M>, M) (<66,0,N>, N)
(<67,0,C>, N) (<67,0,E>, M) (<67,0,H>, 0) (<67,0,M>, M) (<67,0,N>, N)
(<68,0,C>, N) (<68,0,E>, M) (<68,0,H>, 0) (<68,0,M>, M) (<68,0,N>, N)
(<69,0,C>, N) (<69,0,E>, M) (<69,0,H>, 0) (<69,0,M>, M) (<69,0,N>, N)
(<70,0,C>, N) (<70,0,E>, M) (<70,0,H>, 0) (<70,0,M>, M) (<70,0,N>, N)
(<71,0,C>, N) (<71,0,E>, M) (<71,0,H>, 0) (<71,0,M>, M) (<71,0,N>, N)
+ Applied Processor:
ChainProcessor False [25,26,27,28,29,30,31,32,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 25 to obtain the rules [72,73,74,75,76,77] .
* Step 23: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
26. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && 3 >= O && O >= 1 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[26->{33,34,35,36,37,38},27->{33,34,35,36,37,38},28->{33,34,35,36,37,38},29->{33,34,35,36,37,38},30->{33
,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{26,27,28,29,30,31,32,66,67,68,69,70,71
,72,73,74,75,76,77},34->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},35->{26,27,28,29,30,31,32
,66,67,68,69,70,71,72,73,74,75,76,77},36->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},37->{26
,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},38->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74
,75,76,77},39->{33,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34,35,36,37,38}
,43->{33,34,35,36,37,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34
,35,36,37,38},48->{33,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33,34,35,36,37
,38},52->{33,34,35,36,37,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37,38},56->{33
,34,35,36,37,38},57->{33,34,35,36,37,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37,38},60->{33,34,35,36,37
,38},61->{33,34,35,36,37,38},62->{33,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33,34,35,36,37,38},65->{33
,34,35,36,37,38},66->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},67->{26,27,28,29,30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77},68->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},69->{26,27
,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},70->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75
,76,77},71->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},72->{26,27,28,29,30,31,32,66,67,68,69
,70,71,72,73,74,75,76,77},73->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},74->{26,27,28,29,30
,31,32,66,67,68,69,70,71,72,73,74,75,76,77},75->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77}
,76->{26,27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77},77->{26,27,28,29,30,31,32,66,67,68,69,70,71
,72,73,74,75,76,77}]
Sizebounds:
(<26,0,C>, 1 + C + N) (<26,0,E>, 1 + E + M) (<26,0,H>, 1) (<26,0,M>, M) (<26,0,N>, N)
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
(<66,0,C>, N) (<66,0,E>, M) (<66,0,H>, 0) (<66,0,M>, M) (<66,0,N>, N)
(<67,0,C>, N) (<67,0,E>, M) (<67,0,H>, 0) (<67,0,M>, M) (<67,0,N>, N)
(<68,0,C>, N) (<68,0,E>, M) (<68,0,H>, 0) (<68,0,M>, M) (<68,0,N>, N)
(<69,0,C>, N) (<69,0,E>, M) (<69,0,H>, 0) (<69,0,M>, M) (<69,0,N>, N)
(<70,0,C>, N) (<70,0,E>, M) (<70,0,H>, 0) (<70,0,M>, M) (<70,0,N>, N)
(<71,0,C>, N) (<71,0,E>, M) (<71,0,H>, 0) (<71,0,M>, M) (<71,0,N>, N)
(<72,0,C>, N) (<72,0,E>, M) (<72,0,H>, 0) (<72,0,M>, M) (<72,0,N>, N)
(<73,0,C>, N) (<73,0,E>, M) (<73,0,H>, 0) (<73,0,M>, M) (<73,0,N>, N)
(<74,0,C>, N) (<74,0,E>, M) (<74,0,H>, 0) (<74,0,M>, M) (<74,0,N>, N)
(<75,0,C>, N) (<75,0,E>, M) (<75,0,H>, 0) (<75,0,M>, M) (<75,0,N>, N)
(<76,0,C>, N) (<76,0,E>, M) (<76,0,H>, 0) (<76,0,M>, M) (<76,0,N>, N)
(<77,0,C>, N) (<77,0,E>, M) (<77,0,H>, 0) (<77,0,M>, M) (<77,0,N>, N)
+ Applied Processor:
ChainProcessor False [26,27,28,29,30,31,32,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 26 to obtain the rules [78,79,80,81,82,83] .
* Step 24: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
27. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
78. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
79. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[27->{33,34,35,36,37,38},28->{33,34,35,36,37,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33
,34,35,36,37,38},32->{33,34,35,36,37,38},33->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80
,81,82,83},34->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},35->{27,28,29,30,31
,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},36->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74
,75,76,77,78,79,80,81,82,83},37->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83}
,38->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},39->{33,34,35,36,37,38}
,40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34
,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33,34,35,36,37
,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37,38},53->{33
,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33,34,35,36,37
,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37,38},62->{33
,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33,34,35,36,37,38},65->{33,34,35,36,37,38},66->{27,28,29,30,31
,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},67->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74
,75,76,77,78,79,80,81,82,83},68->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83}
,69->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},70->{27,28,29,30,31,32,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},71->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77
,78,79,80,81,82,83},72->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},73->{27,28
,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},74->{27,28,29,30,31,32,66,67,68,69,70,71
,72,73,74,75,76,77,78,79,80,81,82,83},75->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
,82,83},76->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},77->{27,28,29,30,31,32
,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},78->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75
,76,77,78,79,80,81,82,83},79->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83}
,80->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},81->{27,28,29,30,31,32,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83},82->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77
,78,79,80,81,82,83},83->{27,28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83}]
Sizebounds:
(<27,0,C>, 1 + C + N) (<27,0,E>, 1 + E + M) (<27,0,H>, 1) (<27,0,M>, M) (<27,0,N>, N)
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
(<66,0,C>, N) (<66,0,E>, M) (<66,0,H>, 0) (<66,0,M>, M) (<66,0,N>, N)
(<67,0,C>, N) (<67,0,E>, M) (<67,0,H>, 0) (<67,0,M>, M) (<67,0,N>, N)
(<68,0,C>, N) (<68,0,E>, M) (<68,0,H>, 0) (<68,0,M>, M) (<68,0,N>, N)
(<69,0,C>, N) (<69,0,E>, M) (<69,0,H>, 0) (<69,0,M>, M) (<69,0,N>, N)
(<70,0,C>, N) (<70,0,E>, M) (<70,0,H>, 0) (<70,0,M>, M) (<70,0,N>, N)
(<71,0,C>, N) (<71,0,E>, M) (<71,0,H>, 0) (<71,0,M>, M) (<71,0,N>, N)
(<72,0,C>, N) (<72,0,E>, M) (<72,0,H>, 0) (<72,0,M>, M) (<72,0,N>, N)
(<73,0,C>, N) (<73,0,E>, M) (<73,0,H>, 0) (<73,0,M>, M) (<73,0,N>, N)
(<74,0,C>, N) (<74,0,E>, M) (<74,0,H>, 0) (<74,0,M>, M) (<74,0,N>, N)
(<75,0,C>, N) (<75,0,E>, M) (<75,0,H>, 0) (<75,0,M>, M) (<75,0,N>, N)
(<76,0,C>, N) (<76,0,E>, M) (<76,0,H>, 0) (<76,0,M>, M) (<76,0,N>, N)
(<77,0,C>, N) (<77,0,E>, M) (<77,0,H>, 0) (<77,0,M>, M) (<77,0,N>, N)
(<78,0,C>, N) (<78,0,E>, M) (<78,0,H>, 0) (<78,0,M>, M) (<78,0,N>, N)
(<79,0,C>, N) (<79,0,E>, M) (<79,0,H>, 0) (<79,0,M>, M) (<79,0,N>, N)
(<80,0,C>, N) (<80,0,E>, M) (<80,0,H>, 0) (<80,0,M>, M) (<80,0,N>, N)
(<81,0,C>, N) (<81,0,E>, M) (<81,0,H>, 0) (<81,0,M>, M) (<81,0,N>, N)
(<82,0,C>, N) (<82,0,E>, M) (<82,0,H>, 0) (<82,0,M>, M) (<82,0,N>, N)
(<83,0,C>, N) (<83,0,E>, M) (<83,0,H>, 0) (<83,0,M>, M) (<83,0,N>, N)
+ Applied Processor:
ChainProcessor False [27,28,29,30,31,32,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 27 to obtain the rules [84,85,86,87,88,89] .
* Step 25: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
28. f2(C,E,H,M,N) -> f6(C,E,H,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
78. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
79. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
84. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
85. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
87. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
88. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
89. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[28->{33,34,35,36,37,38},29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33
,34,35,36,37,38},33->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88
,89},34->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},35->{28,29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},36->{28,29,30,31,32,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},37->{28,29,30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},38->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77
,78,79,80,81,82,83,84,85,86,87,88,89},39->{33,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33,34,35,36,37
,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37,38},46->{33
,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37
,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33
,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33,34,35,36,37,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37
,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37,38},62->{33,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33
,34,35,36,37,38},65->{33,34,35,36,37,38},66->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
,82,83,84,85,86,87,88,89},67->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86
,87,88,89},68->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89}
,69->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},70->{28,29,30
,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},71->{28,29,30,31,32,66,67,68
,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},72->{28,29,30,31,32,66,67,68,69,70,71,72,73
,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},73->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89},74->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83
,84,85,86,87,88,89},75->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88
,89},76->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},77->{28,29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},78->{28,29,30,31,32,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},79->{28,29,30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},80->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77
,78,79,80,81,82,83,84,85,86,87,88,89},81->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82
,83,84,85,86,87,88,89},82->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87
,88,89},83->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},84->{28
,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},85->{28,29,30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},86->{28,29,30,31,32,66,67,68,69,70,71
,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89},87->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76
,77,78,79,80,81,82,83,84,85,86,87,88,89},88->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
,82,83,84,85,86,87,88,89},89->{28,29,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86
,87,88,89}]
Sizebounds:
(<28,0,C>, 1 + C + N) (<28,0,E>, 1 + E + M) (<28,0,H>, 1) (<28,0,M>, M) (<28,0,N>, N)
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
(<66,0,C>, N) (<66,0,E>, M) (<66,0,H>, 0) (<66,0,M>, M) (<66,0,N>, N)
(<67,0,C>, N) (<67,0,E>, M) (<67,0,H>, 0) (<67,0,M>, M) (<67,0,N>, N)
(<68,0,C>, N) (<68,0,E>, M) (<68,0,H>, 0) (<68,0,M>, M) (<68,0,N>, N)
(<69,0,C>, N) (<69,0,E>, M) (<69,0,H>, 0) (<69,0,M>, M) (<69,0,N>, N)
(<70,0,C>, N) (<70,0,E>, M) (<70,0,H>, 0) (<70,0,M>, M) (<70,0,N>, N)
(<71,0,C>, N) (<71,0,E>, M) (<71,0,H>, 0) (<71,0,M>, M) (<71,0,N>, N)
(<72,0,C>, N) (<72,0,E>, M) (<72,0,H>, 0) (<72,0,M>, M) (<72,0,N>, N)
(<73,0,C>, N) (<73,0,E>, M) (<73,0,H>, 0) (<73,0,M>, M) (<73,0,N>, N)
(<74,0,C>, N) (<74,0,E>, M) (<74,0,H>, 0) (<74,0,M>, M) (<74,0,N>, N)
(<75,0,C>, N) (<75,0,E>, M) (<75,0,H>, 0) (<75,0,M>, M) (<75,0,N>, N)
(<76,0,C>, N) (<76,0,E>, M) (<76,0,H>, 0) (<76,0,M>, M) (<76,0,N>, N)
(<77,0,C>, N) (<77,0,E>, M) (<77,0,H>, 0) (<77,0,M>, M) (<77,0,N>, N)
(<78,0,C>, N) (<78,0,E>, M) (<78,0,H>, 0) (<78,0,M>, M) (<78,0,N>, N)
(<79,0,C>, N) (<79,0,E>, M) (<79,0,H>, 0) (<79,0,M>, M) (<79,0,N>, N)
(<80,0,C>, N) (<80,0,E>, M) (<80,0,H>, 0) (<80,0,M>, M) (<80,0,N>, N)
(<81,0,C>, N) (<81,0,E>, M) (<81,0,H>, 0) (<81,0,M>, M) (<81,0,N>, N)
(<82,0,C>, N) (<82,0,E>, M) (<82,0,H>, 0) (<82,0,M>, M) (<82,0,N>, N)
(<83,0,C>, N) (<83,0,E>, M) (<83,0,H>, 0) (<83,0,M>, M) (<83,0,N>, N)
(<84,0,C>, N) (<84,0,E>, M) (<84,0,H>, 0) (<84,0,M>, M) (<84,0,N>, N)
(<85,0,C>, N) (<85,0,E>, M) (<85,0,H>, 0) (<85,0,M>, M) (<85,0,N>, N)
(<86,0,C>, N) (<86,0,E>, M) (<86,0,H>, 0) (<86,0,M>, M) (<86,0,N>, N)
(<87,0,C>, N) (<87,0,E>, M) (<87,0,H>, 0) (<87,0,M>, M) (<87,0,N>, N)
(<88,0,C>, N) (<88,0,E>, M) (<88,0,H>, 0) (<88,0,M>, M) (<88,0,N>, N)
(<89,0,C>, N) (<89,0,E>, M) (<89,0,H>, 0) (<89,0,M>, M) (<89,0,N>, N)
+ Applied Processor:
ChainProcessor False [28,29,30,31,32,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 28 to obtain the rules [90,91,92,93,94,95] .
* Step 26: ChainProcessor WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
29. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O && 7 >= P && O >= 5 && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
78. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
79. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
84. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
85. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
87. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
88. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
89. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
90. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
91. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
93. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
94. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
95. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[29->{33,34,35,36,37,38},30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},34->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},35->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},36->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},37->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},38->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},39->{33
,34,35,36,37,38},40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37
,38},44->{33,34,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33
,34,35,36,37,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37
,38},53->{33,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33
,34,35,36,37,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37
,38},62->{33,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33,34,35,36,37,38},65->{33,34,35,36,37,38},66->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},67->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},68->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},69->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},70->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},71->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},72->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},73->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},74->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},75->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},76->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},77->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},78->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},79->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},80->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},81->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},82->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},83->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},84->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},85->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},86->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},87->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},88->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},89->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},90->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},91->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},92->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},93->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},94->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95},95->{29
,30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95}]
Sizebounds:
(<29,0,C>, 1 + C + N) (<29,0,E>, 1 + E + M) (<29,0,H>, 1) (<29,0,M>, M) (<29,0,N>, N)
(<30,0,C>, 1 + C + N) (<30,0,E>, 1 + E + M) (<30,0,H>, 1) (<30,0,M>, M) (<30,0,N>, N)
(<31,0,C>, 1 + C + N) (<31,0,E>, 1 + E + M) (<31,0,H>, 1) (<31,0,M>, M) (<31,0,N>, N)
(<32,0,C>, 1 + C + N) (<32,0,E>, 1 + E + M) (<32,0,H>, 1) (<32,0,M>, M) (<32,0,N>, N)
(<33,0,C>, N) (<33,0,E>, M) (<33,0,H>, 0) (<33,0,M>, M) (<33,0,N>, N)
(<34,0,C>, N) (<34,0,E>, M) (<34,0,H>, 0) (<34,0,M>, M) (<34,0,N>, N)
(<35,0,C>, N) (<35,0,E>, M) (<35,0,H>, 0) (<35,0,M>, M) (<35,0,N>, N)
(<36,0,C>, N) (<36,0,E>, M) (<36,0,H>, 0) (<36,0,M>, M) (<36,0,N>, N)
(<37,0,C>, N) (<37,0,E>, M) (<37,0,H>, 0) (<37,0,M>, M) (<37,0,N>, N)
(<38,0,C>, N) (<38,0,E>, M) (<38,0,H>, 0) (<38,0,M>, M) (<38,0,N>, N)
(<39,0,C>, 1 + C + N) (<39,0,E>, 1 + E + M) (<39,0,H>, 1) (<39,0,M>, M) (<39,0,N>, N)
(<40,0,C>, 1 + C + N) (<40,0,E>, 1 + E + M) (<40,0,H>, 1) (<40,0,M>, M) (<40,0,N>, N)
(<41,0,C>, 1 + C + N) (<41,0,E>, 1 + E + M) (<41,0,H>, 1) (<41,0,M>, M) (<41,0,N>, N)
(<42,0,C>, 1 + C + N) (<42,0,E>, 1 + E + M) (<42,0,H>, 1) (<42,0,M>, M) (<42,0,N>, N)
(<43,0,C>, 1 + C + N) (<43,0,E>, 1 + E + M) (<43,0,H>, 1) (<43,0,M>, M) (<43,0,N>, N)
(<44,0,C>, 1 + C + N) (<44,0,E>, 1 + E + M) (<44,0,H>, 1) (<44,0,M>, M) (<44,0,N>, N)
(<45,0,C>, 1 + C + N) (<45,0,E>, 1 + E + M) (<45,0,H>, 1) (<45,0,M>, M) (<45,0,N>, N)
(<46,0,C>, 1 + C + N) (<46,0,E>, 1 + E + M) (<46,0,H>, 1) (<46,0,M>, M) (<46,0,N>, N)
(<47,0,C>, 1 + C + N) (<47,0,E>, 1 + E + M) (<47,0,H>, 1) (<47,0,M>, M) (<47,0,N>, N)
(<48,0,C>, 1 + C + N) (<48,0,E>, 1 + E + M) (<48,0,H>, 1) (<48,0,M>, M) (<48,0,N>, N)
(<49,0,C>, 1 + C + N) (<49,0,E>, 1 + E + M) (<49,0,H>, 1) (<49,0,M>, M) (<49,0,N>, N)
(<50,0,C>, 1 + C + N) (<50,0,E>, 1 + E + M) (<50,0,H>, 1) (<50,0,M>, M) (<50,0,N>, N)
(<51,0,C>, 1 + C + N) (<51,0,E>, 1 + E + M) (<51,0,H>, 1) (<51,0,M>, M) (<51,0,N>, N)
(<52,0,C>, 1 + C + N) (<52,0,E>, 1 + E + M) (<52,0,H>, 1) (<52,0,M>, M) (<52,0,N>, N)
(<53,0,C>, 1 + C + N) (<53,0,E>, 1 + E + M) (<53,0,H>, 1) (<53,0,M>, M) (<53,0,N>, N)
(<54,0,C>, 1 + C + N) (<54,0,E>, 1 + E + M) (<54,0,H>, 1) (<54,0,M>, M) (<54,0,N>, N)
(<55,0,C>, 1 + C + N) (<55,0,E>, 1 + E + M) (<55,0,H>, 1) (<55,0,M>, M) (<55,0,N>, N)
(<56,0,C>, 1 + C + N) (<56,0,E>, 1 + E + M) (<56,0,H>, 1) (<56,0,M>, M) (<56,0,N>, N)
(<57,0,C>, 1 + C + N) (<57,0,E>, 1 + E + M) (<57,0,H>, 1) (<57,0,M>, M) (<57,0,N>, N)
(<58,0,C>, 1 + C + N) (<58,0,E>, 1 + E + M) (<58,0,H>, 1) (<58,0,M>, M) (<58,0,N>, N)
(<59,0,C>, 1 + C + N) (<59,0,E>, 1 + E + M) (<59,0,H>, 1) (<59,0,M>, M) (<59,0,N>, N)
(<60,0,C>, 1 + C + N) (<60,0,E>, 1 + E + M) (<60,0,H>, 1) (<60,0,M>, M) (<60,0,N>, N)
(<61,0,C>, 1 + C + N) (<61,0,E>, 1 + E + M) (<61,0,H>, 1) (<61,0,M>, M) (<61,0,N>, N)
(<62,0,C>, 1 + C + N) (<62,0,E>, 1 + E + M) (<62,0,H>, 1) (<62,0,M>, M) (<62,0,N>, N)
(<63,0,C>, 1 + C + N) (<63,0,E>, 1 + E + M) (<63,0,H>, 1) (<63,0,M>, M) (<63,0,N>, N)
(<64,0,C>, 1 + C + N) (<64,0,E>, 1 + E + M) (<64,0,H>, 1) (<64,0,M>, M) (<64,0,N>, N)
(<65,0,C>, 1 + C + N) (<65,0,E>, 1 + E + M) (<65,0,H>, 1) (<65,0,M>, M) (<65,0,N>, N)
(<66,0,C>, N) (<66,0,E>, M) (<66,0,H>, 0) (<66,0,M>, M) (<66,0,N>, N)
(<67,0,C>, N) (<67,0,E>, M) (<67,0,H>, 0) (<67,0,M>, M) (<67,0,N>, N)
(<68,0,C>, N) (<68,0,E>, M) (<68,0,H>, 0) (<68,0,M>, M) (<68,0,N>, N)
(<69,0,C>, N) (<69,0,E>, M) (<69,0,H>, 0) (<69,0,M>, M) (<69,0,N>, N)
(<70,0,C>, N) (<70,0,E>, M) (<70,0,H>, 0) (<70,0,M>, M) (<70,0,N>, N)
(<71,0,C>, N) (<71,0,E>, M) (<71,0,H>, 0) (<71,0,M>, M) (<71,0,N>, N)
(<72,0,C>, N) (<72,0,E>, M) (<72,0,H>, 0) (<72,0,M>, M) (<72,0,N>, N)
(<73,0,C>, N) (<73,0,E>, M) (<73,0,H>, 0) (<73,0,M>, M) (<73,0,N>, N)
(<74,0,C>, N) (<74,0,E>, M) (<74,0,H>, 0) (<74,0,M>, M) (<74,0,N>, N)
(<75,0,C>, N) (<75,0,E>, M) (<75,0,H>, 0) (<75,0,M>, M) (<75,0,N>, N)
(<76,0,C>, N) (<76,0,E>, M) (<76,0,H>, 0) (<76,0,M>, M) (<76,0,N>, N)
(<77,0,C>, N) (<77,0,E>, M) (<77,0,H>, 0) (<77,0,M>, M) (<77,0,N>, N)
(<78,0,C>, N) (<78,0,E>, M) (<78,0,H>, 0) (<78,0,M>, M) (<78,0,N>, N)
(<79,0,C>, N) (<79,0,E>, M) (<79,0,H>, 0) (<79,0,M>, M) (<79,0,N>, N)
(<80,0,C>, N) (<80,0,E>, M) (<80,0,H>, 0) (<80,0,M>, M) (<80,0,N>, N)
(<81,0,C>, N) (<81,0,E>, M) (<81,0,H>, 0) (<81,0,M>, M) (<81,0,N>, N)
(<82,0,C>, N) (<82,0,E>, M) (<82,0,H>, 0) (<82,0,M>, M) (<82,0,N>, N)
(<83,0,C>, N) (<83,0,E>, M) (<83,0,H>, 0) (<83,0,M>, M) (<83,0,N>, N)
(<84,0,C>, N) (<84,0,E>, M) (<84,0,H>, 0) (<84,0,M>, M) (<84,0,N>, N)
(<85,0,C>, N) (<85,0,E>, M) (<85,0,H>, 0) (<85,0,M>, M) (<85,0,N>, N)
(<86,0,C>, N) (<86,0,E>, M) (<86,0,H>, 0) (<86,0,M>, M) (<86,0,N>, N)
(<87,0,C>, N) (<87,0,E>, M) (<87,0,H>, 0) (<87,0,M>, M) (<87,0,N>, N)
(<88,0,C>, N) (<88,0,E>, M) (<88,0,H>, 0) (<88,0,M>, M) (<88,0,N>, N)
(<89,0,C>, N) (<89,0,E>, M) (<89,0,H>, 0) (<89,0,M>, M) (<89,0,N>, N)
(<90,0,C>, N) (<90,0,E>, M) (<90,0,H>, 0) (<90,0,M>, M) (<90,0,N>, N)
(<91,0,C>, N) (<91,0,E>, M) (<91,0,H>, 0) (<91,0,M>, M) (<91,0,N>, N)
(<92,0,C>, N) (<92,0,E>, M) (<92,0,H>, 0) (<92,0,M>, M) (<92,0,N>, N)
(<93,0,C>, N) (<93,0,E>, M) (<93,0,H>, 0) (<93,0,M>, M) (<93,0,N>, N)
(<94,0,C>, N) (<94,0,E>, M) (<94,0,H>, 0) (<94,0,M>, M) (<94,0,N>, N)
(<95,0,C>, N) (<95,0,E>, M) (<95,0,H>, 0) (<95,0,M>, M) (<95,0,N>, N)
+ Applied Processor:
ChainProcessor False [29,30,31,32,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]
+ Details:
We chained rule 29 to obtain the rules [96,97,98,99,100,101] .
* Step 27: UnsatPaths WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
78. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
79. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
84. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
85. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
87. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
88. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
89. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
90. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
91. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
93. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
94. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
95. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
96. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
97. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{33,34,35,36,37,38},31->{33,34,35,36,37,38},32->{33,34,35,36,37,38},33->{30,31,32,66,67,68,69,70,71
,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},34->{30,31,32
,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100
,101},35->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94
,95,96,97,98,99,100,101},36->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88
,89,90,91,92,93,94,95,96,97,98,99,100,101},37->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82
,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},38->{30,31,32,66,67,68,69,70,71,72,73,74,75,76
,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},39->{33,34,35,36,37,38}
,40->{33,34,35,36,37,38},41->{33,34,35,36,37,38},42->{33,34,35,36,37,38},43->{33,34,35,36,37,38},44->{33,34
,35,36,37,38},45->{33,34,35,36,37,38},46->{33,34,35,36,37,38},47->{33,34,35,36,37,38},48->{33,34,35,36,37
,38},49->{33,34,35,36,37,38},50->{33,34,35,36,37,38},51->{33,34,35,36,37,38},52->{33,34,35,36,37,38},53->{33
,34,35,36,37,38},54->{33,34,35,36,37,38},55->{33,34,35,36,37,38},56->{33,34,35,36,37,38},57->{33,34,35,36,37
,38},58->{33,34,35,36,37,38},59->{33,34,35,36,37,38},60->{33,34,35,36,37,38},61->{33,34,35,36,37,38},62->{33
,34,35,36,37,38},63->{33,34,35,36,37,38},64->{33,34,35,36,37,38},65->{33,34,35,36,37,38},66->{30,31,32,66,67
,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,67->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},68->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},69->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},70->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},71->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},72->{30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,73->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},74->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},75->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},76->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},77->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},78->{30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,79->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},80->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},81->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},82->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},83->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},84->{30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,85->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},86->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},87->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},88->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},89->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},90->{30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,91->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},92->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},93->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},94->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},95->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},96->{30,31,32,66
,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}
,97->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96
,97,98,99,100,101},98->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
,91,92,93,94,95,96,97,98,99,100,101},99->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84
,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},100->{30,31,32,66,67,68,69,70,71,72,73,74,75,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101},101->{30,31,32,66,67,68,69,70,71,72
,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101}]
Sizebounds:
(< 30,0,C>, 1 + C + N) (< 30,0,E>, 1 + E + M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, 1 + C + N) (< 31,0,E>, 1 + E + M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, 1 + C + N) (< 32,0,E>, 1 + E + M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 33,0,C>, N) (< 33,0,E>, M) (< 33,0,H>, 0) (< 33,0,M>, M) (< 33,0,N>, N)
(< 34,0,C>, N) (< 34,0,E>, M) (< 34,0,H>, 0) (< 34,0,M>, M) (< 34,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, 1 + C + N) (< 39,0,E>, 1 + E + M) (< 39,0,H>, 1) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, 1 + C + N) (< 40,0,E>, 1 + E + M) (< 40,0,H>, 1) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C + N) (< 41,0,E>, 1 + E + M) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, 1 + C + N) (< 42,0,E>, 1 + E + M) (< 42,0,H>, 1) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, 1 + C + N) (< 43,0,E>, 1 + E + M) (< 43,0,H>, 1) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C + N) (< 44,0,E>, 1 + E + M) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C + N) (< 45,0,E>, 1 + E + M) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C + N) (< 46,0,E>, 1 + E + M) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 1 + C + N) (< 47,0,E>, 1 + E + M) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, 1 + C + N) (< 48,0,E>, 1 + E + M) (< 48,0,H>, 1) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, 1 + C + N) (< 49,0,E>, 1 + E + M) (< 49,0,H>, 1) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C + N) (< 50,0,E>, 1 + E + M) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, 1 + C + N) (< 51,0,E>, 1 + E + M) (< 51,0,H>, 1) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, 1 + C + N) (< 52,0,E>, 1 + E + M) (< 52,0,H>, 1) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C + N) (< 53,0,E>, 1 + E + M) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C + N) (< 54,0,E>, 1 + E + M) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C + N) (< 55,0,E>, 1 + E + M) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 1 + C + N) (< 56,0,E>, 1 + E + M) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C + N) (< 57,0,E>, 1 + E + M) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C + N) (< 58,0,E>, 1 + E + M) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 1 + C + N) (< 59,0,E>, 1 + E + M) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C + N) (< 60,0,E>, 1 + E + M) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C + N) (< 61,0,E>, 1 + E + M) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 1 + C + N) (< 62,0,E>, 1 + E + M) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 1 + C + N) (< 63,0,E>, 1 + E + M) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 1 + C + N) (< 64,0,E>, 1 + E + M) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 1 + C + N) (< 65,0,E>, 1 + E + M) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 66,0,C>, N) (< 66,0,E>, M) (< 66,0,H>, 0) (< 66,0,M>, M) (< 66,0,N>, N)
(< 67,0,C>, N) (< 67,0,E>, M) (< 67,0,H>, 0) (< 67,0,M>, M) (< 67,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 69,0,C>, N) (< 69,0,E>, M) (< 69,0,H>, 0) (< 69,0,M>, M) (< 69,0,N>, N)
(< 70,0,C>, N) (< 70,0,E>, M) (< 70,0,H>, 0) (< 70,0,M>, M) (< 70,0,N>, N)
(< 71,0,C>, N) (< 71,0,E>, M) (< 71,0,H>, 0) (< 71,0,M>, M) (< 71,0,N>, N)
(< 72,0,C>, N) (< 72,0,E>, M) (< 72,0,H>, 0) (< 72,0,M>, M) (< 72,0,N>, N)
(< 73,0,C>, N) (< 73,0,E>, M) (< 73,0,H>, 0) (< 73,0,M>, M) (< 73,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 75,0,C>, N) (< 75,0,E>, M) (< 75,0,H>, 0) (< 75,0,M>, M) (< 75,0,N>, N)
(< 76,0,C>, N) (< 76,0,E>, M) (< 76,0,H>, 0) (< 76,0,M>, M) (< 76,0,N>, N)
(< 77,0,C>, N) (< 77,0,E>, M) (< 77,0,H>, 0) (< 77,0,M>, M) (< 77,0,N>, N)
(< 78,0,C>, N) (< 78,0,E>, M) (< 78,0,H>, 0) (< 78,0,M>, M) (< 78,0,N>, N)
(< 79,0,C>, N) (< 79,0,E>, M) (< 79,0,H>, 0) (< 79,0,M>, M) (< 79,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 84,0,C>, N) (< 84,0,E>, M) (< 84,0,H>, 0) (< 84,0,M>, M) (< 84,0,N>, N)
(< 85,0,C>, N) (< 85,0,E>, M) (< 85,0,H>, 0) (< 85,0,M>, M) (< 85,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 87,0,C>, N) (< 87,0,E>, M) (< 87,0,H>, 0) (< 87,0,M>, M) (< 87,0,N>, N)
(< 88,0,C>, N) (< 88,0,E>, M) (< 88,0,H>, 0) (< 88,0,M>, M) (< 88,0,N>, N)
(< 89,0,C>, N) (< 89,0,E>, M) (< 89,0,H>, 0) (< 89,0,M>, M) (< 89,0,N>, N)
(< 90,0,C>, N) (< 90,0,E>, M) (< 90,0,H>, 0) (< 90,0,M>, M) (< 90,0,N>, N)
(< 91,0,C>, N) (< 91,0,E>, M) (< 91,0,H>, 0) (< 91,0,M>, M) (< 91,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 93,0,C>, N) (< 93,0,E>, M) (< 93,0,H>, 0) (< 93,0,M>, M) (< 93,0,N>, N)
(< 94,0,C>, N) (< 94,0,E>, M) (< 94,0,H>, 0) (< 94,0,M>, M) (< 94,0,N>, N)
(< 95,0,C>, N) (< 95,0,E>, M) (< 95,0,H>, 0) (< 95,0,M>, M) (< 95,0,N>, N)
(< 96,0,C>, N) (< 96,0,E>, M) (< 96,0,H>, 0) (< 96,0,M>, M) (< 96,0,N>, N)
(< 97,0,C>, N) (< 97,0,E>, M) (< 97,0,H>, 0) (< 97,0,M>, M) (< 97,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
UnsatPaths
+ Details:
We remove following edges from the transition graph: [(30,33)
,(30,34)
,(31,33)
,(31,34)
,(32,33)
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,(97,67)
,(97,68)
,(97,69)
,(97,70)
,(97,71)
,(97,72)
,(97,73)
,(97,74)
,(97,75)
,(97,76)
,(97,77)
,(97,78)
,(97,79)
,(97,80)
,(97,81)
,(97,82)
,(97,83)
,(97,84)
,(97,85)
,(97,86)
,(97,87)
,(97,88)
,(97,89)
,(97,90)
,(97,91)
,(97,92)
,(97,93)
,(97,94)
,(97,95)
,(97,96)
,(97,97)
,(97,98)
,(97,99)
,(97,100)
,(97,101)
,(98,66)
,(98,67)
,(98,69)
,(98,70)
,(98,71)
,(98,72)
,(98,73)
,(98,75)
,(98,76)
,(98,77)
,(98,78)
,(98,79)
,(98,84)
,(98,85)
,(98,87)
,(98,88)
,(98,89)
,(98,90)
,(98,91)
,(98,93)
,(98,94)
,(98,95)
,(98,96)
,(98,97)
,(99,66)
,(99,67)
,(99,69)
,(99,70)
,(99,71)
,(99,72)
,(99,73)
,(99,75)
,(99,76)
,(99,77)
,(99,78)
,(99,79)
,(99,84)
,(99,85)
,(99,87)
,(99,88)
,(99,89)
,(99,90)
,(99,91)
,(99,93)
,(99,94)
,(99,95)
,(99,96)
,(99,97)
,(100,66)
,(100,67)
,(100,69)
,(100,70)
,(100,71)
,(100,72)
,(100,73)
,(100,75)
,(100,76)
,(100,77)
,(100,78)
,(100,79)
,(100,84)
,(100,85)
,(100,87)
,(100,88)
,(100,89)
,(100,90)
,(100,91)
,(100,93)
,(100,94)
,(100,95)
,(100,96)
,(100,97)
,(101,66)
,(101,67)
,(101,69)
,(101,70)
,(101,71)
,(101,72)
,(101,73)
,(101,75)
,(101,76)
,(101,77)
,(101,78)
,(101,79)
,(101,84)
,(101,85)
,(101,87)
,(101,88)
,(101,89)
,(101,90)
,(101,91)
,(101,93)
,(101,94)
,(101,95)
,(101,96)
,(101,97)]
* Step 28: UnreachableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
33. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 0 = 1]
34. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (3 + 13*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 0 = 1]
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
66. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
67. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
69. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
70. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
71. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
72. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
73. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
75. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
76. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
77. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
78. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
79. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
84. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
85. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
87. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
88. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
89. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
90. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
91. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
93. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
94. f2(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
95. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
96. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 0 = 1]
97. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 0 = 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},33->{},34->{},35->{30,31,32,68,74,80,81,82,83,86,92
,98,99,100,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92
,98,99,100,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38}
,42->{35},43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35}
,50->{35,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38}
,57->{35,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38}
,63->{35,36,37,38},64->{35,36,37,38},65->{35,36,37,38},66->{},67->{},68->{30,31,32,68,74,80,81,82,83,86,92
,98,99,100,101},69->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},70->{30,31,32,68,74,80,81,82,83,86,92
,98,99,100,101},71->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},72->{},73->{},74->{30,31,32,68,74,80,81
,82,83,86,92,98,99,100,101},75->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},76->{30,31,32,68,74,80,81
,82,83,86,92,98,99,100,101},77->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},78->{},79->{},80->{30,31,32
,68,74,80,81,82,83,86,92,98,99,100,101},81->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32
,68,74,80,81,82,83,86,92,98,99,100,101},83->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},84->{},85->{}
,86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},87->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101}
,88->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},89->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101}
,90->{},91->{},92->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},93->{30,31,32,68,74,80,81,82,83,86,92,98
,99,100,101},94->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},95->{30,31,32,68,74,80,81,82,83,86,92,98
,99,100,101},96->{},97->{},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30,31,32,68,74,80,81,82
,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30,31,32,68,74,80,81,82
,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, 1 + C + N) (< 30,0,E>, 1 + E + M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, 1 + C + N) (< 31,0,E>, 1 + E + M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, 1 + C + N) (< 32,0,E>, 1 + E + M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 33,0,C>, N) (< 33,0,E>, M) (< 33,0,H>, 0) (< 33,0,M>, M) (< 33,0,N>, N)
(< 34,0,C>, N) (< 34,0,E>, M) (< 34,0,H>, 0) (< 34,0,M>, M) (< 34,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, 1 + C + N) (< 39,0,E>, 1 + E + M) (< 39,0,H>, 1) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, 1 + C + N) (< 40,0,E>, 1 + E + M) (< 40,0,H>, 1) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C + N) (< 41,0,E>, 1 + E + M) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, 1 + C + N) (< 42,0,E>, 1 + E + M) (< 42,0,H>, 1) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, 1 + C + N) (< 43,0,E>, 1 + E + M) (< 43,0,H>, 1) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C + N) (< 44,0,E>, 1 + E + M) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C + N) (< 45,0,E>, 1 + E + M) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C + N) (< 46,0,E>, 1 + E + M) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 1 + C + N) (< 47,0,E>, 1 + E + M) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, 1 + C + N) (< 48,0,E>, 1 + E + M) (< 48,0,H>, 1) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, 1 + C + N) (< 49,0,E>, 1 + E + M) (< 49,0,H>, 1) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C + N) (< 50,0,E>, 1 + E + M) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, 1 + C + N) (< 51,0,E>, 1 + E + M) (< 51,0,H>, 1) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, 1 + C + N) (< 52,0,E>, 1 + E + M) (< 52,0,H>, 1) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C + N) (< 53,0,E>, 1 + E + M) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C + N) (< 54,0,E>, 1 + E + M) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C + N) (< 55,0,E>, 1 + E + M) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 1 + C + N) (< 56,0,E>, 1 + E + M) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C + N) (< 57,0,E>, 1 + E + M) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C + N) (< 58,0,E>, 1 + E + M) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 1 + C + N) (< 59,0,E>, 1 + E + M) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C + N) (< 60,0,E>, 1 + E + M) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C + N) (< 61,0,E>, 1 + E + M) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 1 + C + N) (< 62,0,E>, 1 + E + M) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 1 + C + N) (< 63,0,E>, 1 + E + M) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 1 + C + N) (< 64,0,E>, 1 + E + M) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 1 + C + N) (< 65,0,E>, 1 + E + M) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 66,0,C>, N) (< 66,0,E>, M) (< 66,0,H>, 0) (< 66,0,M>, M) (< 66,0,N>, N)
(< 67,0,C>, N) (< 67,0,E>, M) (< 67,0,H>, 0) (< 67,0,M>, M) (< 67,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 69,0,C>, N) (< 69,0,E>, M) (< 69,0,H>, 0) (< 69,0,M>, M) (< 69,0,N>, N)
(< 70,0,C>, N) (< 70,0,E>, M) (< 70,0,H>, 0) (< 70,0,M>, M) (< 70,0,N>, N)
(< 71,0,C>, N) (< 71,0,E>, M) (< 71,0,H>, 0) (< 71,0,M>, M) (< 71,0,N>, N)
(< 72,0,C>, N) (< 72,0,E>, M) (< 72,0,H>, 0) (< 72,0,M>, M) (< 72,0,N>, N)
(< 73,0,C>, N) (< 73,0,E>, M) (< 73,0,H>, 0) (< 73,0,M>, M) (< 73,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 75,0,C>, N) (< 75,0,E>, M) (< 75,0,H>, 0) (< 75,0,M>, M) (< 75,0,N>, N)
(< 76,0,C>, N) (< 76,0,E>, M) (< 76,0,H>, 0) (< 76,0,M>, M) (< 76,0,N>, N)
(< 77,0,C>, N) (< 77,0,E>, M) (< 77,0,H>, 0) (< 77,0,M>, M) (< 77,0,N>, N)
(< 78,0,C>, N) (< 78,0,E>, M) (< 78,0,H>, 0) (< 78,0,M>, M) (< 78,0,N>, N)
(< 79,0,C>, N) (< 79,0,E>, M) (< 79,0,H>, 0) (< 79,0,M>, M) (< 79,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 84,0,C>, N) (< 84,0,E>, M) (< 84,0,H>, 0) (< 84,0,M>, M) (< 84,0,N>, N)
(< 85,0,C>, N) (< 85,0,E>, M) (< 85,0,H>, 0) (< 85,0,M>, M) (< 85,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 87,0,C>, N) (< 87,0,E>, M) (< 87,0,H>, 0) (< 87,0,M>, M) (< 87,0,N>, N)
(< 88,0,C>, N) (< 88,0,E>, M) (< 88,0,H>, 0) (< 88,0,M>, M) (< 88,0,N>, N)
(< 89,0,C>, N) (< 89,0,E>, M) (< 89,0,H>, 0) (< 89,0,M>, M) (< 89,0,N>, N)
(< 90,0,C>, N) (< 90,0,E>, M) (< 90,0,H>, 0) (< 90,0,M>, M) (< 90,0,N>, N)
(< 91,0,C>, N) (< 91,0,E>, M) (< 91,0,H>, 0) (< 91,0,M>, M) (< 91,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 93,0,C>, N) (< 93,0,E>, M) (< 93,0,H>, 0) (< 93,0,M>, M) (< 93,0,N>, N)
(< 94,0,C>, N) (< 94,0,E>, M) (< 94,0,H>, 0) (< 94,0,M>, M) (< 94,0,N>, N)
(< 95,0,C>, N) (< 95,0,E>, M) (< 95,0,H>, 0) (< 95,0,M>, M) (< 95,0,N>, N)
(< 96,0,C>, N) (< 96,0,E>, M) (< 96,0,H>, 0) (< 96,0,M>, M) (< 96,0,N>, N)
(< 97,0,C>, N) (< 97,0,E>, M) (< 97,0,H>, 0) (< 97,0,M>, M) (< 97,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
UnreachableRules
+ Details:
The following transitions are not reachable from the starting states and are removed: [33
,34
,66
,67
,69
,70
,71
,72
,73
,75
,76
,77
,78
,79
,84
,85
,87
,88
,89
,90
,91
,93
,94
,95
,96
,97]
* Step 29: LocalSizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, 1 + C + N) (< 30,0,E>, 1 + E + M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, 1 + C + N) (< 31,0,E>, 1 + E + M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, 1 + C + N) (< 32,0,E>, 1 + E + M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, 1 + C + N) (< 39,0,E>, 1 + E + M) (< 39,0,H>, 1) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, 1 + C + N) (< 40,0,E>, 1 + E + M) (< 40,0,H>, 1) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C + N) (< 41,0,E>, 1 + E + M) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, 1 + C + N) (< 42,0,E>, 1 + E + M) (< 42,0,H>, 1) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, 1 + C + N) (< 43,0,E>, 1 + E + M) (< 43,0,H>, 1) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C + N) (< 44,0,E>, 1 + E + M) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C + N) (< 45,0,E>, 1 + E + M) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C + N) (< 46,0,E>, 1 + E + M) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 1 + C + N) (< 47,0,E>, 1 + E + M) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, 1 + C + N) (< 48,0,E>, 1 + E + M) (< 48,0,H>, 1) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, 1 + C + N) (< 49,0,E>, 1 + E + M) (< 49,0,H>, 1) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C + N) (< 50,0,E>, 1 + E + M) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, 1 + C + N) (< 51,0,E>, 1 + E + M) (< 51,0,H>, 1) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, 1 + C + N) (< 52,0,E>, 1 + E + M) (< 52,0,H>, 1) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C + N) (< 53,0,E>, 1 + E + M) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C + N) (< 54,0,E>, 1 + E + M) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C + N) (< 55,0,E>, 1 + E + M) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 1 + C + N) (< 56,0,E>, 1 + E + M) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C + N) (< 57,0,E>, 1 + E + M) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C + N) (< 58,0,E>, 1 + E + M) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 1 + C + N) (< 59,0,E>, 1 + E + M) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C + N) (< 60,0,E>, 1 + E + M) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C + N) (< 61,0,E>, 1 + E + M) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 1 + C + N) (< 62,0,E>, 1 + E + M) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 1 + C + N) (< 63,0,E>, 1 + E + M) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 1 + C + N) (< 64,0,E>, 1 + E + M) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 1 + C + N) (< 65,0,E>, 1 + E + M) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
LocalSizeboundsProc
+ Details:
LocalSizebounds generated; rvgraph
(< 30,0,C>, 1 + C, .+ 1) (< 30,0,E>, 1 + E, .+ 1) (< 30,0,H>, 1, .= 1) (< 30,0,M>, M, .= 0) (< 30,0,N>, N, .= 0)
(< 31,0,C>, 1 + C, .+ 1) (< 31,0,E>, 1 + E, .+ 1) (< 31,0,H>, 1, .= 1) (< 31,0,M>, M, .= 0) (< 31,0,N>, N, .= 0)
(< 32,0,C>, 2 + C, .+ 2) (< 32,0,E>, 2 + E, .+ 2) (< 32,0,H>, 1, .= 1) (< 32,0,M>, M, .= 0) (< 32,0,N>, N, .= 0)
(< 35,0,C>, 1 + C, .+ 1) (< 35,0,E>, 1 + E, .+ 1) (< 35,0,H>, 0, .= 0) (< 35,0,M>, M, .= 0) (< 35,0,N>, N, .= 0)
(< 36,0,C>, C, .= 0) (< 36,0,E>, E, .= 0) (< 36,0,H>, 0, .= 0) (< 36,0,M>, M, .= 0) (< 36,0,N>, N, .= 0)
(< 37,0,C>, C, .= 0) (< 37,0,E>, E, .= 0) (< 37,0,H>, 0, .= 0) (< 37,0,M>, M, .= 0) (< 37,0,N>, N, .= 0)
(< 38,0,C>, 1 + C, .+ 1) (< 38,0,E>, 1 + E, .+ 1) (< 38,0,H>, 0, .= 0) (< 38,0,M>, M, .= 0) (< 38,0,N>, N, .= 0)
(< 39,0,C>, C, .= 0) (< 39,0,E>, E, .= 0) (< 39,0,H>, 0, .= 0) (< 39,0,M>, M, .= 0) (< 39,0,N>, N, .= 0)
(< 40,0,C>, C, .= 0) (< 40,0,E>, E, .= 0) (< 40,0,H>, 0, .= 0) (< 40,0,M>, M, .= 0) (< 40,0,N>, N, .= 0)
(< 41,0,C>, 1 + C, .+ 1) (< 41,0,E>, 1 + E, .+ 1) (< 41,0,H>, 1, .= 1) (< 41,0,M>, M, .= 0) (< 41,0,N>, N, .= 0)
(< 42,0,C>, C, .= 0) (< 42,0,E>, E, .= 0) (< 42,0,H>, 0, .= 0) (< 42,0,M>, M, .= 0) (< 42,0,N>, N, .= 0)
(< 43,0,C>, C, .= 0) (< 43,0,E>, E, .= 0) (< 43,0,H>, 0, .= 0) (< 43,0,M>, M, .= 0) (< 43,0,N>, N, .= 0)
(< 44,0,C>, 1 + C, .+ 1) (< 44,0,E>, 1 + E, .+ 1) (< 44,0,H>, 1, .= 1) (< 44,0,M>, M, .= 0) (< 44,0,N>, N, .= 0)
(< 45,0,C>, 1 + C, .+ 1) (< 45,0,E>, 1 + E, .+ 1) (< 45,0,H>, 1, .= 1) (< 45,0,M>, M, .= 0) (< 45,0,N>, N, .= 0)
(< 46,0,C>, 1 + C, .+ 1) (< 46,0,E>, 1 + E, .+ 1) (< 46,0,H>, 1, .= 1) (< 46,0,M>, M, .= 0) (< 46,0,N>, N, .= 0)
(< 47,0,C>, 2 + C, .+ 2) (< 47,0,E>, 2 + E, .+ 2) (< 47,0,H>, 1, .= 1) (< 47,0,M>, M, .= 0) (< 47,0,N>, N, .= 0)
(< 48,0,C>, C, .= 0) (< 48,0,E>, E, .= 0) (< 48,0,H>, 0, .= 0) (< 48,0,M>, M, .= 0) (< 48,0,N>, N, .= 0)
(< 49,0,C>, C, .= 0) (< 49,0,E>, E, .= 0) (< 49,0,H>, 0, .= 0) (< 49,0,M>, M, .= 0) (< 49,0,N>, N, .= 0)
(< 50,0,C>, 1 + C, .+ 1) (< 50,0,E>, 1 + E, .+ 1) (< 50,0,H>, 1, .= 1) (< 50,0,M>, M, .= 0) (< 50,0,N>, N, .= 0)
(< 51,0,C>, C, .= 0) (< 51,0,E>, E, .= 0) (< 51,0,H>, 0, .= 0) (< 51,0,M>, M, .= 0) (< 51,0,N>, N, .= 0)
(< 52,0,C>, C, .= 0) (< 52,0,E>, E, .= 0) (< 52,0,H>, 0, .= 0) (< 52,0,M>, M, .= 0) (< 52,0,N>, N, .= 0)
(< 53,0,C>, 1 + C, .+ 1) (< 53,0,E>, 1 + E, .+ 1) (< 53,0,H>, 1, .= 1) (< 53,0,M>, M, .= 0) (< 53,0,N>, N, .= 0)
(< 54,0,C>, 1 + C, .+ 1) (< 54,0,E>, 1 + E, .+ 1) (< 54,0,H>, 1, .= 1) (< 54,0,M>, M, .= 0) (< 54,0,N>, N, .= 0)
(< 55,0,C>, 1 + C, .+ 1) (< 55,0,E>, 1 + E, .+ 1) (< 55,0,H>, 1, .= 1) (< 55,0,M>, M, .= 0) (< 55,0,N>, N, .= 0)
(< 56,0,C>, 2 + C, .+ 2) (< 56,0,E>, 2 + E, .+ 2) (< 56,0,H>, 1, .= 1) (< 56,0,M>, M, .= 0) (< 56,0,N>, N, .= 0)
(< 57,0,C>, 1 + C, .+ 1) (< 57,0,E>, 1 + E, .+ 1) (< 57,0,H>, 1, .= 1) (< 57,0,M>, M, .= 0) (< 57,0,N>, N, .= 0)
(< 58,0,C>, 1 + C, .+ 1) (< 58,0,E>, 1 + E, .+ 1) (< 58,0,H>, 1, .= 1) (< 58,0,M>, M, .= 0) (< 58,0,N>, N, .= 0)
(< 59,0,C>, 2 + C, .+ 2) (< 59,0,E>, 2 + E, .+ 2) (< 59,0,H>, 1, .= 1) (< 59,0,M>, M, .= 0) (< 59,0,N>, N, .= 0)
(< 60,0,C>, 1 + C, .+ 1) (< 60,0,E>, 1 + E, .+ 1) (< 60,0,H>, 1, .= 1) (< 60,0,M>, M, .= 0) (< 60,0,N>, N, .= 0)
(< 61,0,C>, 1 + C, .+ 1) (< 61,0,E>, 1 + E, .+ 1) (< 61,0,H>, 1, .= 1) (< 61,0,M>, M, .= 0) (< 61,0,N>, N, .= 0)
(< 62,0,C>, 2 + C, .+ 2) (< 62,0,E>, 2 + E, .+ 2) (< 62,0,H>, 1, .= 1) (< 62,0,M>, M, .= 0) (< 62,0,N>, N, .= 0)
(< 63,0,C>, 2 + C, .+ 2) (< 63,0,E>, 2 + E, .+ 2) (< 63,0,H>, 1, .= 1) (< 63,0,M>, M, .= 0) (< 63,0,N>, N, .= 0)
(< 64,0,C>, 2 + C, .+ 2) (< 64,0,E>, 2 + E, .+ 2) (< 64,0,H>, 1, .= 1) (< 64,0,M>, M, .= 0) (< 64,0,N>, N, .= 0)
(< 65,0,C>, 3 + C, .+ 3) (< 65,0,E>, 3 + E, .+ 3) (< 65,0,H>, 1, .= 1) (< 65,0,M>, M, .= 0) (< 65,0,N>, N, .= 0)
(< 68,0,C>, 1 + C, .+ 1) (< 68,0,E>, 1 + E, .+ 1) (< 68,0,H>, 0, .= 0) (< 68,0,M>, M, .= 0) (< 68,0,N>, N, .= 0)
(< 74,0,C>, 1 + C, .+ 1) (< 74,0,E>, 1 + E, .+ 1) (< 74,0,H>, 0, .= 0) (< 74,0,M>, M, .= 0) (< 74,0,N>, N, .= 0)
(< 80,0,C>, 2 + C, .+ 2) (< 80,0,E>, 2 + E, .+ 2) (< 80,0,H>, 0, .= 0) (< 80,0,M>, M, .= 0) (< 80,0,N>, N, .= 0)
(< 81,0,C>, 1 + C, .+ 1) (< 81,0,E>, 1 + E, .+ 1) (< 81,0,H>, 0, .= 0) (< 81,0,M>, M, .= 0) (< 81,0,N>, N, .= 0)
(< 82,0,C>, 1 + C, .+ 1) (< 82,0,E>, 1 + E, .+ 1) (< 82,0,H>, 0, .= 0) (< 82,0,M>, M, .= 0) (< 82,0,N>, N, .= 0)
(< 83,0,C>, 2 + C, .+ 2) (< 83,0,E>, 2 + E, .+ 2) (< 83,0,H>, 0, .= 0) (< 83,0,M>, M, .= 0) (< 83,0,N>, N, .= 0)
(< 86,0,C>, 1 + C, .+ 1) (< 86,0,E>, 1 + E, .+ 1) (< 86,0,H>, 0, .= 0) (< 86,0,M>, M, .= 0) (< 86,0,N>, N, .= 0)
(< 92,0,C>, 1 + C, .+ 1) (< 92,0,E>, 1 + E, .+ 1) (< 92,0,H>, 0, .= 0) (< 92,0,M>, M, .= 0) (< 92,0,N>, N, .= 0)
(< 98,0,C>, 2 + C, .+ 2) (< 98,0,E>, 2 + E, .+ 2) (< 98,0,H>, 0, .= 0) (< 98,0,M>, M, .= 0) (< 98,0,N>, N, .= 0)
(< 99,0,C>, 1 + C, .+ 1) (< 99,0,E>, 1 + E, .+ 1) (< 99,0,H>, 0, .= 0) (< 99,0,M>, M, .= 0) (< 99,0,N>, N, .= 0)
(<100,0,C>, 1 + C, .+ 1) (<100,0,E>, 1 + E, .+ 1) (<100,0,H>, 0, .= 0) (<100,0,M>, M, .= 0) (<100,0,N>, N, .= 0)
(<101,0,C>, 2 + C, .+ 2) (<101,0,E>, 2 + E, .+ 2) (<101,0,H>, 0, .= 0) (<101,0,M>, M, .= 0) (<101,0,N>, N, .= 0)
* Step 30: SizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, ?) (< 30,0,E>, ?) (< 30,0,H>, ?) (< 30,0,M>, ?) (< 30,0,N>, ?)
(< 31,0,C>, ?) (< 31,0,E>, ?) (< 31,0,H>, ?) (< 31,0,M>, ?) (< 31,0,N>, ?)
(< 32,0,C>, ?) (< 32,0,E>, ?) (< 32,0,H>, ?) (< 32,0,M>, ?) (< 32,0,N>, ?)
(< 35,0,C>, ?) (< 35,0,E>, ?) (< 35,0,H>, ?) (< 35,0,M>, ?) (< 35,0,N>, ?)
(< 36,0,C>, ?) (< 36,0,E>, ?) (< 36,0,H>, ?) (< 36,0,M>, ?) (< 36,0,N>, ?)
(< 37,0,C>, ?) (< 37,0,E>, ?) (< 37,0,H>, ?) (< 37,0,M>, ?) (< 37,0,N>, ?)
(< 38,0,C>, ?) (< 38,0,E>, ?) (< 38,0,H>, ?) (< 38,0,M>, ?) (< 38,0,N>, ?)
(< 39,0,C>, ?) (< 39,0,E>, ?) (< 39,0,H>, ?) (< 39,0,M>, ?) (< 39,0,N>, ?)
(< 40,0,C>, ?) (< 40,0,E>, ?) (< 40,0,H>, ?) (< 40,0,M>, ?) (< 40,0,N>, ?)
(< 41,0,C>, ?) (< 41,0,E>, ?) (< 41,0,H>, ?) (< 41,0,M>, ?) (< 41,0,N>, ?)
(< 42,0,C>, ?) (< 42,0,E>, ?) (< 42,0,H>, ?) (< 42,0,M>, ?) (< 42,0,N>, ?)
(< 43,0,C>, ?) (< 43,0,E>, ?) (< 43,0,H>, ?) (< 43,0,M>, ?) (< 43,0,N>, ?)
(< 44,0,C>, ?) (< 44,0,E>, ?) (< 44,0,H>, ?) (< 44,0,M>, ?) (< 44,0,N>, ?)
(< 45,0,C>, ?) (< 45,0,E>, ?) (< 45,0,H>, ?) (< 45,0,M>, ?) (< 45,0,N>, ?)
(< 46,0,C>, ?) (< 46,0,E>, ?) (< 46,0,H>, ?) (< 46,0,M>, ?) (< 46,0,N>, ?)
(< 47,0,C>, ?) (< 47,0,E>, ?) (< 47,0,H>, ?) (< 47,0,M>, ?) (< 47,0,N>, ?)
(< 48,0,C>, ?) (< 48,0,E>, ?) (< 48,0,H>, ?) (< 48,0,M>, ?) (< 48,0,N>, ?)
(< 49,0,C>, ?) (< 49,0,E>, ?) (< 49,0,H>, ?) (< 49,0,M>, ?) (< 49,0,N>, ?)
(< 50,0,C>, ?) (< 50,0,E>, ?) (< 50,0,H>, ?) (< 50,0,M>, ?) (< 50,0,N>, ?)
(< 51,0,C>, ?) (< 51,0,E>, ?) (< 51,0,H>, ?) (< 51,0,M>, ?) (< 51,0,N>, ?)
(< 52,0,C>, ?) (< 52,0,E>, ?) (< 52,0,H>, ?) (< 52,0,M>, ?) (< 52,0,N>, ?)
(< 53,0,C>, ?) (< 53,0,E>, ?) (< 53,0,H>, ?) (< 53,0,M>, ?) (< 53,0,N>, ?)
(< 54,0,C>, ?) (< 54,0,E>, ?) (< 54,0,H>, ?) (< 54,0,M>, ?) (< 54,0,N>, ?)
(< 55,0,C>, ?) (< 55,0,E>, ?) (< 55,0,H>, ?) (< 55,0,M>, ?) (< 55,0,N>, ?)
(< 56,0,C>, ?) (< 56,0,E>, ?) (< 56,0,H>, ?) (< 56,0,M>, ?) (< 56,0,N>, ?)
(< 57,0,C>, ?) (< 57,0,E>, ?) (< 57,0,H>, ?) (< 57,0,M>, ?) (< 57,0,N>, ?)
(< 58,0,C>, ?) (< 58,0,E>, ?) (< 58,0,H>, ?) (< 58,0,M>, ?) (< 58,0,N>, ?)
(< 59,0,C>, ?) (< 59,0,E>, ?) (< 59,0,H>, ?) (< 59,0,M>, ?) (< 59,0,N>, ?)
(< 60,0,C>, ?) (< 60,0,E>, ?) (< 60,0,H>, ?) (< 60,0,M>, ?) (< 60,0,N>, ?)
(< 61,0,C>, ?) (< 61,0,E>, ?) (< 61,0,H>, ?) (< 61,0,M>, ?) (< 61,0,N>, ?)
(< 62,0,C>, ?) (< 62,0,E>, ?) (< 62,0,H>, ?) (< 62,0,M>, ?) (< 62,0,N>, ?)
(< 63,0,C>, ?) (< 63,0,E>, ?) (< 63,0,H>, ?) (< 63,0,M>, ?) (< 63,0,N>, ?)
(< 64,0,C>, ?) (< 64,0,E>, ?) (< 64,0,H>, ?) (< 64,0,M>, ?) (< 64,0,N>, ?)
(< 65,0,C>, ?) (< 65,0,E>, ?) (< 65,0,H>, ?) (< 65,0,M>, ?) (< 65,0,N>, ?)
(< 68,0,C>, ?) (< 68,0,E>, ?) (< 68,0,H>, ?) (< 68,0,M>, ?) (< 68,0,N>, ?)
(< 74,0,C>, ?) (< 74,0,E>, ?) (< 74,0,H>, ?) (< 74,0,M>, ?) (< 74,0,N>, ?)
(< 80,0,C>, ?) (< 80,0,E>, ?) (< 80,0,H>, ?) (< 80,0,M>, ?) (< 80,0,N>, ?)
(< 81,0,C>, ?) (< 81,0,E>, ?) (< 81,0,H>, ?) (< 81,0,M>, ?) (< 81,0,N>, ?)
(< 82,0,C>, ?) (< 82,0,E>, ?) (< 82,0,H>, ?) (< 82,0,M>, ?) (< 82,0,N>, ?)
(< 83,0,C>, ?) (< 83,0,E>, ?) (< 83,0,H>, ?) (< 83,0,M>, ?) (< 83,0,N>, ?)
(< 86,0,C>, ?) (< 86,0,E>, ?) (< 86,0,H>, ?) (< 86,0,M>, ?) (< 86,0,N>, ?)
(< 92,0,C>, ?) (< 92,0,E>, ?) (< 92,0,H>, ?) (< 92,0,M>, ?) (< 92,0,N>, ?)
(< 98,0,C>, ?) (< 98,0,E>, ?) (< 98,0,H>, ?) (< 98,0,M>, ?) (< 98,0,N>, ?)
(< 99,0,C>, ?) (< 99,0,E>, ?) (< 99,0,H>, ?) (< 99,0,M>, ?) (< 99,0,N>, ?)
(<100,0,C>, ?) (<100,0,E>, ?) (<100,0,H>, ?) (<100,0,M>, ?) (<100,0,N>, ?)
(<101,0,C>, ?) (<101,0,E>, ?) (<101,0,H>, ?) (<101,0,M>, ?) (<101,0,N>, ?)
+ Applied Processor:
SizeboundsProc
+ Details:
Sizebounds computed:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
* Step 31: LocationConstraintsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
LocationConstraintsProc
+ Details:
We computed the location constraints 30 : True 31 : True 32 : True 35 : True 36 : True 37 : True 38 : True 39 : True 40 : True 41 : True 42 : True 43 : True 44 : True 45 : True 46 : True 47 : True 48 : True 49 : True 50 : True 51 : True 52 : True 53 : True 54 : True 55 : True 56 : True 57 : True 58 : True 59 : True 60 : True 61 : True 62 : True 63 : True 64 : True 65 : True 68 : True 74 : True 80 : True 81 : True 82 : True 83 : True 86 : True 92 : True 98 : True 99 : True 100 : True 101 : True .
* Step 32: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -11 + -12*x2 + 12*x4
p(f6) = 1 + -12*x2 + 12*x4
p(f8) = 7 + -12*x2 + 12*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
> -35 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 1 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 1 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 1 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 1 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 1 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -11 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -35 + -12*E + 12*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -35 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -35 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -35 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -12*E + 12*M
>= -23 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
* Step 33: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 34: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 35: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -17 + -15*x2 + 15*x4
p(f6) = -2 + -15*x2 + 15*x4
p(f8) = 7 + -15*x2 + 15*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
> -47 + -15*E + 15*M
= f2(2 + C,2 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = -2 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -2 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -2 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = -2 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -2 + -15*E + 15*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -17 + -15*E + 15*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -15*E + 15*M
>= -47 + -15*E + 15*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -47 + -15*E + 15*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -47 + -15*E + 15*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -32 + -15*E + 15*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -17 + -15*E + 15*M
>= -47 + -15*E + 15*M
= f2(2 + C,2 + E,0,M,N)
* Step 36: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 37: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 38: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -11 + -18*x2 + 18*x4
p(f6) = 7 + -18*x2 + 18*x4
p(f8) = 7 + -18*x2 + 18*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
> -47 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= 7 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -11 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -18*E + 18*M
>= -47 + -18*E + 18*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -47 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -47 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -29 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -11 + -18*E + 18*M
>= -47 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
* Step 39: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 40: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -18*x2 + 18*x4
p(f6) = 6 + -18*x2 + 18*x4
p(f8) = 12 + -18*x2 + 18*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
> -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -48 + -18*E + 18*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
* Step 41: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -5 + -12*x2 + 12*x4
p(f6) = 7 + -12*x2 + 12*x4
p(f8) = 7 + -12*x2 + 12*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
> -29 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= 7 + -12*E + 12*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -5 + -12*E + 12*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 7 + -12*E + 12*M
>= -29 + -12*E + 12*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -29 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -29 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -17 + -12*E + 12*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -5 + -12*E + 12*M
>= -29 + -12*E + 12*M
= f2(2 + C,2 + E,0,M,N)
* Step 42: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6*x2 + 6*x4
p(f6) = 6 + -6*x2 + 6*x4
p(f8) = 12 + -6*x2 + 6*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
> -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6*E + 6*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= 6 + -6*E + 6*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6*E + 6*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -6 + -6*E + 6*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -6*E + 6*M
>= -12 + -6*E + 6*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -6 + -6*E + 6*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6*E + 6*M
>= -12 + -6*E + 6*M
= f2(2 + C,2 + E,0,M,N)
* Step 43: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -18*x2 + 18*x4
p(f6) = 6 + -18*x2 + 18*x4
p(f8) = 12 + -18*x2 + 18*x4
The following rules are strictly oriented:
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
> -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18*E + 18*M
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = 6 + -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= 6 + -18*E + 18*M
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -12 + -18*E + 18*M
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -30 + -18*E + 18*M
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = 12 + -18*E + 18*M
>= -48 + -18*E + 18*M
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -18 + -18*E + 18*M
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -18*E + 18*M
>= -36 + -18*E + 18*M
= f2(2 + C,2 + E,0,M,N)
* Step 44: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -30 + -12*x1 + 13*x5
p(f6) = -24 + -12*x1 + 13*x5
p(f8) = -12*x1 + 13*x5
The following rules are strictly oriented:
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = -24 + -12*C + 13*N
> -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = -24 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -24 + -12*C + 13*N
>= -30 + -12*C + 13*N
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -24 + -12*C + 13*N
>= -30 + -12*C + 13*N
= f2(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -24 + -12*C + 13*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -36 + -12*C + 13*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -48 + -12*C + 13*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -12*C + 13*N
>= -60 + -12*C + 13*N
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -54 + -12*C + 13*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -54 + -12*C + 13*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -54 + -12*C + 13*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -42 + -12*C + 13*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -30 + -12*C + 13*N
>= -54 + -12*C + 13*N
= f2(2 + C,2 + E,0,M,N)
* Step 45: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -20 + -19*x1 + 19*x5
p(f6) = -13 + -19*x1 + 19*x5
p(f8) = -19*x1 + 19*x5
The following rules are strictly oriented:
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -13 + -19*C + 19*N
> -20 + -19*C + 19*N
= f2(C,E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = -13 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -13 + -19*C + 19*N
>= -20 + -19*C + 19*N
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = -13 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -13 + -19*C + 19*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -32 + -19*C + 19*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -51 + -19*C + 19*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -19*C + 19*N
>= -70 + -19*C + 19*N
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -58 + -19*C + 19*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -58 + -19*C + 19*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -58 + -19*C + 19*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -39 + -19*C + 19*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -20 + -19*C + 19*N
>= -58 + -19*C + 19*N
= f2(2 + C,2 + E,0,M,N)
* Step 46: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (?,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (19*C + 19*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = -6 + -6*x1 + 6*x5
p(f6) = -6*x1 + 6*x5
p(f8) = -6*x1 + 6*x5
The following rules are strictly oriented:
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -6*C + 6*N
> -6 + -6*C + 6*N
= f2(C,E,0,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] ==>
f6(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
f6(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f2(C,E,0,M,N)
[7 >= O ==>
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
f6(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6*C + 6*N
= f6(C,E,0,M,N)
[7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ ==>
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ ==>
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -6 + -6*C + 6*N
= f6(1 + C,1 + E,1,M,N)
[7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -12 + -6*C + 6*N
= f6(2 + C,2 + E,1,M,N)
[7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] ==>
f8(C,E,H,M,N) = -6*C + 6*N
>= -18 + -6*C + 6*N
= f6(3 + C,3 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -18 + -6*C + 6*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -18 + -6*C + 6*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -18 + -6*C + 6*N
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -12 + -6*C + 6*N
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = -6 + -6*C + 6*N
>= -18 + -6*C + 6*N
= f2(2 + C,2 + E,0,M,N)
* Step 47: PolyRank WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (?,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (6*C + 6*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (19*C + 19*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
PolyRank {useFarkas = True, withSizebounds = [30,31,32,68,74,80,81,82,83,86,92,98,99,100,101], shape = Linear}
+ Details:
We apply a polynomial interpretation of shape linear:
p(f2) = 1
p(f6) = -11*x3
The following rules are strictly oriented:
[7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] ==>
f2(C,E,H,M,N) = 1
> -11
= f6(2 + C,2 + E,1,M,N)
The following rules are weakly oriented:
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] ==>
f2(C,E,H,M,N) = 1
>= -11
= f6(1 + C,1 + E,1,M,N)
[7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] ==>
f2(C,E,H,M,N) = 1
>= -11
= f6(1 + C,1 + E,1,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(2 + C,2 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(1 + C,1 + E,0,M,N)
[7 >= O ==>
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
f2(C,E,H,M,N) = 1
>= 1
= f2(2 + C,2 + E,0,M,N)
We use the following global sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
* Step 48: KnowledgePropagation WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (?,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (?,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (3 + 50*C + 51*N,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (6*C + 6*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (19*C + 19*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
KnowledgePropagation
+ Details:
We propagate bounds from predecessors.
* Step 49: SizeboundsProc WORST_CASE(?,O(n^1))
+ Considered Problem:
Rules:
30. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1] (127 + 50*C + 129*E + 129*M + 51*N,2)
31. f2(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P && P >= 1 && 7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1] (127 + 50*C + 129*E + 129*M + 51*N,2)
32. f2(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P && P >= 1 && 7 >= P$ && P$ >= 1] (3 + 50*C + 51*N,2)
35. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O && 1 >= P && P >= 0 && O >= 1 && M >= 2 + E && N >= 2 + C && M >= 1 && N >= 1 && 7 >= P$ && P$ >= 1] (3 + 13*C + 13*N,2)
36. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (6*C + 6*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 1 = 1]
37. f6(C,E,H,M,N) -> f2(C,E,0,M,N) [7 >= O (19*C + 19*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 1
&& M >= 1 + E
&& N >= 1
&& N >= 1 + C
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 1 = 1]
38. f6(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12*C + 13*N,2)
&& 1 >= P
&& P >= 0
&& O >= 1
&& H = 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$
&& P$ >= 1]
39. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
40. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
41. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
42. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
43. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
44. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
45. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& 3 >= P$
&& P$ >= 1
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
46. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
47. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && 3 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
48. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
49. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
50. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
51. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
52. f8(C,E,H,M,N) -> f6(C,E,0,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= O$$
&& 7 >= P$$
&& O$$ >= 5
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1]
53. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
54. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ (1,4)
&& P$ >= 5
&& 7 >= P$$
&& P$$ >= 1
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1]
55. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= O$$$ && 7 >= P$$$ && O$$$ >= 5 && P$$$ >= 1] (1,4)
56. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 5 && 7 >= P$$ && P$$ >= 1 && 7 >= P$$$ && P$$$ >= 1] (1,4)
57. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ (1,4)
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 7 >= P$$
&& 3 >= O$$
&& O$$ >= 1
&& P$$ >= 1]
58. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
59. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && 3 >= O$ && O$ >= 1 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
60. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
61. f8(C,E,H,M,N) -> f6(1 + C,1 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
62. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= O$ && 7 >= P$ && O$ >= 5 && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
63. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && 3 >= O$$ && O$$ >= 1 && P$$ >= 1] (1,4)
64. f8(C,E,H,M,N) -> f6(2 + C,2 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= O$$ && 7 >= P$$ && O$$ >= 5 && P$$ >= 1] (1,4)
65. f8(C,E,H,M,N) -> f6(3 + C,3 + E,1,M,N) [7 >= P$ && P$ >= 1 && 7 >= P$$ && P$$ >= 1] (1,4)
68. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
74. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
80. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
81. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
82. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
83. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 18*E + 18*M,4)
&& 7 >= P
&& 3 >= O
&& O >= 1
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
86. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& 3 >= O$
&& O$ >= 1
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
92. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= O$
&& 7 >= P$
&& O$ >= 5
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 2 + E
&& N >= 2 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
98. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 15*E + 15*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
99. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& 3 >= O$$$
&& O$$$ >= 1
&& P$$$ >= 1
&& 1 = 1]
100. f2(C,E,H,M,N) -> f2(1 + C,1 + E,0,M,N) [7 >= O (12 + 6*E + 6*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 1
&& M >= 2 + E
&& N >= 1
&& N >= 2 + C
&& 7 >= O$$$
&& 7 >= P$$$
&& O$$$ >= 5
&& P$$$ >= 1
&& 1 = 1]
101. f2(C,E,H,M,N) -> f2(2 + C,2 + E,0,M,N) [7 >= O (7 + 12*E + 12*M,4)
&& 7 >= P
&& O >= 5
&& P >= 1
&& 7 >= P$
&& P$ >= 1
&& 7 >= O$$
&& 1 >= P$$
&& P$$ >= 0
&& O$$ >= 1
&& 1 = 1
&& M >= 3 + E
&& N >= 3 + C
&& M >= 1
&& N >= 1
&& 7 >= P$$$
&& P$$$ >= 1]
Signature:
{(f1,5);(f2,5);(f3,5);(f4,5);(f6,5);(f7,5);(f8,5)}
Flow Graph:
[30->{35,36,37,38},31->{35,36,37,38},32->{35,36,37,38},35->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},36->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},37->{30,31,32,68,74,80,81,82,83,86,92,98,99,100
,101},38->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},39->{35},40->{35},41->{35,36,37,38},42->{35}
,43->{35},44->{35,36,37,38},45->{35,36,37,38},46->{35,36,37,38},47->{35,36,37,38},48->{35},49->{35},50->{35
,36,37,38},51->{35},52->{35},53->{35,36,37,38},54->{35,36,37,38},55->{35,36,37,38},56->{35,36,37,38},57->{35
,36,37,38},58->{35,36,37,38},59->{35,36,37,38},60->{35,36,37,38},61->{35,36,37,38},62->{35,36,37,38},63->{35
,36,37,38},64->{35,36,37,38},65->{35,36,37,38},68->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},74->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},80->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},81->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},82->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},83->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},86->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},92->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},98->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},99->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101},100->{30,31,32,68,74,80,81,82,83,86,92,98,99,100,101},101->{30
,31,32,68,74,80,81,82,83,86,92,98,99,100,101}]
Sizebounds:
(< 30,0,C>, N) (< 30,0,E>, M) (< 30,0,H>, 1) (< 30,0,M>, M) (< 30,0,N>, N)
(< 31,0,C>, N) (< 31,0,E>, M) (< 31,0,H>, 1) (< 31,0,M>, M) (< 31,0,N>, N)
(< 32,0,C>, N) (< 32,0,E>, M) (< 32,0,H>, 1) (< 32,0,M>, M) (< 32,0,N>, N)
(< 35,0,C>, N) (< 35,0,E>, M) (< 35,0,H>, 0) (< 35,0,M>, M) (< 35,0,N>, N)
(< 36,0,C>, N) (< 36,0,E>, M) (< 36,0,H>, 0) (< 36,0,M>, M) (< 36,0,N>, N)
(< 37,0,C>, N) (< 37,0,E>, M) (< 37,0,H>, 0) (< 37,0,M>, M) (< 37,0,N>, N)
(< 38,0,C>, N) (< 38,0,E>, M) (< 38,0,H>, 0) (< 38,0,M>, M) (< 38,0,N>, N)
(< 39,0,C>, C) (< 39,0,E>, E) (< 39,0,H>, 0) (< 39,0,M>, M) (< 39,0,N>, N)
(< 40,0,C>, C) (< 40,0,E>, E) (< 40,0,H>, 0) (< 40,0,M>, M) (< 40,0,N>, N)
(< 41,0,C>, 1 + C) (< 41,0,E>, 1 + E) (< 41,0,H>, 1) (< 41,0,M>, M) (< 41,0,N>, N)
(< 42,0,C>, C) (< 42,0,E>, E) (< 42,0,H>, 0) (< 42,0,M>, M) (< 42,0,N>, N)
(< 43,0,C>, C) (< 43,0,E>, E) (< 43,0,H>, 0) (< 43,0,M>, M) (< 43,0,N>, N)
(< 44,0,C>, 1 + C) (< 44,0,E>, 1 + E) (< 44,0,H>, 1) (< 44,0,M>, M) (< 44,0,N>, N)
(< 45,0,C>, 1 + C) (< 45,0,E>, 1 + E) (< 45,0,H>, 1) (< 45,0,M>, M) (< 45,0,N>, N)
(< 46,0,C>, 1 + C) (< 46,0,E>, 1 + E) (< 46,0,H>, 1) (< 46,0,M>, M) (< 46,0,N>, N)
(< 47,0,C>, 2 + C) (< 47,0,E>, 2 + E) (< 47,0,H>, 1) (< 47,0,M>, M) (< 47,0,N>, N)
(< 48,0,C>, C) (< 48,0,E>, E) (< 48,0,H>, 0) (< 48,0,M>, M) (< 48,0,N>, N)
(< 49,0,C>, C) (< 49,0,E>, E) (< 49,0,H>, 0) (< 49,0,M>, M) (< 49,0,N>, N)
(< 50,0,C>, 1 + C) (< 50,0,E>, 1 + E) (< 50,0,H>, 1) (< 50,0,M>, M) (< 50,0,N>, N)
(< 51,0,C>, C) (< 51,0,E>, E) (< 51,0,H>, 0) (< 51,0,M>, M) (< 51,0,N>, N)
(< 52,0,C>, C) (< 52,0,E>, E) (< 52,0,H>, 0) (< 52,0,M>, M) (< 52,0,N>, N)
(< 53,0,C>, 1 + C) (< 53,0,E>, 1 + E) (< 53,0,H>, 1) (< 53,0,M>, M) (< 53,0,N>, N)
(< 54,0,C>, 1 + C) (< 54,0,E>, 1 + E) (< 54,0,H>, 1) (< 54,0,M>, M) (< 54,0,N>, N)
(< 55,0,C>, 1 + C) (< 55,0,E>, 1 + E) (< 55,0,H>, 1) (< 55,0,M>, M) (< 55,0,N>, N)
(< 56,0,C>, 2 + C) (< 56,0,E>, 2 + E) (< 56,0,H>, 1) (< 56,0,M>, M) (< 56,0,N>, N)
(< 57,0,C>, 1 + C) (< 57,0,E>, 1 + E) (< 57,0,H>, 1) (< 57,0,M>, M) (< 57,0,N>, N)
(< 58,0,C>, 1 + C) (< 58,0,E>, 1 + E) (< 58,0,H>, 1) (< 58,0,M>, M) (< 58,0,N>, N)
(< 59,0,C>, 2 + C) (< 59,0,E>, 2 + E) (< 59,0,H>, 1) (< 59,0,M>, M) (< 59,0,N>, N)
(< 60,0,C>, 1 + C) (< 60,0,E>, 1 + E) (< 60,0,H>, 1) (< 60,0,M>, M) (< 60,0,N>, N)
(< 61,0,C>, 1 + C) (< 61,0,E>, 1 + E) (< 61,0,H>, 1) (< 61,0,M>, M) (< 61,0,N>, N)
(< 62,0,C>, 2 + C) (< 62,0,E>, 2 + E) (< 62,0,H>, 1) (< 62,0,M>, M) (< 62,0,N>, N)
(< 63,0,C>, 2 + C) (< 63,0,E>, 2 + E) (< 63,0,H>, 1) (< 63,0,M>, M) (< 63,0,N>, N)
(< 64,0,C>, 2 + C) (< 64,0,E>, 2 + E) (< 64,0,H>, 1) (< 64,0,M>, M) (< 64,0,N>, N)
(< 65,0,C>, 3 + C) (< 65,0,E>, 3 + E) (< 65,0,H>, 1) (< 65,0,M>, M) (< 65,0,N>, N)
(< 68,0,C>, N) (< 68,0,E>, M) (< 68,0,H>, 0) (< 68,0,M>, M) (< 68,0,N>, N)
(< 74,0,C>, N) (< 74,0,E>, M) (< 74,0,H>, 0) (< 74,0,M>, M) (< 74,0,N>, N)
(< 80,0,C>, N) (< 80,0,E>, M) (< 80,0,H>, 0) (< 80,0,M>, M) (< 80,0,N>, N)
(< 81,0,C>, N) (< 81,0,E>, M) (< 81,0,H>, 0) (< 81,0,M>, M) (< 81,0,N>, N)
(< 82,0,C>, N) (< 82,0,E>, M) (< 82,0,H>, 0) (< 82,0,M>, M) (< 82,0,N>, N)
(< 83,0,C>, N) (< 83,0,E>, M) (< 83,0,H>, 0) (< 83,0,M>, M) (< 83,0,N>, N)
(< 86,0,C>, N) (< 86,0,E>, M) (< 86,0,H>, 0) (< 86,0,M>, M) (< 86,0,N>, N)
(< 92,0,C>, N) (< 92,0,E>, M) (< 92,0,H>, 0) (< 92,0,M>, M) (< 92,0,N>, N)
(< 98,0,C>, N) (< 98,0,E>, M) (< 98,0,H>, 0) (< 98,0,M>, M) (< 98,0,N>, N)
(< 99,0,C>, N) (< 99,0,E>, M) (< 99,0,H>, 0) (< 99,0,M>, M) (< 99,0,N>, N)
(<100,0,C>, N) (<100,0,E>, M) (<100,0,H>, 0) (<100,0,M>, M) (<100,0,N>, N)
(<101,0,C>, N) (<101,0,E>, M) (<101,0,H>, 0) (<101,0,M>, M) (<101,0,N>, N)
+ Applied Processor:
SizeboundsProc
+ Details:
The problem is already solved.
WORST_CASE(?,O(n^1))