WORST_CASE(?,O(1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f62(A,B,C,D,E,F,G,H,I,J,K,L) -> f63(A,B,C,D,E,F,G,H,I,J,K,L) [0 >= 1 + A] (?,1) 1. f62(A,B,C,D,E,F,G,H,I,J,K,L) -> f63(A,B,C,D,E,F,G,H,I,J,K,L) [A >= 1] (?,1) 2. f0(A,B,C,D,E,F,G,H,I,J,K,L) -> f13(1,12,1,1,M,0,G,H,I,J,K,L) True (1,1) 3. f13(A,B,C,D,E,F,G,H,I,J,K,L) -> f13(A,B,C,D,E,1 + F,G,H,I,J,K,L) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,E,F,G,H,I,J,K,L) -> f22(A,B,C,D,E,F,G,H,I,J,K,L) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,E,F,G,H,I,J,K,L) -> f22(A,B,C,D,E,F,G,H,I,J,K,L) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,E,F,G,H,I,J,K,L) -> f19(A,B,1,D,E,1 + F,1,H,I,J,K,L) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,E,F,G,H,I,J,K,L) -> f19(A,B,0,D,E,1 + F,0,H,I,J,K,L) [M >= 0] (?,1) 8. f22(A,B,C,D,E,F,G,H,I,J,K,L) -> f19(A,B,0,D,E,1 + F,0,H,I,J,K,L) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,E,F,G,H,I,J,K,L) -> f19(A,B,0,D,E,1 + F,0,H,I,J,K,L) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,E,F,G,H,I,J,K,L) -> f35(A,B,C,D,E,F,G,1 + F,I,J,K,L) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,E,F,G,H,I,J,K,L) -> f38(A,B,C,D,E,F,G,H,I,J,K,L) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,E,F,G,H,I,J,K,L) -> f38(A,B,C,D,E,F,G,H,I,J,K,L) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,E,F,G,H,I,J,K,L) -> f35(1,B,C,D,E,F,G,1 + H,1,J,K,L) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,E,F,G,H,I,J,K,L) -> f35(1,B,C,D,E,F,G,1 + H,1,J,K,L) True (?,1) 15. f38(A,B,C,D,E,F,G,H,I,J,K,L) -> f35(0,B,C,D,E,F,G,1 + H,0,J,K,L) True (?,1) 16. f35(A,B,C,D,E,F,G,H,I,J,K,L) -> f35(0,B,C,D,E,F,G,1 + H,0,J,K,L) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f52(A,B,C,D,E,F,G,H,I,M,K,L) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f52(A,B,C,D,E,F,G,H,I,M,K,L) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,1,E,1 + F,G,H,I,J,1,L) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,1,E,1 + F,G,H,I,J,1,L) [J >= 1] (?,1) 21. f52(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,0,E,1 + F,G,H,I,0,0,L) [J = 0] (?,1) 22. f52(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,0,E,1 + F,G,H,I,J,0,L) True (?,1) 23. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,0,E,1 + F,G,H,I,M,0,L) [B >= 2 + F && D = 0] (?,1) 24. f63(A,B,C,D,E,F,G,H,I,J,K,L) -> f71(A,B,C,D,E,F,G,H,I,J,K,0) [0 >= 1 + D] (?,1) 25. f63(A,B,C,D,E,F,G,H,I,J,K,L) -> f71(A,B,C,D,E,F,G,H,I,J,K,0) [D >= 1] (?,1) 26. f63(A,B,C,D,E,F,G,H,I,J,K,L) -> f71(A,B,C,0,E,F,G,H,I,J,K,1) [D = 0] (?,1) 27. f62(A,B,C,D,E,F,G,H,I,J,K,L) -> f71(0,B,C,D,E,F,G,H,I,J,K,1) [A = 0] (?,1) 28. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f62(A,B,C,D,E,F,G,H,I,J,K,L) [0 >= 1 + C && 1 + F >= B] (?,1) 29. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f62(A,B,C,D,E,F,G,H,I,J,K,L) [C >= 1 && 1 + F >= B] (?,1) 30. f48(A,B,C,D,E,F,G,H,I,J,K,L) -> f71(A,B,0,D,E,F,G,H,I,J,K,1) [1 + F >= B && C = 0] (?,1) 31. f35(A,B,C,D,E,F,G,H,I,J,K,L) -> f32(A,B,C,D,E,1 + F,G,H,I,J,K,L) [H >= B] (?,1) 32. f32(A,B,C,D,E,F,G,H,I,J,K,L) -> f48(A,B,C,D,E,0,G,H,I,J,K,L) [1 + F >= B] (?,1) 33. f19(A,B,C,D,E,F,G,H,I,J,K,L) -> f32(A,B,C,D,E,0,G,H,I,J,K,L) [F >= B] (?,1) 34. f13(A,B,C,D,E,F,G,H,I,J,K,L) -> f19(A,B,C,D,E,0,G,H,I,J,K,L) [F >= B] (?,1) Signature: {(f0,12) ;(f13,12) ;(f19,12) ;(f22,12) ;(f32,12) ;(f35,12) ;(f38,12) ;(f48,12) ;(f52,12) ;(f62,12) ;(f63,12) ;(f71,12)} Flow Graph: [0->{24,25,26},1->{24,25,26},2->{3,34},3->{3,34},4->{6,7,8},5->{6,7,8},6->{4,5,9,33},7->{4,5,9,33},8->{4,5 ,9,33},9->{4,5,9,33},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16,31} ,15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23,28,29,30},20->{17,18 ,23,28,29,30},21->{17,18,23,28,29,30},22->{17,18,23,28,29,30},23->{17,18,23,28,29,30},24->{},25->{},26->{} ,27->{},28->{0,1,27},29->{0,1,27},30->{},31->{10,32},32->{17,18,23,28,29,30},33->{10,32},34->{4,5,9,33}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [E,G,I,K,L] . * Step 2: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [0 >= 1 + A] (?,1) 1. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [A >= 1] (?,1) 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 24. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [0 >= 1 + D] (?,1) 25. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [D >= 1] (?,1) 26. f63(A,B,C,D,F,H,J) -> f71(A,B,C,0,F,H,J) [D = 0] (?,1) 27. f62(A,B,C,D,F,H,J) -> f71(0,B,C,D,F,H,J) [A = 0] (?,1) 28. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [0 >= 1 + C && 1 + F >= B] (?,1) 29. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [C >= 1 && 1 + F >= B] (?,1) 30. f48(A,B,C,D,F,H,J) -> f71(A,B,0,D,F,H,J) [1 + F >= B && C = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (?,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [0->{24,25,26},1->{24,25,26},2->{3,34},3->{3,34},4->{6,7,8},5->{6,7,8},6->{4,5,9,33},7->{4,5,9,33},8->{4,5 ,9,33},9->{4,5,9,33},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16,31} ,15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23,28,29,30},20->{17,18 ,23,28,29,30},21->{17,18,23,28,29,30},22->{17,18,23,28,29,30},23->{17,18,23,28,29,30},24->{},25->{},26->{} ,27->{},28->{0,1,27},29->{0,1,27},30->{},31->{10,32},32->{17,18,23,28,29,30},33->{10,32},34->{4,5,9,33}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (< 0,0,A>, A, .= 0) (< 0,0,B>, B, .= 0) (< 0,0,C>, C, .= 0) (< 0,0,D>, D, .= 0) (< 0,0,F>, F, .= 0) (< 0,0,H>, H, .= 0) (< 0,0,J>, J, .= 0) (< 1,0,A>, A, .= 0) (< 1,0,B>, B, .= 0) (< 1,0,C>, C, .= 0) (< 1,0,D>, D, .= 0) (< 1,0,F>, F, .= 0) (< 1,0,H>, H, .= 0) (< 1,0,J>, J, .= 0) (< 2,0,A>, 1, .= 1) (< 2,0,B>, 12, .= 12) (< 2,0,C>, 1, .= 1) (< 2,0,D>, 1, .= 1) (< 2,0,F>, 0, .= 0) (< 2,0,H>, H, .= 0) (< 2,0,J>, J, .= 0) (< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,D>, D, .= 0) (< 3,0,F>, 1 + F, .+ 1) (< 3,0,H>, H, .= 0) (< 3,0,J>, J, .= 0) (< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,D>, D, .= 0) (< 4,0,F>, F, .= 0) (< 4,0,H>, H, .= 0) (< 4,0,J>, J, .= 0) (< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,D>, D, .= 0) (< 5,0,F>, F, .= 0) (< 5,0,H>, H, .= 0) (< 5,0,J>, J, .= 0) (< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, 1, .= 1) (< 6,0,D>, D, .= 0) (< 6,0,F>, 1 + F, .+ 1) (< 6,0,H>, H, .= 0) (< 6,0,J>, J, .= 0) (< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, 0, .= 0) (< 7,0,D>, D, .= 0) (< 7,0,F>, 1 + F, .+ 1) (< 7,0,H>, H, .= 0) (< 7,0,J>, J, .= 0) (< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, 0, .= 0) (< 8,0,D>, D, .= 0) (< 8,0,F>, 1 + F, .+ 1) (< 8,0,H>, H, .= 0) (< 8,0,J>, J, .= 0) (< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, 0, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,F>, 1 + F, .+ 1) (< 9,0,H>, H, .= 0) (< 9,0,J>, J, .= 0) (<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,D>, D, .= 0) (<10,0,F>, F, .= 0) (<10,0,H>, 1 + F, .+ 1) (<10,0,J>, J, .= 0) (<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0) (<11,0,D>, D, .= 0) (<11,0,F>, F, .= 0) (<11,0,H>, H, .= 0) (<11,0,J>, J, .= 0) (<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, C, .= 0) (<12,0,D>, D, .= 0) (<12,0,F>, F, .= 0) (<12,0,H>, H, .= 0) (<12,0,J>, J, .= 0) (<13,0,A>, 1, .= 1) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,D>, D, .= 0) (<13,0,F>, F, .= 0) (<13,0,H>, 1 + H, .+ 1) (<13,0,J>, J, .= 0) (<14,0,A>, 1, .= 1) (<14,0,B>, B, .= 0) (<14,0,C>, C, .= 0) (<14,0,D>, D, .= 0) (<14,0,F>, F, .= 0) (<14,0,H>, 1 + H, .+ 1) (<14,0,J>, J, .= 0) (<15,0,A>, 0, .= 0) (<15,0,B>, B, .= 0) (<15,0,C>, C, .= 0) (<15,0,D>, D, .= 0) (<15,0,F>, F, .= 0) (<15,0,H>, 1 + H, .+ 1) (<15,0,J>, J, .= 0) (<16,0,A>, 0, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, C, .= 0) (<16,0,D>, D, .= 0) (<16,0,F>, F, .= 0) (<16,0,H>, 1 + H, .+ 1) (<16,0,J>, J, .= 0) (<17,0,A>, A, .= 0) (<17,0,B>, B, .= 0) (<17,0,C>, C, .= 0) (<17,0,D>, D, .= 0) (<17,0,F>, F, .= 0) (<17,0,H>, H, .= 0) (<17,0,J>, ?, .?) (<18,0,A>, A, .= 0) (<18,0,B>, B, .= 0) (<18,0,C>, C, .= 0) (<18,0,D>, D, .= 0) (<18,0,F>, F, .= 0) (<18,0,H>, H, .= 0) (<18,0,J>, ?, .?) (<19,0,A>, A, .= 0) (<19,0,B>, B, .= 0) (<19,0,C>, C, .= 0) (<19,0,D>, 1, .= 1) (<19,0,F>, 1 + F, .+ 1) (<19,0,H>, H, .= 0) (<19,0,J>, J, .= 0) (<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,C>, C, .= 0) (<20,0,D>, 1, .= 1) (<20,0,F>, 1 + F, .+ 1) (<20,0,H>, H, .= 0) (<20,0,J>, J, .= 0) (<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,C>, C, .= 0) (<21,0,D>, 0, .= 0) (<21,0,F>, 1 + F, .+ 1) (<21,0,H>, H, .= 0) (<21,0,J>, 0, .= 0) (<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, C, .= 0) (<22,0,D>, 0, .= 0) (<22,0,F>, 1 + F, .+ 1) (<22,0,H>, H, .= 0) (<22,0,J>, J, .= 0) (<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,D>, 0, .= 0) (<23,0,F>, 1 + F, .+ 1) (<23,0,H>, H, .= 0) (<23,0,J>, ?, .?) (<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,C>, C, .= 0) (<24,0,D>, D, .= 0) (<24,0,F>, F, .= 0) (<24,0,H>, H, .= 0) (<24,0,J>, J, .= 0) (<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,C>, C, .= 0) (<25,0,D>, D, .= 0) (<25,0,F>, F, .= 0) (<25,0,H>, H, .= 0) (<25,0,J>, J, .= 0) (<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,C>, C, .= 0) (<26,0,D>, 0, .= 0) (<26,0,F>, F, .= 0) (<26,0,H>, H, .= 0) (<26,0,J>, J, .= 0) (<27,0,A>, 0, .= 0) (<27,0,B>, B, .= 0) (<27,0,C>, C, .= 0) (<27,0,D>, D, .= 0) (<27,0,F>, F, .= 0) (<27,0,H>, H, .= 0) (<27,0,J>, J, .= 0) (<28,0,A>, A, .= 0) (<28,0,B>, B, .= 0) (<28,0,C>, C, .= 0) (<28,0,D>, D, .= 0) (<28,0,F>, F, .= 0) (<28,0,H>, H, .= 0) (<28,0,J>, J, .= 0) (<29,0,A>, A, .= 0) (<29,0,B>, B, .= 0) (<29,0,C>, C, .= 0) (<29,0,D>, D, .= 0) (<29,0,F>, F, .= 0) (<29,0,H>, H, .= 0) (<29,0,J>, J, .= 0) (<30,0,A>, A, .= 0) (<30,0,B>, B, .= 0) (<30,0,C>, 0, .= 0) (<30,0,D>, D, .= 0) (<30,0,F>, F, .= 0) (<30,0,H>, H, .= 0) (<30,0,J>, J, .= 0) (<31,0,A>, A, .= 0) (<31,0,B>, B, .= 0) (<31,0,C>, C, .= 0) (<31,0,D>, D, .= 0) (<31,0,F>, 1 + F, .+ 1) (<31,0,H>, H, .= 0) (<31,0,J>, J, .= 0) (<32,0,A>, A, .= 0) (<32,0,B>, B, .= 0) (<32,0,C>, C, .= 0) (<32,0,D>, D, .= 0) (<32,0,F>, 0, .= 0) (<32,0,H>, H, .= 0) (<32,0,J>, J, .= 0) (<33,0,A>, A, .= 0) (<33,0,B>, B, .= 0) (<33,0,C>, C, .= 0) (<33,0,D>, D, .= 0) (<33,0,F>, 0, .= 0) (<33,0,H>, H, .= 0) (<33,0,J>, J, .= 0) (<34,0,A>, A, .= 0) (<34,0,B>, B, .= 0) (<34,0,C>, C, .= 0) (<34,0,D>, D, .= 0) (<34,0,F>, 0, .= 0) (<34,0,H>, H, .= 0) (<34,0,J>, J, .= 0) * Step 3: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [0 >= 1 + A] (?,1) 1. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [A >= 1] (?,1) 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 24. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [0 >= 1 + D] (?,1) 25. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [D >= 1] (?,1) 26. f63(A,B,C,D,F,H,J) -> f71(A,B,C,0,F,H,J) [D = 0] (?,1) 27. f62(A,B,C,D,F,H,J) -> f71(0,B,C,D,F,H,J) [A = 0] (?,1) 28. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [0 >= 1 + C && 1 + F >= B] (?,1) 29. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [C >= 1 && 1 + F >= B] (?,1) 30. f48(A,B,C,D,F,H,J) -> f71(A,B,0,D,F,H,J) [1 + F >= B && C = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (?,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [0->{24,25,26},1->{24,25,26},2->{3,34},3->{3,34},4->{6,7,8},5->{6,7,8},6->{4,5,9,33},7->{4,5,9,33},8->{4,5 ,9,33},9->{4,5,9,33},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16,31} ,15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23,28,29,30},20->{17,18 ,23,28,29,30},21->{17,18,23,28,29,30},22->{17,18,23,28,29,30},23->{17,18,23,28,29,30},24->{},25->{},26->{} ,27->{},28->{0,1,27},29->{0,1,27},30->{},31->{10,32},32->{17,18,23,28,29,30},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 0,0,D>, ?) (< 0,0,F>, ?) (< 0,0,H>, ?) (< 0,0,J>, ?) (< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (< 1,0,D>, ?) (< 1,0,F>, ?) (< 1,0,H>, ?) (< 1,0,J>, ?) (< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,F>, ?) (< 2,0,H>, ?) (< 2,0,J>, ?) (< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,F>, ?) (< 3,0,H>, ?) (< 3,0,J>, ?) (< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,F>, ?) (< 4,0,H>, ?) (< 4,0,J>, ?) (< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,F>, ?) (< 5,0,H>, ?) (< 5,0,J>, ?) (< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,F>, ?) (< 6,0,H>, ?) (< 6,0,J>, ?) (< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,F>, ?) (< 7,0,H>, ?) (< 7,0,J>, ?) (< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,F>, ?) (< 8,0,H>, ?) (< 8,0,J>, ?) (< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,F>, ?) (< 9,0,H>, ?) (< 9,0,J>, ?) (<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,F>, ?) (<10,0,H>, ?) (<10,0,J>, ?) (<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,F>, ?) (<11,0,H>, ?) (<11,0,J>, ?) (<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,F>, ?) (<12,0,H>, ?) (<12,0,J>, ?) (<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,F>, ?) (<13,0,H>, ?) (<13,0,J>, ?) (<14,0,A>, ?) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,F>, ?) (<14,0,H>, ?) (<14,0,J>, ?) (<15,0,A>, ?) (<15,0,B>, ?) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,F>, ?) (<15,0,H>, ?) (<15,0,J>, ?) (<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,F>, ?) (<16,0,H>, ?) (<16,0,J>, ?) (<17,0,A>, ?) (<17,0,B>, ?) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,F>, ?) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, ?) (<18,0,B>, ?) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,F>, ?) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, ?) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,F>, ?) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, ?) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,F>, ?) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, ?) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,F>, ?) (<21,0,H>, ?) (<21,0,J>, ?) (<22,0,A>, ?) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,F>, ?) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, ?) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,F>, ?) (<23,0,H>, ?) (<23,0,J>, ?) (<24,0,A>, ?) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,F>, ?) (<24,0,H>, ?) (<24,0,J>, ?) (<25,0,A>, ?) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,F>, ?) (<25,0,H>, ?) (<25,0,J>, ?) (<26,0,A>, ?) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,F>, ?) (<26,0,H>, ?) (<26,0,J>, ?) (<27,0,A>, ?) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,F>, ?) (<27,0,H>, ?) (<27,0,J>, ?) (<28,0,A>, ?) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,F>, ?) (<28,0,H>, ?) (<28,0,J>, ?) (<29,0,A>, ?) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,F>, ?) (<29,0,H>, ?) (<29,0,J>, ?) (<30,0,A>, ?) (<30,0,B>, ?) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,F>, ?) (<30,0,H>, ?) (<30,0,J>, ?) (<31,0,A>, ?) (<31,0,B>, ?) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, ?) (<32,0,A>, ?) (<32,0,B>, ?) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,F>, ?) (<32,0,H>, ?) (<32,0,J>, ?) (<33,0,A>, ?) (<33,0,B>, ?) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,F>, ?) (<33,0,H>, ?) (<33,0,J>, ?) (<34,0,A>, ?) (<34,0,B>, ?) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,F>, ?) (<34,0,H>, ?) (<34,0,J>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 0,0,A>, 1) (< 0,0,B>, 12) (< 0,0,C>, 1) (< 0,0,D>, 1) (< 0,0,F>, 12) (< 0,0,H>, ?) (< 0,0,J>, ?) (< 1,0,A>, 1) (< 1,0,B>, 12) (< 1,0,C>, 1) (< 1,0,D>, 1) (< 1,0,F>, 12) (< 1,0,H>, ?) (< 1,0,J>, ?) (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<24,0,A>, 1) (<24,0,B>, 12) (<24,0,C>, 1) (<24,0,D>, 1) (<24,0,F>, 12) (<24,0,H>, ?) (<24,0,J>, ?) (<25,0,A>, 1) (<25,0,B>, 12) (<25,0,C>, 1) (<25,0,D>, 1) (<25,0,F>, 12) (<25,0,H>, ?) (<25,0,J>, ?) (<26,0,A>, 1) (<26,0,B>, 12) (<26,0,C>, 1) (<26,0,D>, 0) (<26,0,F>, 12) (<26,0,H>, ?) (<26,0,J>, ?) (<27,0,A>, 0) (<27,0,B>, 12) (<27,0,C>, 1) (<27,0,D>, 1) (<27,0,F>, 12) (<27,0,H>, ?) (<27,0,J>, ?) (<28,0,A>, 1) (<28,0,B>, 12) (<28,0,C>, 1) (<28,0,D>, 1) (<28,0,F>, 12) (<28,0,H>, ?) (<28,0,J>, ?) (<29,0,A>, 1) (<29,0,B>, 12) (<29,0,C>, 1) (<29,0,D>, 1) (<29,0,F>, 12) (<29,0,H>, ?) (<29,0,J>, ?) (<30,0,A>, 1) (<30,0,B>, 12) (<30,0,C>, 0) (<30,0,D>, 1) (<30,0,F>, 12) (<30,0,H>, ?) (<30,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [0 >= 1 + A] (?,1) 1. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [A >= 1] (?,1) 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 24. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [0 >= 1 + D] (?,1) 25. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [D >= 1] (?,1) 26. f63(A,B,C,D,F,H,J) -> f71(A,B,C,0,F,H,J) [D = 0] (?,1) 27. f62(A,B,C,D,F,H,J) -> f71(0,B,C,D,F,H,J) [A = 0] (?,1) 28. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [0 >= 1 + C && 1 + F >= B] (?,1) 29. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [C >= 1 && 1 + F >= B] (?,1) 30. f48(A,B,C,D,F,H,J) -> f71(A,B,0,D,F,H,J) [1 + F >= B && C = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (?,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [0->{24,25,26},1->{24,25,26},2->{3,34},3->{3,34},4->{6,7,8},5->{6,7,8},6->{4,5,9,33},7->{4,5,9,33},8->{4,5 ,9,33},9->{4,5,9,33},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16,31} ,15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23,28,29,30},20->{17,18 ,23,28,29,30},21->{17,18,23,28,29,30},22->{17,18,23,28,29,30},23->{17,18,23,28,29,30},24->{},25->{},26->{} ,27->{},28->{0,1,27},29->{0,1,27},30->{},31->{10,32},32->{17,18,23,28,29,30},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 0,0,A>, 1) (< 0,0,B>, 12) (< 0,0,C>, 1) (< 0,0,D>, 1) (< 0,0,F>, 12) (< 0,0,H>, ?) (< 0,0,J>, ?) (< 1,0,A>, 1) (< 1,0,B>, 12) (< 1,0,C>, 1) (< 1,0,D>, 1) (< 1,0,F>, 12) (< 1,0,H>, ?) (< 1,0,J>, ?) (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<24,0,A>, 1) (<24,0,B>, 12) (<24,0,C>, 1) (<24,0,D>, 1) (<24,0,F>, 12) (<24,0,H>, ?) (<24,0,J>, ?) (<25,0,A>, 1) (<25,0,B>, 12) (<25,0,C>, 1) (<25,0,D>, 1) (<25,0,F>, 12) (<25,0,H>, ?) (<25,0,J>, ?) (<26,0,A>, 1) (<26,0,B>, 12) (<26,0,C>, 1) (<26,0,D>, 0) (<26,0,F>, 12) (<26,0,H>, ?) (<26,0,J>, ?) (<27,0,A>, 0) (<27,0,B>, 12) (<27,0,C>, 1) (<27,0,D>, 1) (<27,0,F>, 12) (<27,0,H>, ?) (<27,0,J>, ?) (<28,0,A>, 1) (<28,0,B>, 12) (<28,0,C>, 1) (<28,0,D>, 1) (<28,0,F>, 12) (<28,0,H>, ?) (<28,0,J>, ?) (<29,0,A>, 1) (<29,0,B>, 12) (<29,0,C>, 1) (<29,0,D>, 1) (<29,0,F>, 12) (<29,0,H>, ?) (<29,0,J>, ?) (<30,0,A>, 1) (<30,0,B>, 12) (<30,0,C>, 0) (<30,0,D>, 1) (<30,0,F>, 12) (<30,0,H>, ?) (<30,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,34) ,(6,4) ,(6,9) ,(7,4) ,(7,5) ,(8,4) ,(8,5) ,(9,4) ,(9,5) ,(10,31) ,(13,11) ,(13,16) ,(14,11) ,(14,16) ,(15,11) ,(15,12) ,(16,11) ,(16,12) ,(19,17) ,(19,23) ,(20,17) ,(20,23) ,(21,17) ,(21,18) ,(22,17) ,(22,18) ,(23,17) ,(23,18)] * Step 5: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [0 >= 1 + A] (?,1) 1. f62(A,B,C,D,F,H,J) -> f63(A,B,C,D,F,H,J) [A >= 1] (?,1) 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 24. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [0 >= 1 + D] (?,1) 25. f63(A,B,C,D,F,H,J) -> f71(A,B,C,D,F,H,J) [D >= 1] (?,1) 26. f63(A,B,C,D,F,H,J) -> f71(A,B,C,0,F,H,J) [D = 0] (?,1) 27. f62(A,B,C,D,F,H,J) -> f71(0,B,C,D,F,H,J) [A = 0] (?,1) 28. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [0 >= 1 + C && 1 + F >= B] (?,1) 29. f48(A,B,C,D,F,H,J) -> f62(A,B,C,D,F,H,J) [C >= 1 && 1 + F >= B] (?,1) 30. f48(A,B,C,D,F,H,J) -> f71(A,B,0,D,F,H,J) [1 + F >= B && C = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (?,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [0->{24,25,26},1->{24,25,26},2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9 ,33},10->{11,12,16},11->{13,14,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20 ,21,22},18->{19,20,21,22},19->{18,28,29,30},20->{18,28,29,30},21->{23,28,29,30},22->{23,28,29,30},23->{23,28 ,29,30},24->{},25->{},26->{},27->{},28->{0,1,27},29->{0,1,27},30->{},31->{10,32},32->{17,18,23,28,29,30} ,33->{10,32},34->{4,5,9,33}] Sizebounds: (< 0,0,A>, 1) (< 0,0,B>, 12) (< 0,0,C>, 1) (< 0,0,D>, 1) (< 0,0,F>, 12) (< 0,0,H>, ?) (< 0,0,J>, ?) (< 1,0,A>, 1) (< 1,0,B>, 12) (< 1,0,C>, 1) (< 1,0,D>, 1) (< 1,0,F>, 12) (< 1,0,H>, ?) (< 1,0,J>, ?) (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<24,0,A>, 1) (<24,0,B>, 12) (<24,0,C>, 1) (<24,0,D>, 1) (<24,0,F>, 12) (<24,0,H>, ?) (<24,0,J>, ?) (<25,0,A>, 1) (<25,0,B>, 12) (<25,0,C>, 1) (<25,0,D>, 1) (<25,0,F>, 12) (<25,0,H>, ?) (<25,0,J>, ?) (<26,0,A>, 1) (<26,0,B>, 12) (<26,0,C>, 1) (<26,0,D>, 0) (<26,0,F>, 12) (<26,0,H>, ?) (<26,0,J>, ?) (<27,0,A>, 0) (<27,0,B>, 12) (<27,0,C>, 1) (<27,0,D>, 1) (<27,0,F>, 12) (<27,0,H>, ?) (<27,0,J>, ?) (<28,0,A>, 1) (<28,0,B>, 12) (<28,0,C>, 1) (<28,0,D>, 1) (<28,0,F>, 12) (<28,0,H>, ?) (<28,0,J>, ?) (<29,0,A>, 1) (<29,0,B>, 12) (<29,0,C>, 1) (<29,0,D>, 1) (<29,0,F>, 12) (<29,0,H>, ?) (<29,0,J>, ?) (<30,0,A>, 1) (<30,0,B>, 12) (<30,0,C>, 0) (<30,0,D>, 1) (<30,0,F>, 12) (<30,0,H>, ?) (<30,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [28,29,0,1,24,25,26,27,30] * Step 6: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (?,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 1 p(f13) = 1 p(f19) = 0 p(f22) = 0 p(f32) = 0 p(f35) = 0 p(f38) = 0 p(f48) = 0 p(f52) = 0 The following rules are strictly oriented: [F >= B] ==> f13(A,B,C,D,F,H,J) = 1 > 0 = f19(A,B,C,D,0,H,J) The following rules are weakly oriented: True ==> f0(A,B,C,D,F,H,J) = 1 >= 1 = f13(1,12,1,1,0,H,J) [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = 1 >= 1 = f13(A,B,C,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 0 >= 0 = f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 0 >= 0 = f22(A,B,C,D,F,H,J) [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = 0 >= 0 = f19(A,B,1,D,1 + F,H,J) [M >= 0] ==> f22(A,B,C,D,F,H,J) = 0 >= 0 = f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] ==> f22(A,B,C,D,F,H,J) = 0 >= 0 = f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = 0 >= 0 = f19(A,B,0,D,1 + F,H,J) [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = 0 >= 0 = f35(A,B,C,D,F,1 + F,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 0 >= 0 = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 0 >= 0 = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 0 >= 0 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 0 >= 0 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 0 >= 0 = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = 0 >= 0 = f35(0,B,C,D,F,1 + H,J) [0 >= 1 + D && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f52(A,B,C,D,F,H,M) [0 >= 1 + J] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,1,1 + F,H,J) [J >= 1] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,1,1 + F,H,J) [J = 0] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,0) True ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,J) [B >= 2 + F && D = 0] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,M) [H >= B] ==> f35(A,B,C,D,F,H,J) = 0 >= 0 = f32(A,B,C,D,1 + F,H,J) [1 + F >= B] ==> f32(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,D,0,H,J) [F >= B] ==> f19(A,B,C,D,F,H,J) = 0 >= 0 = f32(A,B,C,D,0,H,J) * Step 7: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (?,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 8: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (?,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 1 p(f13) = 1 p(f19) = 1 p(f22) = 1 p(f32) = 1 p(f35) = 1 p(f38) = 1 p(f48) = 0 p(f52) = 0 The following rules are strictly oriented: [1 + F >= B] ==> f32(A,B,C,D,F,H,J) = 1 > 0 = f48(A,B,C,D,0,H,J) The following rules are weakly oriented: True ==> f0(A,B,C,D,F,H,J) = 1 >= 1 = f13(1,12,1,1,0,H,J) [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = 1 >= 1 = f13(A,B,C,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 1 >= 1 = f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 1 >= 1 = f22(A,B,C,D,F,H,J) [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = 1 >= 1 = f19(A,B,1,D,1 + F,H,J) [M >= 0] ==> f22(A,B,C,D,F,H,J) = 1 >= 1 = f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] ==> f22(A,B,C,D,F,H,J) = 1 >= 1 = f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = 1 >= 1 = f19(A,B,0,D,1 + F,H,J) [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = 1 >= 1 = f35(A,B,C,D,F,1 + F,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) [0 >= 1 + D && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f52(A,B,C,D,F,H,M) [0 >= 1 + J] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,1,1 + F,H,J) [J >= 1] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,1,1 + F,H,J) [J = 0] ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,0) True ==> f52(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,J) [B >= 2 + F && D = 0] ==> f48(A,B,C,D,F,H,J) = 0 >= 0 = f48(A,B,C,0,1 + F,H,M) [H >= B] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f32(A,B,C,D,1 + F,H,J) [F >= B] ==> f19(A,B,C,D,F,H,J) = 1 >= 1 = f32(A,B,C,D,0,H,J) [F >= B] ==> f13(A,B,C,D,F,H,J) = 1 >= 1 = f19(A,B,C,D,0,H,J) * Step 9: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 10: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (?,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 2 p(f13) = 2 p(f19) = 2 p(f22) = 2 p(f32) = 1 p(f35) = 1 p(f38) = 1 p(f48) = 1 p(f52) = 1 The following rules are strictly oriented: [F >= B] ==> f19(A,B,C,D,F,H,J) = 2 > 1 = f32(A,B,C,D,0,H,J) The following rules are weakly oriented: True ==> f0(A,B,C,D,F,H,J) = 2 >= 2 = f13(1,12,1,1,0,H,J) [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = 2 >= 2 = f13(A,B,C,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 2 >= 2 = f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 2 >= 2 = f22(A,B,C,D,F,H,J) [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = 2 >= 2 = f19(A,B,1,D,1 + F,H,J) [M >= 0] ==> f22(A,B,C,D,F,H,J) = 2 >= 2 = f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] ==> f22(A,B,C,D,F,H,J) = 2 >= 2 = f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = 2 >= 2 = f19(A,B,0,D,1 + F,H,J) [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = 1 >= 1 = f35(A,B,C,D,F,1 + F,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) [0 >= 1 + D && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 1 >= 1 = f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = 1 >= 1 = f52(A,B,C,D,F,H,M) [0 >= 1 + J] ==> f52(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,1,1 + F,H,J) [J >= 1] ==> f52(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,1,1 + F,H,J) [J = 0] ==> f52(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,0,1 + F,H,0) True ==> f52(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,0,1 + F,H,J) [B >= 2 + F && D = 0] ==> f48(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,0,1 + F,H,M) [H >= B] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f32(A,B,C,D,1 + F,H,J) [1 + F >= B] ==> f32(A,B,C,D,F,H,J) = 1 >= 1 = f48(A,B,C,D,0,H,J) [F >= B] ==> f13(A,B,C,D,F,H,J) = 2 >= 2 = f19(A,B,C,D,0,H,J) * Step 11: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (?,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 12 p(f13) = x2 p(f19) = x2 p(f22) = x2 p(f32) = x2 p(f35) = x2 p(f38) = x2 p(f48) = x2 + -1*x5 p(f52) = -1 + x2 + -1*x5 The following rules are strictly oriented: [0 >= 1 + D && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f52(A,B,C,D,F,H,M) [B >= 2 + F && D = 0] ==> f48(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f48(A,B,C,0,1 + F,H,M) The following rules are weakly oriented: True ==> f0(A,B,C,D,F,H,J) = 12 >= 12 = f13(1,12,1,1,0,H,J) [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = B >= B = f13(A,B,C,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = B >= B = f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = B >= B = f22(A,B,C,D,F,H,J) [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,1,D,1 + F,H,J) [M >= 0] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = B >= B = f35(A,B,C,D,F,1 + F,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B >= B = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B >= B = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = B >= B = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = B >= B = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = B >= B = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B >= B = f35(0,B,C,D,F,1 + H,J) [D >= 1 && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = B + -1*F >= -1 + B + -1*F = f52(A,B,C,D,F,H,M) [0 >= 1 + J] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,1,1 + F,H,J) [J >= 1] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,1,1 + F,H,J) [J = 0] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,0,1 + F,H,0) True ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,0,1 + F,H,J) [H >= B] ==> f35(A,B,C,D,F,H,J) = B >= B = f32(A,B,C,D,1 + F,H,J) [1 + F >= B] ==> f32(A,B,C,D,F,H,J) = B >= B = f48(A,B,C,D,0,H,J) [F >= B] ==> f19(A,B,C,D,F,H,J) = B >= B = f32(A,B,C,D,0,H,J) [F >= B] ==> f13(A,B,C,D,F,H,J) = B >= B = f19(A,B,C,D,0,H,J) * Step 12: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 12 p(f13) = x2 p(f19) = x2 p(f22) = x2 p(f32) = x2 p(f35) = x2 p(f38) = x2 p(f48) = x2 + -1*x5 p(f52) = -1 + x2 + -1*x5 The following rules are strictly oriented: [0 >= 1 + D && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] ==> f48(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f52(A,B,C,D,F,H,M) [B >= 2 + F && D = 0] ==> f48(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f48(A,B,C,0,1 + F,H,M) The following rules are weakly oriented: True ==> f0(A,B,C,D,F,H,J) = 12 >= 12 = f13(1,12,1,1,0,H,J) [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = B >= B = f13(A,B,C,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = B >= B = f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = B >= B = f22(A,B,C,D,F,H,J) [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,1,D,1 + F,H,J) [M >= 0] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] ==> f22(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = B >= B = f19(A,B,0,D,1 + F,H,J) [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = B >= B = f35(A,B,C,D,F,1 + F,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B >= B = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B >= B = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = B >= B = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = B >= B = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = B >= B = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B >= B = f35(0,B,C,D,F,1 + H,J) [0 >= 1 + J] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,1,1 + F,H,J) [J >= 1] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,1,1 + F,H,J) [J = 0] ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,0,1 + F,H,0) True ==> f52(A,B,C,D,F,H,J) = -1 + B + -1*F >= -1 + B + -1*F = f48(A,B,C,0,1 + F,H,J) [H >= B] ==> f35(A,B,C,D,F,H,J) = B >= B = f32(A,B,C,D,1 + F,H,J) [1 + F >= B] ==> f32(A,B,C,D,F,H,J) = B >= B = f48(A,B,C,D,0,H,J) [F >= B] ==> f19(A,B,C,D,F,H,J) = B >= B = f32(A,B,C,D,0,H,J) [F >= B] ==> f13(A,B,C,D,F,H,J) = B >= B = f19(A,B,C,D,0,H,J) * Step 13: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (?,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (?,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (?,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 14: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (?,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [3], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f13) = x2 + -1*x5 The following rules are strictly oriented: [B >= 1 + F] ==> f13(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f13(A,B,C,D,1 + F,H,J) The following rules are weakly oriented: We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 15: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (?,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [6,5], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f19) = 2 + x2 + -1*x5 p(f22) = 1 + x2 + -1*x5 The following rules are strictly oriented: [C >= 1 && B >= 1 + F] ==> f19(A,B,C,D,F,H,J) = 2 + B + -1*F > 1 + B + -1*F = f22(A,B,C,D,F,H,J) The following rules are weakly oriented: [M >= 0 && B >= 1 + N] ==> f22(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f19(A,B,1,D,1 + F,H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 16: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (?,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (?,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (?,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 17: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (?,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [9], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f19) = x2 + -1*x5 The following rules are strictly oriented: [B >= 1 + F && C = 0] ==> f19(A,B,C,D,F,H,J) = B + -1*F > -1 + B + -1*F = f19(A,B,0,D,1 + F,H,J) The following rules are weakly oriented: We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 18: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (?,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [10,31,13,11,12,14,15,16], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f32) = 2 + x2 + -1*x5 p(f35) = 1 + x2 + -1*x5 p(f38) = 1 + x2 + -1*x5 The following rules are strictly oriented: [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = 2 + B + -1*F > 1 + B + -1*F = f35(A,B,C,D,F,1 + F,J) The following rules are weakly oriented: [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f35(0,B,C,D,F,1 + H,J) [H >= B] ==> f35(A,B,C,D,F,H,J) = 1 + B + -1*F >= 1 + B + -1*F = f32(A,B,C,D,1 + F,H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 19: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (?,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 20: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (?,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [31,13,11,12,14,15,16], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f32) = 0 p(f35) = 1 p(f38) = 1 The following rules are strictly oriented: [H >= B] ==> f35(A,B,C,D,F,H,J) = 1 > 0 = f32(A,B,C,D,1 + F,H,J) The following rules are weakly oriented: [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = 1 >= 1 = f35(0,B,C,D,F,1 + H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 21: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (?,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [10,31,13,12,14,15,16], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f32) = x1 p(f35) = x1 p(f38) = 1 The following rules are strictly oriented: True ==> f38(A,B,C,D,F,H,J) = 1 > 0 = f35(0,B,C,D,F,1 + H,J) The following rules are weakly oriented: [B >= 2 + F] ==> f32(A,B,C,D,F,H,J) = A >= A = f35(A,B,C,D,F,1 + F,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = A >= 1 = f38(A,B,C,D,F,H,J) [M >= 1 + N] ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) True ==> f38(A,B,C,D,F,H,J) = 1 >= 1 = f35(1,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = A >= 0 = f35(0,B,C,D,F,1 + H,J) [H >= B] ==> f35(A,B,C,D,F,H,J) = A >= A = f32(A,B,C,D,1 + F,H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) * Step 22: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 4. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [0 >= 1 + C && B >= 1 + F] (1,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},4->{6,7,8},5->{6,7,8},6->{5,33},7->{9,33},8->{9,33},9->{9,33},10->{11,12,16},11->{13,14 ,15},12->{13,14,15},13->{12,31},14->{12,31},15->{16,31},16->{16,31},17->{19,20,21,22},18->{19,20,21,22} ,19->{18},20->{18},21->{23},22->{23},23->{23},31->{10,32},32->{17,18,23},33->{10,32},34->{4,5,9,33}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 4,0,A>, 1) (< 4,0,B>, 12) (< 4,0,C>, 1) (< 4,0,D>, 1) (< 4,0,F>, 12) (< 4,0,H>, H) (< 4,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) + Applied Processor: ChainProcessor False [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,31,32,33,34] + Details: We chained rule 4 to obtain the rules [35,36,37] . * Step 23: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 5. f19(A,B,C,D,F,H,J) -> f22(A,B,C,D,F,H,J) [C >= 1 && B >= 1 + F] (39,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},5->{6,7,8},6->{5,9,33,35,36,37},7->{5,9,33,35,36,37},8->{5,9,33,35,36,37},9->{5,9,33 ,35,36,37},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16,31},15->{11,12,16 ,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23},20->{17,18,23},21->{17,18,23} ,22->{17,18,23},23->{17,18,23},31->{10,32},32->{17,18,23},33->{10,32},34->{5,9,33,35,36,37},35->{5,9,33,35 ,36,37},36->{5,9,33,35,36,37},37->{5,9,33,35,36,37}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 5,0,A>, 1) (< 5,0,B>, 12) (< 5,0,C>, 1) (< 5,0,D>, 1) (< 5,0,F>, 12) (< 5,0,H>, H) (< 5,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) + Applied Processor: ChainProcessor False [2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,31,32,33,34,35,36,37] + Details: We chained rule 5 to obtain the rules [38,39,40] . * Step 24: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 6. f22(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [M >= 0 && B >= 1 + N] (40,1) 7. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [M >= 0] (40,1) 8. f22(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + M] (40,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},6->{9,33,35,36,37,38,39,40},7->{9,33,35,36,37,38,39,40},8->{9,33,35,36,37,38,39,40} ,9->{9,33,35,36,37,38,39,40},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11,12,16,31},14->{11,12,16 ,31},15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23},20->{17,18,23} ,21->{17,18,23},22->{17,18,23},23->{17,18,23},31->{10,32},32->{17,18,23},33->{10,32},34->{9,33,35,36,37,38 ,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37,38,39,40},38->{9,33,35 ,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37,38,39,40}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 6,0,A>, 1) (< 6,0,B>, 12) (< 6,0,C>, 1) (< 6,0,D>, 1) (< 6,0,F>, 12) (< 6,0,H>, H) (< 6,0,J>, J) (< 7,0,A>, 1) (< 7,0,B>, 12) (< 7,0,C>, 0) (< 7,0,D>, 1) (< 7,0,F>, 12) (< 7,0,H>, H) (< 7,0,J>, J) (< 8,0,A>, 1) (< 8,0,B>, 12) (< 8,0,C>, 0) (< 8,0,D>, 1) (< 8,0,F>, 12) (< 8,0,H>, H) (< 8,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [6,7,8] * Step 25: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 11. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [0 >= 1 + A && B >= 1 + H] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{11,12,16,31},11->{13,14,15},12->{13,14,15},13->{11 ,12,16,31},14->{11,12,16,31},15->{11,12,16,31},16->{11,12,16,31},17->{19,20,21,22},18->{19,20,21,22},19->{17 ,18,23},20->{17,18,23},21->{17,18,23},22->{17,18,23},23->{17,18,23},31->{10,32},32->{17,18,23},33->{10,32} ,34->{9,33,35,36,37,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37 ,38,39,40},38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37,38,39,40}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<11,0,A>, 1) (<11,0,B>, 12) (<11,0,C>, 1) (<11,0,D>, 1) (<11,0,F>, ?) (<11,0,H>, 12) (<11,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) + Applied Processor: ChainProcessor False [2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,31,32,33,34,35,36,37,38,39,40] + Details: We chained rule 11 to obtain the rules [41,42,43] . * Step 26: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 12. f35(A,B,C,D,F,H,J) -> f38(A,B,C,D,F,H,J) [A >= 1 && B >= 1 + H] (?,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{12,16,31,41,42,43},12->{13,14,15},13->{12,16,31,41 ,42,43},14->{12,16,31,41,42,43},15->{12,16,31,41,42,43},16->{12,16,31,41,42,43},17->{19,20,21,22},18->{19,20 ,21,22},19->{17,18,23},20->{17,18,23},21->{17,18,23},22->{17,18,23},23->{17,18,23},31->{10,32},32->{17,18 ,23},33->{10,32},34->{9,33,35,36,37,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40} ,37->{9,33,35,36,37,38,39,40},38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37 ,38,39,40},41->{12,16,31,41,42,43},42->{12,16,31,41,42,43},43->{12,16,31,41,42,43}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<12,0,A>, 1) (<12,0,B>, 12) (<12,0,C>, 1) (<12,0,D>, 1) (<12,0,F>, ?) (<12,0,H>, 12) (<12,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) + Applied Processor: ChainProcessor False [2,3,9,10,12,13,14,15,16,17,18,19,20,21,22,23,31,32,33,34,35,36,37,38,39,40,41,42,43] + Details: We chained rule 12 to obtain the rules [44,45,46] . * Step 27: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 13. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [M >= 1 + N] (?,1) 14. f38(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) True (?,1) 15. f38(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) True (30,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,31,41,42,43,44,45,46},13->{16,31,41,42,43,44,45 ,46},14->{16,31,41,42,43,44,45,46},15->{16,31,41,42,43,44,45,46},16->{16,31,41,42,43,44,45,46},17->{19,20,21 ,22},18->{19,20,21,22},19->{17,18,23},20->{17,18,23},21->{17,18,23},22->{17,18,23},23->{17,18,23},31->{10 ,32},32->{17,18,23},33->{10,32},34->{9,33,35,36,37,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37 ,38,39,40},37->{9,33,35,36,37,38,39,40},38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33 ,35,36,37,38,39,40},41->{16,31,41,42,43,44,45,46},42->{16,31,41,42,43,44,45,46},43->{16,31,41,42,43,44,45 ,46},44->{16,31,41,42,43,44,45,46},45->{16,31,41,42,43,44,45,46},46->{16,31,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<13,0,A>, 1) (<13,0,B>, 12) (<13,0,C>, 1) (<13,0,D>, 1) (<13,0,F>, ?) (<13,0,H>, 12) (<13,0,J>, J) (<14,0,A>, 1) (<14,0,B>, 12) (<14,0,C>, 1) (<14,0,D>, 1) (<14,0,F>, ?) (<14,0,H>, 12) (<14,0,J>, J) (<15,0,A>, 0) (<15,0,B>, 12) (<15,0,C>, 1) (<15,0,D>, 1) (<15,0,F>, ?) (<15,0,H>, 12) (<15,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [13,14,15] * Step 28: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 17. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [0 >= 1 + D && B >= 2 + F] (1,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,31,41,42,43,44,45,46},16->{16,31,41,42,43,44,45 ,46},17->{19,20,21,22},18->{19,20,21,22},19->{17,18,23},20->{17,18,23},21->{17,18,23},22->{17,18,23},23->{17 ,18,23},31->{10,32},32->{17,18,23},33->{10,32},34->{9,33,35,36,37,38,39,40},35->{9,33,35,36,37,38,39,40} ,36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37,38,39,40},38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37 ,38,39,40},40->{9,33,35,36,37,38,39,40},41->{16,31,41,42,43,44,45,46},42->{16,31,41,42,43,44,45,46},43->{16 ,31,41,42,43,44,45,46},44->{16,31,41,42,43,44,45,46},45->{16,31,41,42,43,44,45,46},46->{16,31,41,42,43,44,45 ,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<17,0,A>, 1) (<17,0,B>, 12) (<17,0,C>, 1) (<17,0,D>, 1) (<17,0,F>, 12) (<17,0,H>, ?) (<17,0,J>, ?) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) + Applied Processor: ChainProcessor False [2,3,9,10,16,17,18,19,20,21,22,23,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46] + Details: We chained rule 17 to obtain the rules [47,48,49,50] . * Step 29: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 18. f48(A,B,C,D,F,H,J) -> f52(A,B,C,D,F,H,M) [D >= 1 && B >= 2 + F] (12,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,31,41,42,43,44,45,46},16->{16,31,41,42,43,44,45 ,46},18->{19,20,21,22},19->{18,23,47,48,49,50},20->{18,23,47,48,49,50},21->{18,23,47,48,49,50},22->{18,23,47 ,48,49,50},23->{18,23,47,48,49,50},31->{10,32},32->{18,23,47,48,49,50},33->{10,32},34->{9,33,35,36,37,38,39 ,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37,38,39,40},38->{9,33,35,36 ,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37,38,39,40},41->{16,31,41,42,43,44,45,46} ,42->{16,31,41,42,43,44,45,46},43->{16,31,41,42,43,44,45,46},44->{16,31,41,42,43,44,45,46},45->{16,31,41,42 ,43,44,45,46},46->{16,31,41,42,43,44,45,46},47->{18,23,47,48,49,50},48->{18,23,47,48,49,50},49->{18,23,47,48 ,49,50},50->{18,23,47,48,49,50}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<18,0,A>, 1) (<18,0,B>, 12) (<18,0,C>, 1) (<18,0,D>, 1) (<18,0,F>, 12) (<18,0,H>, ?) (<18,0,J>, ?) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) + Applied Processor: ChainProcessor False [2,3,9,10,16,18,19,20,21,22,23,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50] + Details: We chained rule 18 to obtain the rules [51,52,53,54] . * Step 30: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 19. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [0 >= 1 + J] (13,1) 20. f52(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,J) [J >= 1] (13,1) 21. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [J = 0] (13,1) 22. f52(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,J) True (13,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,31,41,42,43,44,45,46},16->{16,31,41,42,43,44,45 ,46},19->{23,47,48,49,50,51,52,53,54},20->{23,47,48,49,50,51,52,53,54},21->{23,47,48,49,50,51,52,53,54} ,22->{23,47,48,49,50,51,52,53,54},23->{23,47,48,49,50,51,52,53,54},31->{10,32},32->{23,47,48,49,50,51,52,53 ,54},33->{10,32},34->{9,33,35,36,37,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40} ,37->{9,33,35,36,37,38,39,40},38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37 ,38,39,40},41->{16,31,41,42,43,44,45,46},42->{16,31,41,42,43,44,45,46},43->{16,31,41,42,43,44,45,46},44->{16 ,31,41,42,43,44,45,46},45->{16,31,41,42,43,44,45,46},46->{16,31,41,42,43,44,45,46},47->{23,47,48,49,50,51,52 ,53,54},48->{23,47,48,49,50,51,52,53,54},49->{23,47,48,49,50,51,52,53,54},50->{23,47,48,49,50,51,52,53,54} ,51->{23,47,48,49,50,51,52,53,54},52->{23,47,48,49,50,51,52,53,54},53->{23,47,48,49,50,51,52,53,54},54->{23 ,47,48,49,50,51,52,53,54}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<19,0,A>, 1) (<19,0,B>, 12) (<19,0,C>, 1) (<19,0,D>, 1) (<19,0,F>, 12) (<19,0,H>, ?) (<19,0,J>, ?) (<20,0,A>, 1) (<20,0,B>, 12) (<20,0,C>, 1) (<20,0,D>, 1) (<20,0,F>, 12) (<20,0,H>, ?) (<20,0,J>, ?) (<21,0,A>, 1) (<21,0,B>, 12) (<21,0,C>, 1) (<21,0,D>, 0) (<21,0,F>, 12) (<21,0,H>, ?) (<21,0,J>, 0) (<22,0,A>, 1) (<22,0,B>, 12) (<22,0,C>, 1) (<22,0,D>, 0) (<22,0,F>, 12) (<22,0,H>, ?) (<22,0,J>, ?) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [19,20,21,22] * Step 31: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 31. f35(A,B,C,D,F,H,J) -> f32(A,B,C,D,1 + F,H,J) [H >= B] (28,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,31,41,42,43,44,45,46},16->{16,31,41,42,43,44,45 ,46},23->{23,47,48,49,50,51,52,53,54},31->{10,32},32->{23,47,48,49,50,51,52,53,54},33->{10,32},34->{9,33,35 ,36,37,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37,38,39,40} ,38->{9,33,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37,38,39,40},41->{16,31,41,42,43 ,44,45,46},42->{16,31,41,42,43,44,45,46},43->{16,31,41,42,43,44,45,46},44->{16,31,41,42,43,44,45,46},45->{16 ,31,41,42,43,44,45,46},46->{16,31,41,42,43,44,45,46},47->{23,47,48,49,50,51,52,53,54},48->{23,47,48,49,50,51 ,52,53,54},49->{23,47,48,49,50,51,52,53,54},50->{23,47,48,49,50,51,52,53,54},51->{23,47,48,49,50,51,52,53 ,54},52->{23,47,48,49,50,51,52,53,54},53->{23,47,48,49,50,51,52,53,54},54->{23,47,48,49,50,51,52,53,54}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<31,0,A>, 1) (<31,0,B>, 12) (<31,0,C>, 1) (<31,0,D>, 1) (<31,0,F>, ?) (<31,0,H>, ?) (<31,0,J>, J) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) + Applied Processor: ChainProcessor False [2,3,9,10,16,23,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54] + Details: We chained rule 31 to obtain the rules [55,56] . * Step 32: ChainProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 33. f19(A,B,C,D,F,H,J) -> f32(A,B,C,D,0,H,J) [F >= B] (2,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,33,35,36,37,38,39,40},10->{16,41,42,43,44,45,46,55,56},16->{16,41,42,43,44,45 ,46,55,56},23->{23,47,48,49,50,51,52,53,54},32->{23,47,48,49,50,51,52,53,54},33->{10,32},34->{9,33,35,36,37 ,38,39,40},35->{9,33,35,36,37,38,39,40},36->{9,33,35,36,37,38,39,40},37->{9,33,35,36,37,38,39,40},38->{9,33 ,35,36,37,38,39,40},39->{9,33,35,36,37,38,39,40},40->{9,33,35,36,37,38,39,40},41->{16,41,42,43,44,45,46,55 ,56},42->{16,41,42,43,44,45,46,55,56},43->{16,41,42,43,44,45,46,55,56},44->{16,41,42,43,44,45,46,55,56} ,45->{16,41,42,43,44,45,46,55,56},46->{16,41,42,43,44,45,46,55,56},47->{23,47,48,49,50,51,52,53,54},48->{23 ,47,48,49,50,51,52,53,54},49->{23,47,48,49,50,51,52,53,54},50->{23,47,48,49,50,51,52,53,54},51->{23,47,48,49 ,50,51,52,53,54},52->{23,47,48,49,50,51,52,53,54},53->{23,47,48,49,50,51,52,53,54},54->{23,47,48,49,50,51,52 ,53,54},55->{16,41,42,43,44,45,46,55,56},56->{23,47,48,49,50,51,52,53,54}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<33,0,A>, 1) (<33,0,B>, 12) (<33,0,C>, 1) (<33,0,D>, 1) (<33,0,F>, 0) (<33,0,H>, H) (<33,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 12) (<55,0,H>, ?) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, ?) (<56,0,J>, J) + Applied Processor: ChainProcessor False [2,3,9,10,16,23,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] + Details: We chained rule 33 to obtain the rules [57,58] . * Step 33: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 10. f32(A,B,C,D,F,H,J) -> f35(A,B,C,D,F,1 + F,J) [B >= 2 + F] (28,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 32. f32(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [1 + F >= B] (1,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) 58. f19(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [F >= B && 1 >= B] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,35,36,37,38,39,40,57,58},10->{16,41,42,43,44,45,46,55,56},16->{16,41,42,43,44 ,45,46,55,56},23->{23,47,48,49,50,51,52,53,54},32->{23,47,48,49,50,51,52,53,54},34->{9,35,36,37,38,39,40,57 ,58},35->{9,35,36,37,38,39,40,57,58},36->{9,35,36,37,38,39,40,57,58},37->{9,35,36,37,38,39,40,57,58},38->{9 ,35,36,37,38,39,40,57,58},39->{9,35,36,37,38,39,40,57,58},40->{9,35,36,37,38,39,40,57,58},41->{16,41,42,43 ,44,45,46,55,56},42->{16,41,42,43,44,45,46,55,56},43->{16,41,42,43,44,45,46,55,56},44->{16,41,42,43,44,45,46 ,55,56},45->{16,41,42,43,44,45,46,55,56},46->{16,41,42,43,44,45,46,55,56},47->{23,47,48,49,50,51,52,53,54} ,48->{23,47,48,49,50,51,52,53,54},49->{23,47,48,49,50,51,52,53,54},50->{23,47,48,49,50,51,52,53,54},51->{23 ,47,48,49,50,51,52,53,54},52->{23,47,48,49,50,51,52,53,54},53->{23,47,48,49,50,51,52,53,54},54->{23,47,48,49 ,50,51,52,53,54},55->{16,41,42,43,44,45,46,55,56},56->{23,47,48,49,50,51,52,53,54},57->{16,41,42,43,44,45,46 ,55,56},58->{23,47,48,49,50,51,52,53,54}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<10,0,A>, 1) (<10,0,B>, 12) (<10,0,C>, 1) (<10,0,D>, 1) (<10,0,F>, 12) (<10,0,H>, ?) (<10,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<32,0,A>, 1) (<32,0,B>, 12) (<32,0,C>, 1) (<32,0,D>, 1) (<32,0,F>, 0) (<32,0,H>, ?) (<32,0,J>, J) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 12) (<55,0,H>, ?) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, ?) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 12) (<57,0,H>, ?) (<57,0,J>, J) (<58,0,A>, 1) (<58,0,B>, 12) (<58,0,C>, 1) (<58,0,D>, 1) (<58,0,F>, 0) (<58,0,H>, ?) (<58,0,J>, J) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [10,32] * Step 34: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) 58. f19(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [F >= B && 1 >= B] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3,34},3->{3,34},9->{9,35,36,37,38,39,40,57,58},16->{16,41,42,43,44,45,46,55,56},23->{23,47,48,49,50 ,51,52,53,54},34->{9,35,36,37,38,39,40,57,58},35->{9,35,36,37,38,39,40,57,58},36->{9,35,36,37,38,39,40,57 ,58},37->{9,35,36,37,38,39,40,57,58},38->{9,35,36,37,38,39,40,57,58},39->{9,35,36,37,38,39,40,57,58},40->{9 ,35,36,37,38,39,40,57,58},41->{16,41,42,43,44,45,46,55,56},42->{16,41,42,43,44,45,46,55,56},43->{16,41,42,43 ,44,45,46,55,56},44->{16,41,42,43,44,45,46,55,56},45->{16,41,42,43,44,45,46,55,56},46->{16,41,42,43,44,45,46 ,55,56},47->{23,47,48,49,50,51,52,53,54},48->{23,47,48,49,50,51,52,53,54},49->{23,47,48,49,50,51,52,53,54} ,50->{23,47,48,49,50,51,52,53,54},51->{23,47,48,49,50,51,52,53,54},52->{23,47,48,49,50,51,52,53,54},53->{23 ,47,48,49,50,51,52,53,54},54->{23,47,48,49,50,51,52,53,54},55->{16,41,42,43,44,45,46,55,56},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46,55,56},58->{23,47,48,49,50,51,52,53,54}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 12) (<55,0,H>, ?) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, ?) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 12) (<57,0,H>, ?) (<57,0,J>, J) (<58,0,A>, 1) (<58,0,B>, 12) (<58,0,C>, 1) (<58,0,D>, 1) (<58,0,F>, 0) (<58,0,H>, ?) (<58,0,J>, J) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,34) ,(9,35) ,(9,36) ,(9,37) ,(9,38) ,(9,39) ,(9,40) ,(16,41) ,(16,42) ,(16,43) ,(16,44) ,(16,45) ,(16,46) ,(23,47) ,(23,48) ,(23,49) ,(23,50) ,(23,51) ,(23,52) ,(23,53) ,(23,54) ,(34,57) ,(35,9) ,(35,35) ,(35,36) ,(35,37) ,(36,35) ,(36,36) ,(36,37) ,(36,38) ,(36,39) ,(36,40) ,(37,35) ,(37,36) ,(37,37) ,(37,38) ,(37,39) ,(37,40) ,(38,9) ,(38,35) ,(38,36) ,(38,37) ,(39,35) ,(39,36) ,(39,37) ,(39,38) ,(39,39) ,(39,40) ,(40,35) ,(40,36) ,(40,37) ,(40,38) ,(40,39) ,(40,40) ,(41,16) ,(41,41) ,(41,42) ,(41,43) ,(42,16) ,(42,41) ,(42,42) ,(42,43) ,(43,41) ,(43,42) ,(43,43) ,(43,44) ,(43,45) ,(43,46) ,(44,16) ,(44,41) ,(44,42) ,(44,43) ,(45,16) ,(45,41) ,(45,42) ,(45,43) ,(46,41) ,(46,42) ,(46,43) ,(46,44) ,(46,45) ,(46,46) ,(47,23) ,(47,47) ,(47,48) ,(47,49) ,(47,50) ,(48,23) ,(48,47) ,(48,48) ,(48,49) ,(48,50) ,(49,47) ,(49,48) ,(49,49) ,(49,50) ,(49,51) ,(49,52) ,(49,53) ,(49,54) ,(50,47) ,(50,48) ,(50,49) ,(50,50) ,(50,51) ,(50,52) ,(50,53) ,(50,54) ,(51,23) ,(51,47) ,(51,48) ,(51,49) ,(51,50) ,(52,23) ,(52,47) ,(52,48) ,(52,49) ,(52,50) ,(53,47) ,(53,48) ,(53,49) ,(53,50) ,(53,51) ,(53,52) ,(53,53) ,(53,54) ,(54,47) ,(54,48) ,(54,49) ,(54,50) ,(54,51) ,(54,52) ,(54,53) ,(54,54) ,(55,55) ,(55,56) ,(57,55) ,(57,56) ,(58,23) ,(58,47) ,(58,48) ,(58,49) ,(58,50) ,(58,51) ,(58,52) ,(58,53) ,(58,54)] * Step 35: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) 58. f19(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [F >= B && 1 >= B] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57,58},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40,58},35->{38,39,40,57,58} ,36->{9,57,58},37->{9,57,58},38->{38,39,40,57,58},39->{9,57,58},40->{9,57,58},41->{44,45,46,55,56},42->{44 ,45,46,55,56},43->{16,55,56},44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54} ,48->{51,52,53,54},49->{23},50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43 ,44,45,46},56->{23,47,48,49,50,51,52,53,54},57->{16,41,42,43,44,45,46},58->{}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 12) (<55,0,H>, ?) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, ?) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 12) (<57,0,H>, ?) (<57,0,J>, J) (<58,0,A>, 1) (<58,0,B>, 12) (<58,0,C>, 1) (<58,0,D>, 1) (<58,0,F>, 0) (<58,0,H>, ?) (<58,0,J>, J) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [58] * Step 36: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 12) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, ?) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 12) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 12) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 12) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 12) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 12) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 12) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 12) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, ?) (<41,0,H>, 12) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, ?) (<42,0,H>, 12) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, ?) (<43,0,H>, 12) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, ?) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, ?) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, ?) (<46,0,H>, 12) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 12) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 12) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 12) (<49,0,H>, ?) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 12) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 12) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 12) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 12) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 12) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 12) (<55,0,H>, ?) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, ?) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 12) (<57,0,H>, ?) (<57,0,J>, J) + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (< 2,0,A>, 1, .= 1) (< 2,0,B>, 12, .= 12) (< 2,0,C>, 1, .= 1) (< 2,0,D>, 1, .= 1) (< 2,0,F>, 0, .= 0) (< 2,0,H>, H, .= 0) (< 2,0,J>, J, .= 0) (< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,D>, D, .= 0) (< 3,0,F>, 1 + F, .+ 1) (< 3,0,H>, H, .= 0) (< 3,0,J>, J, .= 0) (< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, 0, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,F>, 1 + F, .+ 1) (< 9,0,H>, H, .= 0) (< 9,0,J>, J, .= 0) (<16,0,A>, 0, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, C, .= 0) (<16,0,D>, D, .= 0) (<16,0,F>, F, .= 0) (<16,0,H>, 1 + H, .+ 1) (<16,0,J>, J, .= 0) (<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,D>, 0, .= 0) (<23,0,F>, 1 + F, .+ 1) (<23,0,H>, H, .= 0) (<23,0,J>, ?, .?) (<34,0,A>, A, .= 0) (<34,0,B>, B, .= 0) (<34,0,C>, C, .= 0) (<34,0,D>, D, .= 0) (<34,0,F>, 0, .= 0) (<34,0,H>, H, .= 0) (<34,0,J>, J, .= 0) (<35,0,A>, A, .= 0) (<35,0,B>, B, .= 0) (<35,0,C>, 1, .= 1) (<35,0,D>, D, .= 0) (<35,0,F>, 1 + F, .+ 1) (<35,0,H>, H, .= 0) (<35,0,J>, J, .= 0) (<36,0,A>, A, .= 0) (<36,0,B>, B, .= 0) (<36,0,C>, 0, .= 0) (<36,0,D>, D, .= 0) (<36,0,F>, 1 + F, .+ 1) (<36,0,H>, H, .= 0) (<36,0,J>, J, .= 0) (<37,0,A>, A, .= 0) (<37,0,B>, B, .= 0) (<37,0,C>, 0, .= 0) (<37,0,D>, D, .= 0) (<37,0,F>, 1 + F, .+ 1) (<37,0,H>, H, .= 0) (<37,0,J>, J, .= 0) (<38,0,A>, A, .= 0) (<38,0,B>, B, .= 0) (<38,0,C>, 1, .= 1) (<38,0,D>, D, .= 0) (<38,0,F>, 1 + F, .+ 1) (<38,0,H>, H, .= 0) (<38,0,J>, J, .= 0) (<39,0,A>, A, .= 0) (<39,0,B>, B, .= 0) (<39,0,C>, 0, .= 0) (<39,0,D>, D, .= 0) (<39,0,F>, 1 + F, .+ 1) (<39,0,H>, H, .= 0) (<39,0,J>, J, .= 0) (<40,0,A>, A, .= 0) (<40,0,B>, B, .= 0) (<40,0,C>, 0, .= 0) (<40,0,D>, D, .= 0) (<40,0,F>, 1 + F, .+ 1) (<40,0,H>, H, .= 0) (<40,0,J>, J, .= 0) (<41,0,A>, 1, .= 1) (<41,0,B>, B, .= 0) (<41,0,C>, C, .= 0) (<41,0,D>, D, .= 0) (<41,0,F>, F, .= 0) (<41,0,H>, 1 + H, .+ 1) (<41,0,J>, J, .= 0) (<42,0,A>, 1, .= 1) (<42,0,B>, B, .= 0) (<42,0,C>, C, .= 0) (<42,0,D>, D, .= 0) (<42,0,F>, F, .= 0) (<42,0,H>, 1 + H, .+ 1) (<42,0,J>, J, .= 0) (<43,0,A>, 0, .= 0) (<43,0,B>, B, .= 0) (<43,0,C>, C, .= 0) (<43,0,D>, D, .= 0) (<43,0,F>, F, .= 0) (<43,0,H>, 1 + H, .+ 1) (<43,0,J>, J, .= 0) (<44,0,A>, 1, .= 1) (<44,0,B>, B, .= 0) (<44,0,C>, C, .= 0) (<44,0,D>, D, .= 0) (<44,0,F>, F, .= 0) (<44,0,H>, 1 + H, .+ 1) (<44,0,J>, J, .= 0) (<45,0,A>, 1, .= 1) (<45,0,B>, B, .= 0) (<45,0,C>, C, .= 0) (<45,0,D>, D, .= 0) (<45,0,F>, F, .= 0) (<45,0,H>, 1 + H, .+ 1) (<45,0,J>, J, .= 0) (<46,0,A>, 0, .= 0) (<46,0,B>, B, .= 0) (<46,0,C>, C, .= 0) (<46,0,D>, D, .= 0) (<46,0,F>, F, .= 0) (<46,0,H>, 1 + H, .+ 1) (<46,0,J>, J, .= 0) (<47,0,A>, A, .= 0) (<47,0,B>, B, .= 0) (<47,0,C>, C, .= 0) (<47,0,D>, 1, .= 1) (<47,0,F>, 1 + F, .+ 1) (<47,0,H>, H, .= 0) (<47,0,J>, ?, .?) (<48,0,A>, A, .= 0) (<48,0,B>, B, .= 0) (<48,0,C>, C, .= 0) (<48,0,D>, 1, .= 1) (<48,0,F>, 1 + F, .+ 1) (<48,0,H>, H, .= 0) (<48,0,J>, ?, .?) (<49,0,A>, A, .= 0) (<49,0,B>, B, .= 0) (<49,0,C>, C, .= 0) (<49,0,D>, 0, .= 0) (<49,0,F>, 1 + F, .+ 1) (<49,0,H>, H, .= 0) (<49,0,J>, 0, .= 0) (<50,0,A>, A, .= 0) (<50,0,B>, B, .= 0) (<50,0,C>, C, .= 0) (<50,0,D>, 0, .= 0) (<50,0,F>, 1 + F, .+ 1) (<50,0,H>, H, .= 0) (<50,0,J>, ?, .?) (<51,0,A>, A, .= 0) (<51,0,B>, B, .= 0) (<51,0,C>, C, .= 0) (<51,0,D>, 1, .= 1) (<51,0,F>, 1 + F, .+ 1) (<51,0,H>, H, .= 0) (<51,0,J>, ?, .?) (<52,0,A>, A, .= 0) (<52,0,B>, B, .= 0) (<52,0,C>, C, .= 0) (<52,0,D>, 1, .= 1) (<52,0,F>, 1 + F, .+ 1) (<52,0,H>, H, .= 0) (<52,0,J>, ?, .?) (<53,0,A>, A, .= 0) (<53,0,B>, B, .= 0) (<53,0,C>, C, .= 0) (<53,0,D>, 0, .= 0) (<53,0,F>, 1 + F, .+ 1) (<53,0,H>, H, .= 0) (<53,0,J>, 0, .= 0) (<54,0,A>, A, .= 0) (<54,0,B>, B, .= 0) (<54,0,C>, C, .= 0) (<54,0,D>, 0, .= 0) (<54,0,F>, 1 + F, .+ 1) (<54,0,H>, H, .= 0) (<54,0,J>, ?, .?) (<55,0,A>, A, .= 0) (<55,0,B>, B, .= 0) (<55,0,C>, C, .= 0) (<55,0,D>, D, .= 0) (<55,0,F>, 1 + F, .+ 1) (<55,0,H>, 2 + F, .+ 2) (<55,0,J>, J, .= 0) (<56,0,A>, A, .= 0) (<56,0,B>, B, .= 0) (<56,0,C>, C, .= 0) (<56,0,D>, D, .= 0) (<56,0,F>, 0, .= 0) (<56,0,H>, H, .= 0) (<56,0,J>, J, .= 0) (<57,0,A>, A, .= 0) (<57,0,B>, B, .= 0) (<57,0,C>, C, .= 0) (<57,0,D>, D, .= 0) (<57,0,F>, 0, .= 0) (<57,0,H>, 1, .= 1) (<57,0,J>, J, .= 0) * Step 37: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,F>, ?) (< 2,0,H>, ?) (< 2,0,J>, ?) (< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,F>, ?) (< 3,0,H>, ?) (< 3,0,J>, ?) (< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,F>, ?) (< 9,0,H>, ?) (< 9,0,J>, ?) (<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,F>, ?) (<16,0,H>, ?) (<16,0,J>, ?) (<23,0,A>, ?) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,F>, ?) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, ?) (<34,0,B>, ?) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,F>, ?) (<34,0,H>, ?) (<34,0,J>, ?) (<35,0,A>, ?) (<35,0,B>, ?) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,F>, ?) (<35,0,H>, ?) (<35,0,J>, ?) (<36,0,A>, ?) (<36,0,B>, ?) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,F>, ?) (<36,0,H>, ?) (<36,0,J>, ?) (<37,0,A>, ?) (<37,0,B>, ?) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,F>, ?) (<37,0,H>, ?) (<37,0,J>, ?) (<38,0,A>, ?) (<38,0,B>, ?) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,F>, ?) (<38,0,H>, ?) (<38,0,J>, ?) (<39,0,A>, ?) (<39,0,B>, ?) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,F>, ?) (<39,0,H>, ?) (<39,0,J>, ?) (<40,0,A>, ?) (<40,0,B>, ?) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,F>, ?) (<40,0,H>, ?) (<40,0,J>, ?) (<41,0,A>, ?) (<41,0,B>, ?) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,F>, ?) (<41,0,H>, ?) (<41,0,J>, ?) (<42,0,A>, ?) (<42,0,B>, ?) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,F>, ?) (<42,0,H>, ?) (<42,0,J>, ?) (<43,0,A>, ?) (<43,0,B>, ?) (<43,0,C>, ?) (<43,0,D>, ?) (<43,0,F>, ?) (<43,0,H>, ?) (<43,0,J>, ?) (<44,0,A>, ?) (<44,0,B>, ?) (<44,0,C>, ?) (<44,0,D>, ?) (<44,0,F>, ?) (<44,0,H>, ?) (<44,0,J>, ?) (<45,0,A>, ?) (<45,0,B>, ?) (<45,0,C>, ?) (<45,0,D>, ?) (<45,0,F>, ?) (<45,0,H>, ?) (<45,0,J>, ?) (<46,0,A>, ?) (<46,0,B>, ?) (<46,0,C>, ?) (<46,0,D>, ?) (<46,0,F>, ?) (<46,0,H>, ?) (<46,0,J>, ?) (<47,0,A>, ?) (<47,0,B>, ?) (<47,0,C>, ?) (<47,0,D>, ?) (<47,0,F>, ?) (<47,0,H>, ?) (<47,0,J>, ?) (<48,0,A>, ?) (<48,0,B>, ?) (<48,0,C>, ?) (<48,0,D>, ?) (<48,0,F>, ?) (<48,0,H>, ?) (<48,0,J>, ?) (<49,0,A>, ?) (<49,0,B>, ?) (<49,0,C>, ?) (<49,0,D>, ?) (<49,0,F>, ?) (<49,0,H>, ?) (<49,0,J>, ?) (<50,0,A>, ?) (<50,0,B>, ?) (<50,0,C>, ?) (<50,0,D>, ?) (<50,0,F>, ?) (<50,0,H>, ?) (<50,0,J>, ?) (<51,0,A>, ?) (<51,0,B>, ?) (<51,0,C>, ?) (<51,0,D>, ?) (<51,0,F>, ?) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, ?) (<52,0,B>, ?) (<52,0,C>, ?) (<52,0,D>, ?) (<52,0,F>, ?) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, ?) (<53,0,B>, ?) (<53,0,C>, ?) (<53,0,D>, ?) (<53,0,F>, ?) (<53,0,H>, ?) (<53,0,J>, ?) (<54,0,A>, ?) (<54,0,B>, ?) (<54,0,C>, ?) (<54,0,D>, ?) (<54,0,F>, ?) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, ?) (<55,0,B>, ?) (<55,0,C>, ?) (<55,0,D>, ?) (<55,0,F>, ?) (<55,0,H>, ?) (<55,0,J>, ?) (<56,0,A>, ?) (<56,0,B>, ?) (<56,0,C>, ?) (<56,0,D>, ?) (<56,0,F>, ?) (<56,0,H>, ?) (<56,0,J>, ?) (<57,0,A>, ?) (<57,0,B>, ?) (<57,0,C>, ?) (<57,0,D>, ?) (<57,0,F>, ?) (<57,0,H>, ?) (<57,0,J>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 38: LocationConstraintsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: LocationConstraintsProc + Details: We computed the location constraints 2 : True 3 : True 9 : True 16 : True 23 : True 34 : [False] 35 : [False] 36 : [False] 37 : [False] 38 : True 39 : True 40 : True 41 : True 42 : True 43 : True 44 : True 45 : True 46 : True 47 : [H >= B] 48 : [H >= B] 49 : [H >= B] 50 : [H >= B] 51 : True 52 : True 53 : True 54 : True 55 : True 56 : True 57 : True . * Step 39: LoopRecurrenceProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: LoopRecurrenceProcessor [3] + Details: Applying the recurrence pattern linear * f to the expression B-F yields the solution B + -1*F . * Step 40: LoopRecurrenceProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (39,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: LoopRecurrenceProcessor [38] + Details: Applying the recurrence pattern linear * f to the expression B-F yields the solution B + -1*F . * Step 41: LoopRecurrenceProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: LoopRecurrenceProcessor [9] + Details: Applying the recurrence pattern linear * f to the expression B-F yields the solution B + -1*F . * Step 42: LoopRecurrenceProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: LoopRecurrenceProcessor [23] + Details: Applying the recurrence pattern linear * f to the expression B-F yields the solution B + -1*F . * Step 43: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1973) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, ?) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 40) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 41) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 41) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, ?) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, ?) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, ?) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, ?) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 44: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [16,43,41,42,44,45,46], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f35) = x2 + -1*x6 The following rules are strictly oriented: [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) The following rules are weakly oriented: [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 45: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (?,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [16,43,41,42,44,45,46], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f35) = x2 + -1*x6 The following rules are strictly oriented: [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) The following rules are weakly oriented: [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 46: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (?,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [16,43,41,42,44,45,46], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f35) = x2 + -1*x6 The following rules are strictly oriented: [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) The following rules are weakly oriented: [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B + -1*H >= -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 47: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (?,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (1202,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [16,43,41,42,44,45,46], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f35) = x2 + -1*x6 The following rules are strictly oriented: [B >= 1 + H && A = 0] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] ==> f35(A,B,C,D,F,H,J) = B + -1*H > -1 + B + -1*H = f35(0,B,C,D,F,1 + H,J) The following rules are weakly oriented: We use the following global sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) * Step 48: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 2. f0(A,B,C,D,F,H,J) -> f13(1,12,1,1,0,H,J) True (1,1) 3. f13(A,B,C,D,F,H,J) -> f13(A,B,C,D,1 + F,H,J) [B >= 1 + F] (12,1) 9. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [B >= 1 + F && C = 0] (1932,1) 16. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [B >= 1 + H && A = 0] (1202,1) 23. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [B >= 2 + F && D = 0] (12,1) 34. f13(A,B,C,D,F,H,J) -> f19(A,B,C,D,0,H,J) [F >= B] (1,1) 35. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (1,2) 36. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && M$ >= 0] (1,2) 37. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [0 >= 1 + C && B >= 1 + F && 0 >= 1 + M$] (1,2) 38. f19(A,B,C,D,F,H,J) -> f19(A,B,1,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0 && B >= 1 + N$] (23,2) 39. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && M$ >= 0] (39,2) 40. f19(A,B,C,D,F,H,J) -> f19(A,B,0,D,1 + F,H,J) [C >= 1 && B >= 1 + F && 0 >= 1 + M$] (39,2) 41. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H && M$ >= 1 + N$] (28,2) 42. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 43. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [0 >= 1 + A && B >= 1 + H] (28,2) 44. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H && M$ >= 1 + N$] (1202,2) 45. f35(A,B,C,D,F,H,J) -> f35(1,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 46. f35(A,B,C,D,F,H,J) -> f35(0,B,C,D,F,1 + H,J) [A >= 1 && B >= 1 + H] (1202,2) 47. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && 0 >= 1 + M] (1,2) 48. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [0 >= 1 + D && B >= 2 + F && M >= 1] (1,2) 49. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [0 >= 1 + D && B >= 2 + F && M = 0] (1,2) 50. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [0 >= 1 + D && B >= 2 + F] (1,2) 51. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && 0 >= 1 + M] (12,2) 52. f48(A,B,C,D,F,H,J) -> f48(A,B,C,1,1 + F,H,M) [D >= 1 && B >= 2 + F && M >= 1] (12,2) 53. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,0) [D >= 1 && B >= 2 + F && M = 0] (12,2) 54. f48(A,B,C,D,F,H,J) -> f48(A,B,C,0,1 + F,H,M) [D >= 1 && B >= 2 + F] (12,2) 55. f35(A,B,C,D,F,H,J) -> f35(A,B,C,D,1 + F,2 + F,J) [H >= B && B >= 3 + F] (28,2) 56. f35(A,B,C,D,F,H,J) -> f48(A,B,C,D,0,H,J) [H >= B && 2 + F >= B] (28,2) 57. f19(A,B,C,D,F,H,J) -> f35(A,B,C,D,0,1,J) [F >= B && B >= 2] (2,2) Signature: {(f0,7);(f13,7);(f19,7);(f22,7);(f32,7);(f35,7);(f38,7);(f48,7);(f52,7);(f62,7);(f63,7);(f71,7)} Flow Graph: [2->{3},3->{3,34},9->{9,57},16->{16,55,56},23->{23},34->{9,35,36,37,38,39,40},35->{38,39,40,57},36->{9,57} ,37->{9,57},38->{38,39,40,57},39->{9,57},40->{9,57},41->{44,45,46,55,56},42->{44,45,46,55,56},43->{16,55,56} ,44->{44,45,46,55,56},45->{44,45,46,55,56},46->{16,55,56},47->{51,52,53,54},48->{51,52,53,54},49->{23} ,50->{23},51->{51,52,53,54},52->{51,52,53,54},53->{23},54->{23},55->{16,41,42,43,44,45,46},56->{23,47,48,49 ,50,51,52,53,54},57->{16,41,42,43,44,45,46}] Sizebounds: (< 2,0,A>, 1) (< 2,0,B>, 12) (< 2,0,C>, 1) (< 2,0,D>, 1) (< 2,0,F>, 0) (< 2,0,H>, H) (< 2,0,J>, J) (< 3,0,A>, 1) (< 3,0,B>, 12) (< 3,0,C>, 1) (< 3,0,D>, 1) (< 3,0,F>, 12) (< 3,0,H>, H) (< 3,0,J>, J) (< 9,0,A>, 1) (< 9,0,B>, 12) (< 9,0,C>, 0) (< 9,0,D>, 1) (< 9,0,F>, 1957) (< 9,0,H>, H) (< 9,0,J>, J) (<16,0,A>, 0) (<16,0,B>, 12) (<16,0,C>, 1) (<16,0,D>, 1) (<16,0,F>, 28) (<16,0,H>, 12) (<16,0,J>, J) (<23,0,A>, 1) (<23,0,B>, 12) (<23,0,C>, 1) (<23,0,D>, 0) (<23,0,F>, 38) (<23,0,H>, 32) (<23,0,J>, ?) (<34,0,A>, 1) (<34,0,B>, 12) (<34,0,C>, 1) (<34,0,D>, 1) (<34,0,F>, 0) (<34,0,H>, H) (<34,0,J>, J) (<35,0,A>, 1) (<35,0,B>, 12) (<35,0,C>, 1) (<35,0,D>, 1) (<35,0,F>, 1) (<35,0,H>, H) (<35,0,J>, J) (<36,0,A>, 1) (<36,0,B>, 12) (<36,0,C>, 0) (<36,0,D>, 1) (<36,0,F>, 1) (<36,0,H>, H) (<36,0,J>, J) (<37,0,A>, 1) (<37,0,B>, 12) (<37,0,C>, 0) (<37,0,D>, 1) (<37,0,F>, 1) (<37,0,H>, H) (<37,0,J>, J) (<38,0,A>, 1) (<38,0,B>, 12) (<38,0,C>, 1) (<38,0,D>, 1) (<38,0,F>, 24) (<38,0,H>, H) (<38,0,J>, J) (<39,0,A>, 1) (<39,0,B>, 12) (<39,0,C>, 0) (<39,0,D>, 1) (<39,0,F>, 25) (<39,0,H>, H) (<39,0,J>, J) (<40,0,A>, 1) (<40,0,B>, 12) (<40,0,C>, 0) (<40,0,D>, 1) (<40,0,F>, 25) (<40,0,H>, H) (<40,0,J>, J) (<41,0,A>, 1) (<41,0,B>, 12) (<41,0,C>, 1) (<41,0,D>, 1) (<41,0,F>, 28) (<41,0,H>, 31) (<41,0,J>, J) (<42,0,A>, 1) (<42,0,B>, 12) (<42,0,C>, 1) (<42,0,D>, 1) (<42,0,F>, 28) (<42,0,H>, 31) (<42,0,J>, J) (<43,0,A>, 0) (<43,0,B>, 12) (<43,0,C>, 1) (<43,0,D>, 1) (<43,0,F>, 28) (<43,0,H>, 31) (<43,0,J>, J) (<44,0,A>, 1) (<44,0,B>, 12) (<44,0,C>, 1) (<44,0,D>, 1) (<44,0,F>, 28) (<44,0,H>, 12) (<44,0,J>, J) (<45,0,A>, 1) (<45,0,B>, 12) (<45,0,C>, 1) (<45,0,D>, 1) (<45,0,F>, 28) (<45,0,H>, 12) (<45,0,J>, J) (<46,0,A>, 0) (<46,0,B>, 12) (<46,0,C>, 1) (<46,0,D>, 1) (<46,0,F>, 28) (<46,0,H>, 32) (<46,0,J>, J) (<47,0,A>, 1) (<47,0,B>, 12) (<47,0,C>, 1) (<47,0,D>, 1) (<47,0,F>, 1) (<47,0,H>, 32) (<47,0,J>, ?) (<48,0,A>, 1) (<48,0,B>, 12) (<48,0,C>, 1) (<48,0,D>, 1) (<48,0,F>, 1) (<48,0,H>, 32) (<48,0,J>, ?) (<49,0,A>, 1) (<49,0,B>, 12) (<49,0,C>, 1) (<49,0,D>, 0) (<49,0,F>, 1) (<49,0,H>, 32) (<49,0,J>, 0) (<50,0,A>, 1) (<50,0,B>, 12) (<50,0,C>, 1) (<50,0,D>, 0) (<50,0,F>, 1) (<50,0,H>, 32) (<50,0,J>, ?) (<51,0,A>, 1) (<51,0,B>, 12) (<51,0,C>, 1) (<51,0,D>, 1) (<51,0,F>, 25) (<51,0,H>, 32) (<51,0,J>, ?) (<52,0,A>, 1) (<52,0,B>, 12) (<52,0,C>, 1) (<52,0,D>, 1) (<52,0,F>, 25) (<52,0,H>, 32) (<52,0,J>, ?) (<53,0,A>, 1) (<53,0,B>, 12) (<53,0,C>, 1) (<53,0,D>, 0) (<53,0,F>, 26) (<53,0,H>, 32) (<53,0,J>, 0) (<54,0,A>, 1) (<54,0,B>, 12) (<54,0,C>, 1) (<54,0,D>, 0) (<54,0,F>, 26) (<54,0,H>, 32) (<54,0,J>, ?) (<55,0,A>, 1) (<55,0,B>, 12) (<55,0,C>, 1) (<55,0,D>, 1) (<55,0,F>, 28) (<55,0,H>, 30) (<55,0,J>, J) (<56,0,A>, 1) (<56,0,B>, 12) (<56,0,C>, 1) (<56,0,D>, 1) (<56,0,F>, 0) (<56,0,H>, 32) (<56,0,J>, J) (<57,0,A>, 1) (<57,0,B>, 12) (<57,0,C>, 1) (<57,0,D>, 1) (<57,0,F>, 0) (<57,0,H>, 1) (<57,0,J>, J) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))