WORST_CASE(?,O(n^3)) * Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (?,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 3. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + A] (?,1) 4. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + C] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6,7},3->{16},4->{16},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13} ,11->{13},12->{14},13->{8,9},14->{15},15->{2,3,4},16->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (< 0,0,A>, A, .= 0) (< 0,0,B>, B, .= 0) (< 0,0,C>, C, .= 0) (< 0,0,D>, D, .= 0) (< 0,0,E>, E, .= 0) (< 1,0,A>, B, .= 0) (< 1,0,B>, B, .= 0) (< 1,0,C>, 0, .= 0) (< 1,0,D>, D, .= 0) (< 1,0,E>, E, .= 0) (< 2,0,A>, A, .= 0) (< 2,0,B>, B, .= 0) (< 2,0,C>, C, .= 0) (< 2,0,D>, D, .= 0) (< 2,0,E>, E, .= 0) (< 3,0,A>, A, .= 0) (< 3,0,B>, B, .= 0) (< 3,0,C>, C, .= 0) (< 3,0,D>, D, .= 0) (< 3,0,E>, E, .= 0) (< 4,0,A>, A, .= 0) (< 4,0,B>, B, .= 0) (< 4,0,C>, C, .= 0) (< 4,0,D>, D, .= 0) (< 4,0,E>, E, .= 0) (< 5,0,A>, A, .= 0) (< 5,0,B>, B, .= 0) (< 5,0,C>, C, .= 0) (< 5,0,D>, C, .= 0) (< 5,0,E>, E, .= 0) (< 6,0,A>, A, .= 0) (< 6,0,B>, B, .= 0) (< 6,0,C>, C, .= 0) (< 6,0,D>, C, .= 0) (< 6,0,E>, E, .= 0) (< 7,0,A>, A, .= 0) (< 7,0,B>, B, .= 0) (< 7,0,C>, C, .= 0) (< 7,0,D>, A, .= 0) (< 7,0,E>, C, .= 0) (< 8,0,A>, A, .= 0) (< 8,0,B>, B, .= 0) (< 8,0,C>, C, .= 0) (< 8,0,D>, D, .= 0) (< 8,0,E>, E, .= 0) (< 9,0,A>, A, .= 0) (< 9,0,B>, B, .= 0) (< 9,0,C>, C, .= 0) (< 9,0,D>, D, .= 0) (< 9,0,E>, E, .= 0) (<10,0,A>, A, .= 0) (<10,0,B>, B, .= 0) (<10,0,C>, C, .= 0) (<10,0,D>, D, .= 0) (<10,0,E>, E, .= 0) (<11,0,A>, A, .= 0) (<11,0,B>, B, .= 0) (<11,0,C>, C, .= 0) (<11,0,D>, D, .= 0) (<11,0,E>, E, .= 0) (<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, C, .= 0) (<12,0,D>, D, .= 0) (<12,0,E>, E, .= 0) (<13,0,A>, A, .= 0) (<13,0,B>, B, .= 0) (<13,0,C>, C, .= 0) (<13,0,D>, 1 + D, .+ 1) (<13,0,E>, E, .= 0) (<14,0,A>, A, .= 0) (<14,0,B>, B, .= 0) (<14,0,C>, C, .= 0) (<14,0,D>, 1 + A, .+ 1) (<14,0,E>, D, .= 0) (<15,0,A>, D, .= 0) (<15,0,B>, B, .= 0) (<15,0,C>, 1 + E, .+ 1) (<15,0,D>, D, .= 0) (<15,0,E>, E, .= 0) (<16,0,A>, A, .= 0) (<16,0,B>, B, .= 0) (<16,0,C>, C, .= 0) (<16,0,D>, D, .= 0) (<16,0,E>, E, .= 0) * Step 2: SizeboundsProc WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (?,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 3. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + A] (?,1) 4. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + C] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6,7},3->{16},4->{16},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13} ,11->{13},12->{14},13->{8,9},14->{15},15->{2,3,4},16->{}] Sizebounds: (< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 0,0,D>, ?) (< 0,0,E>, ?) (< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (< 1,0,D>, ?) (< 1,0,E>, ?) (< 2,0,A>, ?) (< 2,0,B>, ?) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 3,0,A>, ?) (< 3,0,B>, ?) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 4,0,A>, ?) (< 4,0,B>, ?) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, ?) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, ?) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, ?) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, ?) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, ?) (< 9,0,C>, ?) (< 9,0,D>, ?) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, ?) (<10,0,C>, ?) (<10,0,D>, ?) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, ?) (<11,0,C>, ?) (<11,0,D>, ?) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?) (<12,0,D>, ?) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, ?) (<13,0,C>, ?) (<13,0,D>, ?) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, ?) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, ?) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, ?) (<16,0,B>, ?) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 3,0,A>, ?) (< 3,0,B>, B) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?) * Step 3: UnsatPaths WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (?,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 3. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + A] (?,1) 4. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + C] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6,7},3->{16},4->{16},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13} ,11->{13},12->{14},13->{8,9},14->{15},15->{2,3,4},16->{}] Sizebounds: (< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 3,0,A>, ?) (< 3,0,B>, B) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,4)] * Step 4: LeafRules WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (?,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 3. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + A] (?,1) 4. evalfbb7in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [0 >= 1 + C] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{5,6,7},3->{16},4->{16},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13} ,11->{13},12->{14},13->{8,9},14->{15},15->{2,3,4},16->{}] Sizebounds: (< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 3,0,A>, ?) (< 3,0,B>, B) (< 3,0,C>, ?) (< 3,0,D>, ?) (< 3,0,E>, ?) (< 4,0,A>, ?) (< 4,0,B>, B) (< 4,0,C>, ?) (< 4,0,D>, ?) (< 4,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, ?) (<16,0,B>, B) (<16,0,C>, ?) (<16,0,D>, ?) (<16,0,E>, ?) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [3,4,16] * Step 5: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (?,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2},2->{5,6,7},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13},11->{13},12->{14} ,13->{8,9},14->{15},15->{2}] Sizebounds: (< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 0 p(evalfbb3in) = 0 p(evalfbb4in) = 0 p(evalfbb5in) = 0 p(evalfbb6in) = 0 p(evalfbb7in) = 0 p(evalfbbin) = 0 p(evalfentryin) = 1 p(evalfstart) = 1 The following rules are strictly oriented: True ==> evalfentryin(A,B,C,D,E) = 1 > 0 = evalfbb7in(B,B,0,D,E) The following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E) = 1 >= 1 = evalfentryin(A,B,C,D,E) [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 0 >= 0 = evalfbbin(A,B,C,D,E) [0 >= 1 + F] ==> evalfbbin(A,B,C,D,E) = 0 >= 0 = evalfbb3in(A,B,C,C,E) [F >= 1] ==> evalfbbin(A,B,C,D,E) = 0 >= 0 = evalfbb3in(A,B,C,C,E) True ==> evalfbbin(A,B,C,D,E) = 0 >= 0 = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 0 >= 0 = evalfbb5in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 0 >= 0 = evalfbb4in(A,B,C,D,E) [0 >= 1 + F] ==> evalfbb4in(A,B,C,D,E) = 0 >= 0 = evalfbb2in(A,B,C,D,E) [F >= 1] ==> evalfbb4in(A,B,C,D,E) = 0 >= 0 = evalfbb2in(A,B,C,D,E) True ==> evalfbb4in(A,B,C,D,E) = 0 >= 0 = evalfbb5in(A,B,C,D,E) True ==> evalfbb2in(A,B,C,D,E) = 0 >= 0 = evalfbb3in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = 0 >= 0 = evalfbb6in(A,B,C,-1 + A,D) True ==> evalfbb6in(A,B,C,D,E) = 0 >= 0 = evalfbb7in(D,B,-1 + E,D,E) * Step 6: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2},2->{5,6,7},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13},11->{13},12->{14} ,13->{8,9},14->{15},15->{2}] Sizebounds: (< 0,0,A>, A) (< 0,0,B>, B) (< 0,0,C>, C) (< 0,0,D>, D) (< 0,0,E>, E) (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) + Applied Processor: ChainProcessor False [0,1,2,5,6,7,8,9,10,11,12,13,14,15] + Details: We chained rule 0 to obtain the rules [16] . * Step 7: UnreachableRules WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 1. evalfentryin(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,1) 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [1->{2},2->{5,6,7},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13},11->{13},12->{14},13->{8,9} ,14->{15},15->{2},16->{2}] Sizebounds: (< 1,0,A>, B) (< 1,0,B>, B) (< 1,0,C>, 0) (< 1,0,D>, D) (< 1,0,E>, E) (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [1] * Step 8: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 2. evalfbb7in(A,B,C,D,E) -> evalfbbin(A,B,C,D,E) [A >= 0 && C >= 0] (?,1) 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [2->{5,6,7},5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13},11->{13},12->{14},13->{8,9},14->{15} ,15->{2},16->{2}] Sizebounds: (< 2,0,A>, ?) (< 2,0,B>, B) (< 2,0,C>, ?) (< 2,0,D>, ?) (< 2,0,E>, ?) (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) + Applied Processor: ChainProcessor False [2,5,6,7,8,9,10,11,12,13,14,15,16] + Details: We chained rule 2 to obtain the rules [17,18,19] . * Step 9: UnreachableRules WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 5. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [0 >= 1 + F] (?,1) 6. evalfbbin(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [F >= 1] (?,1) 7. evalfbbin(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) True (?,1) 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [5->{8,9},6->{8,9},7->{15},8->{14},9->{10,11,12},10->{13},11->{13},12->{14},13->{8,9},14->{15},15->{17,18 ,19},16->{17,18,19},17->{8,9},18->{8,9},19->{15}] Sizebounds: (< 5,0,A>, ?) (< 5,0,B>, B) (< 5,0,C>, ?) (< 5,0,D>, ?) (< 5,0,E>, ?) (< 6,0,A>, ?) (< 6,0,B>, B) (< 6,0,C>, ?) (< 6,0,D>, ?) (< 6,0,E>, ?) (< 7,0,A>, ?) (< 7,0,B>, B) (< 7,0,C>, ?) (< 7,0,D>, ?) (< 7,0,E>, ?) (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [5,6,7] * Step 10: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 8. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [D >= 1 + B] (?,1) 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [8->{14},9->{10,11,12},10->{13},11->{13},12->{14},13->{8,9},14->{15},15->{17,18,19},16->{17,18,19},17->{8 ,9},18->{8,9},19->{15}] Sizebounds: (< 8,0,A>, ?) (< 8,0,B>, B) (< 8,0,C>, ?) (< 8,0,D>, ?) (< 8,0,E>, ?) (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) + Applied Processor: ChainProcessor False [8,9,10,11,12,13,14,15,16,17,18,19] + Details: We chained rule 8 to obtain the rules [20] . * Step 11: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 9. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,E) [B >= D] (?,1) 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [9->{10,11,12},10->{13},11->{13},12->{14},13->{9,20},14->{15},15->{17,18,19},16->{17,18,19},17->{9,20} ,18->{9,20},19->{15},20->{15}] Sizebounds: (< 9,0,A>, ?) (< 9,0,B>, B) (< 9,0,C>, ?) (< 9,0,D>, B) (< 9,0,E>, ?) (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) + Applied Processor: ChainProcessor False [9,10,11,12,13,14,15,16,17,18,19,20] + Details: We chained rule 9 to obtain the rules [21,22,23] . * Step 12: UnreachableRules WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 10. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [0 >= 1 + F] (?,1) 11. evalfbb4in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [F >= 1] (?,1) 12. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) True (?,1) 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [10->{13},11->{13},12->{14},13->{20,21,22,23},14->{15},15->{17,18,19},16->{17,18,19},17->{20,21,22,23} ,18->{20,21,22,23},19->{15},20->{15},21->{13},22->{13},23->{14}] Sizebounds: (<10,0,A>, ?) (<10,0,B>, B) (<10,0,C>, ?) (<10,0,D>, B) (<10,0,E>, ?) (<11,0,A>, ?) (<11,0,B>, B) (<11,0,C>, ?) (<11,0,D>, B) (<11,0,E>, ?) (<12,0,A>, ?) (<12,0,B>, B) (<12,0,C>, ?) (<12,0,D>, B) (<12,0,E>, ?) (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [10,11,12] * Step 13: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 13. evalfbb2in(A,B,C,D,E) -> evalfbb3in(A,B,C,1 + D,E) True (?,1) 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [13->{20,21,22,23},14->{15},15->{17,18,19},16->{17,18,19},17->{20,21,22,23},18->{20,21,22,23},19->{15} ,20->{15},21->{13},22->{13},23->{14}] Sizebounds: (<13,0,A>, ?) (<13,0,B>, B) (<13,0,C>, ?) (<13,0,D>, B) (<13,0,E>, ?) (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) + Applied Processor: ChainProcessor False [13,14,15,16,17,18,19,20,21,22,23] + Details: We chained rule 13 to obtain the rules [24,25,26,27] . * Step 14: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 14. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) True (?,1) 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [14->{15},15->{17,18,19},16->{17,18,19},17->{20,21,22,23},18->{20,21,22,23},19->{15},20->{15},21->{24,25 ,26,27},22->{24,25,26,27},23->{14},24->{15},25->{24,25,26,27},26->{24,25,26,27},27->{14}] Sizebounds: (<14,0,A>, ?) (<14,0,B>, B) (<14,0,C>, ?) (<14,0,D>, ?) (<14,0,E>, ?) (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) + Applied Processor: ChainProcessor False [14,15,16,17,18,19,20,21,22,23,24,25,26,27] + Details: We chained rule 14 to obtain the rules [28] . * Step 15: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 15. evalfbb6in(A,B,C,D,E) -> evalfbb7in(D,B,-1 + E,D,E) True (?,1) 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [15->{17,18,19},16->{17,18,19},17->{20,21,22,23},18->{20,21,22,23},19->{15},20->{15},21->{24,25,26,27} ,22->{24,25,26,27},23->{28},24->{15},25->{24,25,26,27},26->{24,25,26,27},27->{28},28->{17,18,19}] Sizebounds: (<15,0,A>, ?) (<15,0,B>, B) (<15,0,C>, ?) (<15,0,D>, ?) (<15,0,E>, ?) (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) + Applied Processor: ChainProcessor False [15,16,17,18,19,20,21,22,23,24,25,26,27,28] + Details: We chained rule 15 to obtain the rules [29,30,31] . * Step 16: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 16. evalfstart(A,B,C,D,E) -> evalfbb7in(B,B,0,D,E) True (1,2) 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [16->{17,18,19},17->{20,21,22,23},18->{20,21,22,23},19->{29,30,31},20->{29,30,31},21->{24,25,26,27} ,22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26,27},26->{24,25,26,27},27->{28},28->{17,18,19} ,29->{20,21,22,23},30->{20,21,22,23},31->{29,30,31}] Sizebounds: (<16,0,A>, B) (<16,0,B>, B) (<16,0,C>, 0) (<16,0,D>, D) (<16,0,E>, E) (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) + Applied Processor: ChainProcessor False [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] + Details: We chained rule 16 to obtain the rules [32,33,34] . * Step 17: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 17. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$] (?,2) 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [17->{20,21,22,23},18->{20,21,22,23},19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27} ,23->{28},24->{29,30,31},25->{24,25,26,27},26->{24,25,26,27},27->{28},28->{17,18,19},29->{20,21,22,23} ,30->{20,21,22,23},31->{29,30,31},32->{20,21,22,23},33->{20,21,22,23},34->{29,30,31}] Sizebounds: (<17,0,A>, ?) (<17,0,B>, B) (<17,0,C>, ?) (<17,0,D>, ?) (<17,0,E>, ?) (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, ?) (<32,0,B>, B) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<33,0,A>, ?) (<33,0,B>, B) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<34,0,A>, ?) (<34,0,B>, B) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,E>, ?) + Applied Processor: ChainProcessor False [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34] + Details: We chained rule 17 to obtain the rules [35,36,37,38] . * Step 18: ChainProcessor WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 18. evalfbb7in(A,B,C,D,E) -> evalfbb3in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1] (?,2) 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [18->{20,21,22,23},19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30 ,31},25->{24,25,26,27},26->{24,25,26,27},27->{28},28->{18,19,35,36,37,38},29->{20,21,22,23},30->{20,21,22 ,23},31->{29,30,31},32->{20,21,22,23},33->{20,21,22,23},34->{29,30,31},35->{29,30,31},36->{24,25,26,27} ,37->{24,25,26,27},38->{28}] Sizebounds: (<18,0,A>, ?) (<18,0,B>, B) (<18,0,C>, ?) (<18,0,D>, ?) (<18,0,E>, ?) (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, ?) (<32,0,B>, B) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<33,0,A>, ?) (<33,0,B>, B) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<34,0,A>, ?) (<34,0,B>, B) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,E>, ?) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, B) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, B) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, B) (<38,0,E>, ?) + Applied Processor: ChainProcessor False [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] + Details: We chained rule 18 to obtain the rules [39,40,41,42] . * Step 19: UnsatPaths WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{20,21,22,23},33->{20,21,22,23},34->{29,30,31},35->{29,30,31},36->{24,25,26,27},37->{24,25,26 ,27},38->{28},39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, ?) (<32,0,B>, B) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<33,0,A>, ?) (<33,0,B>, B) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<34,0,A>, ?) (<34,0,B>, B) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,E>, ?) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, B) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, B) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, B) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, B) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, B) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, B) (<42,0,E>, ?) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(32,20),(33,20),(34,29),(34,30),(34,31)] * Step 20: LocalSizeboundsProc WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, ?) (<32,0,B>, B) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<33,0,A>, ?) (<33,0,B>, B) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<34,0,A>, ?) (<34,0,B>, B) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,E>, ?) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, B) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, B) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, B) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, B) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, B) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, B) (<42,0,E>, ?) + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (<19,0,A>, A, .= 0) (<19,0,B>, B, .= 0) (<19,0,C>, C, .= 0) (<19,0,D>, A, .= 0) (<19,0,E>, C, .= 0) (<20,0,A>, A, .= 0) (<20,0,B>, B, .= 0) (<20,0,C>, C, .= 0) (<20,0,D>, 1 + A, .+ 1) (<20,0,E>, D, .= 0) (<21,0,A>, A, .= 0) (<21,0,B>, B, .= 0) (<21,0,C>, C, .= 0) (<21,0,D>, D, .= 0) (<21,0,E>, E, .= 0) (<22,0,A>, A, .= 0) (<22,0,B>, B, .= 0) (<22,0,C>, C, .= 0) (<22,0,D>, D, .= 0) (<22,0,E>, E, .= 0) (<23,0,A>, A, .= 0) (<23,0,B>, B, .= 0) (<23,0,C>, C, .= 0) (<23,0,D>, D, .= 0) (<23,0,E>, E, .= 0) (<24,0,A>, A, .= 0) (<24,0,B>, B, .= 0) (<24,0,C>, C, .= 0) (<24,0,D>, 1 + A, .+ 1) (<24,0,E>, 1 + D, .+ 1) (<25,0,A>, A, .= 0) (<25,0,B>, B, .= 0) (<25,0,C>, C, .= 0) (<25,0,D>, 1 + D, .+ 1) (<25,0,E>, E, .= 0) (<26,0,A>, A, .= 0) (<26,0,B>, B, .= 0) (<26,0,C>, C, .= 0) (<26,0,D>, 1 + D, .+ 1) (<26,0,E>, E, .= 0) (<27,0,A>, A, .= 0) (<27,0,B>, B, .= 0) (<27,0,C>, C, .= 0) (<27,0,D>, 1 + D, .+ 1) (<27,0,E>, E, .= 0) (<28,0,A>, 1 + A, .+ 1) (<28,0,B>, B, .= 0) (<28,0,C>, 1 + D, .+ 1) (<28,0,D>, 1 + A, .+ 1) (<28,0,E>, D, .= 0) (<29,0,A>, D, .= 0) (<29,0,B>, B, .= 0) (<29,0,C>, 1 + E, .+ 1) (<29,0,D>, 1 + E, .+ 1) (<29,0,E>, E, .= 0) (<30,0,A>, D, .= 0) (<30,0,B>, B, .= 0) (<30,0,C>, 1 + E, .+ 1) (<30,0,D>, 1 + E, .+ 1) (<30,0,E>, E, .= 0) (<31,0,A>, D, .= 0) (<31,0,B>, B, .= 0) (<31,0,C>, 1 + E, .+ 1) (<31,0,D>, D, .= 0) (<31,0,E>, 1 + E, .+ 1) (<32,0,A>, B, .= 0) (<32,0,B>, B, .= 0) (<32,0,C>, 0, .= 0) (<32,0,D>, 0, .= 0) (<32,0,E>, E, .= 0) (<33,0,A>, B, .= 0) (<33,0,B>, B, .= 0) (<33,0,C>, 0, .= 0) (<33,0,D>, 0, .= 0) (<33,0,E>, E, .= 0) (<34,0,A>, B, .= 0) (<34,0,B>, B, .= 0) (<34,0,C>, 0, .= 0) (<34,0,D>, B, .= 0) (<34,0,E>, 0, .= 0) (<35,0,A>, A, .= 0) (<35,0,B>, B, .= 0) (<35,0,C>, C, .= 0) (<35,0,D>, 1 + A, .+ 1) (<35,0,E>, C, .= 0) (<36,0,A>, A, .= 0) (<36,0,B>, B, .= 0) (<36,0,C>, C, .= 0) (<36,0,D>, C, .= 0) (<36,0,E>, E, .= 0) (<37,0,A>, A, .= 0) (<37,0,B>, B, .= 0) (<37,0,C>, C, .= 0) (<37,0,D>, C, .= 0) (<37,0,E>, E, .= 0) (<38,0,A>, A, .= 0) (<38,0,B>, B, .= 0) (<38,0,C>, C, .= 0) (<38,0,D>, C, .= 0) (<38,0,E>, E, .= 0) (<39,0,A>, A, .= 0) (<39,0,B>, B, .= 0) (<39,0,C>, C, .= 0) (<39,0,D>, 1 + A, .+ 1) (<39,0,E>, C, .= 0) (<40,0,A>, A, .= 0) (<40,0,B>, B, .= 0) (<40,0,C>, C, .= 0) (<40,0,D>, C, .= 0) (<40,0,E>, E, .= 0) (<41,0,A>, A, .= 0) (<41,0,B>, B, .= 0) (<41,0,C>, C, .= 0) (<41,0,D>, C, .= 0) (<41,0,E>, E, .= 0) (<42,0,A>, A, .= 0) (<42,0,B>, B, .= 0) (<42,0,C>, C, .= 0) (<42,0,D>, C, .= 0) (<42,0,E>, E, .= 0) * Step 21: SizeboundsProc WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, ?) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, ?) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, ?) (<21,0,C>, ?) (<21,0,D>, ?) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, ?) (<22,0,C>, ?) (<22,0,D>, ?) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, ?) (<23,0,C>, ?) (<23,0,D>, ?) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, ?) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, ?) (<25,0,C>, ?) (<25,0,D>, ?) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, ?) (<26,0,C>, ?) (<26,0,D>, ?) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, ?) (<27,0,C>, ?) (<27,0,D>, ?) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, ?) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, ?) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, ?) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, ?) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, ?) (<32,0,B>, ?) (<32,0,C>, ?) (<32,0,D>, ?) (<32,0,E>, ?) (<33,0,A>, ?) (<33,0,B>, ?) (<33,0,C>, ?) (<33,0,D>, ?) (<33,0,E>, ?) (<34,0,A>, ?) (<34,0,B>, ?) (<34,0,C>, ?) (<34,0,D>, ?) (<34,0,E>, ?) (<35,0,A>, ?) (<35,0,B>, ?) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, ?) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, ?) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, ?) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, ?) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, ?) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, ?) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, ?) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 22: LocationConstraintsProc WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: LocationConstraintsProc + Details: We computed the location constraints 19 : True 20 : True 21 : True 22 : True 23 : True 24 : True 25 : True 26 : True 27 : True 28 : True 29 : True 30 : True 31 : True 32 : True 33 : True 34 : True 35 : True 36 : True 37 : True 38 : True 39 : True 40 : True 41 : True 42 : True . * Step 23: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (?,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) * Step 24: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (?,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (1 + B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) * Step 25: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (?,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (1 + B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (1 + B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) * Step 26: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (?,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (1 + B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (1 + B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (1 + B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 + x1 p(evalfbb3in) = 1 + x1 p(evalfbb5in) = 1 + x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = 1 + A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,C,E) * Step 27: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (?,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (1 + B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (1 + B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (1 + B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (1 + B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = x2 The following rules are strictly oriented: [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > -1 + A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= -1 + A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= -1 + A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = D >= D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = B >= B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = B >= B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = B >= B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= -1 + A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) * Step 28: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (?,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb2in(A,B,C,C,E) * Step 29: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (?,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,C) * Step 30: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (?,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 + x1 p(evalfbb3in) = 1 + x1 p(evalfbb5in) = 1 + x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = 1 + A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,C,E) * Step 31: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (?,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D > D = evalfbb3in(D,B,-1 + E,-1 + E,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) * Step 32: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (?,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x1 p(evalfbb3in) = x1 p(evalfbb5in) = x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 1 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D > D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D > D = evalfbb3in(D,B,-1 + E,-1 + E,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B > B = evalfbb3in(B,B,0,0,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + A > A = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb6in(A,B,C,A,C) [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = A >= A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = A >= A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) * Step 33: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (?,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 + x1 p(evalfbb3in) = 1 + x1 p(evalfbb5in) = 1 + x1 p(evalfbb6in) = 1 + x4 p(evalfbb7in) = 2 + x1 p(evalfstart) = 1 + x2 The following rules are strictly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 2 + A > 1 + A = evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 2 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 2 + A > 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 2 + A > 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 2 + A > 1 + A = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 2 + A > A = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 2 + A > 1 + A = evalfbb2in(A,B,C,C,E) The following rules are weakly oriented: [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= A = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = 1 + A >= 1 + A = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(D,B,-1 + E,D,-1 + E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0] ==> evalfstart(A,B,C,D,E) = 1 + B >= 1 + B = evalfbb6in(B,B,0,B,0) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 2 + A >= 1 + A = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 2 + A >= 1 + A = evalfbb5in(A,B,C,C,E) * Step 34: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (?,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [19,28,23,20,24,21,22,25,26,36,37,40,41,31,35,39,27,38,42], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 p(evalfbb3in) = 1 p(evalfbb5in) = 1 p(evalfbb6in) = 0 p(evalfbb7in) = 1 The following rules are strictly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 > 0 = evalfbb6in(A,B,C,A,C) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 > 0 = evalfbb6in(A,B,C,-1 + A,1 + D) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 > 0 = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 > 0 = evalfbb6in(A,B,C,-1 + A,C) The following rules are weakly oriented: [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 >= 0 = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb5in(A,B,C,D,E) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = 1 >= 1 = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 0 >= 0 = evalfbb6in(D,B,-1 + E,D,-1 + E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 >= 1 = evalfbb5in(A,B,C,C,E) We use the following global sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 35: KnowledgePropagation WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (?,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (?,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (?,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (?,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 36: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (?,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [28,23,29,20,30,24,21,22,25,26,31,35,39,27,38,42], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 p(evalfbb3in) = 1 p(evalfbb5in) = -1*x2 + x4 p(evalfbb6in) = 1 p(evalfbb7in) = -1*x2 + x3 The following rules are strictly oriented: [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 > 1 + -1*B + D = evalfbb5in(A,B,C,1 + D,E) The following rules are weakly oriented: [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 >= -1*B + D = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = 1 >= 1 = evalfbb2in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = -1*B + D >= -1 + -1*B + D = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = 1 >= 1 = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = 1 >= 1 = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = 1 >= 1 = evalfbb6in(D,B,-1 + E,D,-1 + E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = -1*B + C >= 1 = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = -1*B + C >= -1*B + C = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = -1*B + C >= 1 = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = -1*B + C >= -1*B + C = evalfbb5in(A,B,C,C,E) We use the following global sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 37: KnowledgePropagation WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (5 + 5*B,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (?,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 38: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (?,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (5 + 5*B,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (9 + 9*B,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [19,23,29,30,21,22,25,26,36,37,40,41,31,35,39,27,38,42], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x2 + -1*x4 p(evalfbb3in) = x2 + -1*x4 p(evalfbb5in) = x2 + -1*x4 p(evalfbb6in) = x2 p(evalfbb7in) = x2 The following rules are strictly oriented: [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = B + -1*D > -1 + B + -1*D = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = B + -1*D > -1 + B + -1*D = evalfbb5in(A,B,C,1 + D,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,A,C) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb5in(A,B,C,D,E) [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = B + -1*D >= -1 + B + -1*D = evalfbb2in(A,B,C,1 + D,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = B >= 1 + B + -1*E = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = B >= 1 + B + -1*E = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = B >= B = evalfbb6in(D,B,-1 + E,D,-1 + E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb5in(A,B,C,C,E) We use the following global sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 39: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (?,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (17*B + 13*B^2,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (5 + 5*B,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (9 + 9*B,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [19,23,29,30,21,22,25,26,36,37,40,41,31,35,39,27,38,42], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = x2 + -1*x4 p(evalfbb3in) = x2 + -1*x4 p(evalfbb5in) = x2 + -1*x4 p(evalfbb6in) = x2 p(evalfbb7in) = x2 The following rules are strictly oriented: [B >= 1 + D && 0 >= 1 + F$$] ==> evalfbb2in(A,B,C,D,E) = B + -1*D > -1 + B + -1*D = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] ==> evalfbb2in(A,B,C,D,E) = B + -1*D > -1 + B + -1*D = evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = B + -1*D > -1 + B + -1*D = evalfbb5in(A,B,C,1 + D,E) The following rules are weakly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,A,C) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = B + -1*D >= B + -1*D = evalfbb5in(A,B,C,D,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = B >= 1 + B + -1*E = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = B >= 1 + B + -1*E = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = B >= B = evalfbb6in(D,B,-1 + E,D,-1 + E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = B >= B = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = B >= B + -1*C = evalfbb5in(A,B,C,C,E) We use the following global sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 40: PolyRank WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (17*B + 13*B^2,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (17*B + 13*B^2,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (5 + 5*B,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (9 + 9*B,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (?,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [19,28,23,29,20,30,24,21,22,36,37,40,41,31,35,39,27,38,42], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb2in) = 1 + x4 p(evalfbb3in) = 1 + x4 p(evalfbb5in) = x4 p(evalfbb6in) = x5 p(evalfbb7in) = 1 + x3 The following rules are strictly oriented: [A >= 0 && C >= 0] ==> evalfbb7in(A,B,C,D,E) = 1 + C > C = evalfbb6in(A,B,C,A,C) [D >= 0 && -1 + E >= 0] ==> evalfbb6in(A,B,C,D,E) = E > -1 + E = evalfbb6in(D,B,-1 + E,D,-1 + E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + C > C = evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + C > C = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] ==> evalfbb7in(A,B,C,D,E) = 1 + C > C = evalfbb5in(A,B,C,C,E) The following rules are weakly oriented: [D >= 1 + B] ==> evalfbb3in(A,B,C,D,E) = 1 + D >= D = evalfbb6in(A,B,C,-1 + A,D) [B >= D && 0 >= 1 + F$] ==> evalfbb3in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] ==> evalfbb3in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb2in(A,B,C,D,E) [B >= D] ==> evalfbb3in(A,B,C,D,E) = 1 + D >= D = evalfbb5in(A,B,C,D,E) [1 + D >= 1 + B] ==> evalfbb2in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb6in(A,B,C,-1 + A,1 + D) [B >= 1 + D] ==> evalfbb2in(A,B,C,D,E) = 1 + D >= 1 + D = evalfbb5in(A,B,C,1 + D,E) True ==> evalfbb5in(A,B,C,D,E) = D >= D = evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] ==> evalfbb6in(A,B,C,D,E) = E >= E = evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] ==> evalfbb6in(A,B,C,D,E) = E >= E = evalfbb3in(D,B,-1 + E,-1 + E,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] ==> evalfbb7in(A,B,C,D,E) = 1 + C >= C = evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + C >= 1 + C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + C >= 1 + C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] ==> evalfbb7in(A,B,C,D,E) = 1 + C >= 1 + C = evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] ==> evalfbb7in(A,B,C,D,E) = 1 + C >= 1 + C = evalfbb2in(A,B,C,C,E) We use the following global sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) * Step 41: KnowledgePropagation WORST_CASE(?,O(n^3)) + Considered Problem: Rules: 19. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,A,C) [A >= 0 && C >= 0] (1 + B,2) 20. evalfbb3in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,D) [D >= 1 + B] (2 + 2*B,2) 21. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && 0 >= 1 + F$] (4 + 2*B,2) 22. evalfbb3in(A,B,C,D,E) -> evalfbb2in(A,B,C,D,E) [B >= D && F$ >= 1] (4 + 2*B,2) 23. evalfbb3in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [B >= D] (4 + 2*B,2) 24. evalfbb2in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,1 + D) [1 + D >= 1 + B] (4 + 2*B,3) 25. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && 0 >= 1 + F$$] (17*B + 13*B^2,3) 26. evalfbb2in(A,B,C,D,E) -> evalfbb2in(A,B,C,1 + D,E) [B >= 1 + D && F$$ >= 1] (17*B + 13*B^2,3) 27. evalfbb2in(A,B,C,D,E) -> evalfbb5in(A,B,C,1 + D,E) [B >= 1 + D] (5 + 5*B,3) 28. evalfbb5in(A,B,C,D,E) -> evalfbb7in(-1 + A,B,-1 + D,-1 + A,D) True (9 + 9*B,2) 29. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && 0 >= 1 + F$$] (1 + B,3) 30. evalfbb6in(A,B,C,D,E) -> evalfbb3in(D,B,-1 + E,-1 + E,E) [D >= 0 && -1 + E >= 0 && F$$ >= 1] (1 + B,3) 31. evalfbb6in(A,B,C,D,E) -> evalfbb6in(D,B,-1 + E,D,-1 + E) [D >= 0 && -1 + E >= 0] (2 + 34*B + 60*B^2 + 26*B^3,3) 32. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && 0 >= 1 + F$$] (1,4) 33. evalfstart(A,B,C,D,E) -> evalfbb3in(B,B,0,0,E) [B >= 0 && 0 >= 0 && F$$ >= 1] (1,4) 34. evalfstart(A,B,C,D,E) -> evalfbb6in(B,B,0,B,0) [B >= 0 && 0 >= 0] (1,4) 35. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && 0 >= 1 + F$ && C >= 1 + B] (1 + B,4) 36. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && 0 >= 1 + F$$] (1 + B,4) 37. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C && F$$ >= 1] (1 + B,4) 38. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && 0 >= 1 + F$ && B >= C] (B,4) 39. evalfbb7in(A,B,C,D,E) -> evalfbb6in(A,B,C,-1 + A,C) [A >= 0 && C >= 0 && F$ >= 1 && C >= 1 + B] (B,4) 40. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && 0 >= 1 + F$$] (B,4) 41. evalfbb7in(A,B,C,D,E) -> evalfbb2in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C && F$$ >= 1] (B,4) 42. evalfbb7in(A,B,C,D,E) -> evalfbb5in(A,B,C,C,E) [A >= 0 && C >= 0 && F$ >= 1 && B >= C] (B,4) Signature: {(evalfbb2in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbbin,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [19->{29,30,31},20->{29,30,31},21->{24,25,26,27},22->{24,25,26,27},23->{28},24->{29,30,31},25->{24,25,26 ,27},26->{24,25,26,27},27->{28},28->{19,35,36,37,38,39,40,41,42},29->{20,21,22,23},30->{20,21,22,23},31->{29 ,30,31},32->{21,22,23},33->{21,22,23},34->{},35->{29,30,31},36->{24,25,26,27},37->{24,25,26,27},38->{28} ,39->{29,30,31},40->{24,25,26,27},41->{24,25,26,27},42->{28}] Sizebounds: (<19,0,A>, ?) (<19,0,B>, B) (<19,0,C>, ?) (<19,0,D>, ?) (<19,0,E>, ?) (<20,0,A>, ?) (<20,0,B>, B) (<20,0,C>, ?) (<20,0,D>, ?) (<20,0,E>, ?) (<21,0,A>, ?) (<21,0,B>, B) (<21,0,C>, ?) (<21,0,D>, B) (<21,0,E>, ?) (<22,0,A>, ?) (<22,0,B>, B) (<22,0,C>, ?) (<22,0,D>, B) (<22,0,E>, ?) (<23,0,A>, ?) (<23,0,B>, B) (<23,0,C>, ?) (<23,0,D>, B) (<23,0,E>, ?) (<24,0,A>, ?) (<24,0,B>, B) (<24,0,C>, ?) (<24,0,D>, ?) (<24,0,E>, ?) (<25,0,A>, ?) (<25,0,B>, B) (<25,0,C>, ?) (<25,0,D>, B) (<25,0,E>, ?) (<26,0,A>, ?) (<26,0,B>, B) (<26,0,C>, ?) (<26,0,D>, B) (<26,0,E>, ?) (<27,0,A>, ?) (<27,0,B>, B) (<27,0,C>, ?) (<27,0,D>, B) (<27,0,E>, ?) (<28,0,A>, ?) (<28,0,B>, B) (<28,0,C>, ?) (<28,0,D>, ?) (<28,0,E>, ?) (<29,0,A>, ?) (<29,0,B>, B) (<29,0,C>, ?) (<29,0,D>, ?) (<29,0,E>, ?) (<30,0,A>, ?) (<30,0,B>, B) (<30,0,C>, ?) (<30,0,D>, ?) (<30,0,E>, ?) (<31,0,A>, ?) (<31,0,B>, B) (<31,0,C>, ?) (<31,0,D>, ?) (<31,0,E>, ?) (<32,0,A>, B) (<32,0,B>, B) (<32,0,C>, 0) (<32,0,D>, 0) (<32,0,E>, E) (<33,0,A>, B) (<33,0,B>, B) (<33,0,C>, 0) (<33,0,D>, 0) (<33,0,E>, E) (<34,0,A>, B) (<34,0,B>, B) (<34,0,C>, 0) (<34,0,D>, B) (<34,0,E>, 0) (<35,0,A>, ?) (<35,0,B>, B) (<35,0,C>, ?) (<35,0,D>, ?) (<35,0,E>, ?) (<36,0,A>, ?) (<36,0,B>, B) (<36,0,C>, ?) (<36,0,D>, ?) (<36,0,E>, ?) (<37,0,A>, ?) (<37,0,B>, B) (<37,0,C>, ?) (<37,0,D>, ?) (<37,0,E>, ?) (<38,0,A>, ?) (<38,0,B>, B) (<38,0,C>, ?) (<38,0,D>, ?) (<38,0,E>, ?) (<39,0,A>, ?) (<39,0,B>, B) (<39,0,C>, ?) (<39,0,D>, ?) (<39,0,E>, ?) (<40,0,A>, ?) (<40,0,B>, B) (<40,0,C>, ?) (<40,0,D>, ?) (<40,0,E>, ?) (<41,0,A>, ?) (<41,0,B>, B) (<41,0,C>, ?) (<41,0,D>, ?) (<41,0,E>, ?) (<42,0,A>, ?) (<42,0,B>, B) (<42,0,C>, ?) (<42,0,D>, ?) (<42,0,E>, ?) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(n^3))