YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) Signature: {(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1,16},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9},9->{},10->{8,9} ,11->{7,10},12->{6,11},13->{5,12},14->{4,13},15->{3,14},16->{2,15}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (1,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (1,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (1,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (1,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (1,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (1,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (1,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (1,1) Signature: {(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1,16},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9},9->{},10->{8,9} ,11->{7,10},12->{6,11},13->{5,12},14->{4,13},15->{3,14},16->{2,15}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,16) ,(10,9) ,(11,10) ,(12,11) ,(13,12) ,(14,13) ,(15,14) ,(16,15)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (1,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (1,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (1,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (1,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (1,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (1,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (1,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (1,1) Signature: {(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9},9->{},10->{8} ,11->{7},12->{6},13->{5},14->{4},15->{3},16->{2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) 17. f83(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1,16},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9,17},9->{},10->{8 ,9,17},11->{7,10},12->{6,11},13->{5,12},14->{4,13},15->{3,14},16->{2,15},17->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,16) ,(10,9) ,(11,10) ,(12,11) ,(13,12) ,(14,13) ,(15,14) ,(16,15)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) 17. f83(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9,17},9->{},10->{8,17} ,11->{7},12->{6},13->{5},14->{4},15->{3},16->{2},17->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | +- p:[1] c: [1] | +- p:[2] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | +- p:[6] c: [6] | +- p:[7] c: [7] | `- p:[8] c: [8] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H,I) -> f17(0,J,K,0,E,F,G,H,I) True (1,1) 1. f17(A,B,C,D,E,F,G,H,I) -> f17(A,B,C,1 + D,E,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= D] (?,1) 2. f27(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,1 + E,F,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= E] 3. f37(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,1 + F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && 49 >= F] 4. f45(A,B,C,D,E,F,G,H,I) -> f45(1 + A,B,C,D,E,F,G,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 5. f55(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,1 + G,H,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= G] 6. f65(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,1 + H,I) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= H] 7. f75(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,1 + I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && 49 >= I] 8. f83(A,B,C,D,E,F,G,H,I) -> f83(1 + A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && 49 >= A] 9. f83(A,B,C,D,E,F,G,H,I) -> f93(A,B,C,D,E,F,G,H,I) [-50 + I >= 0 (?,1) && -100 + H + I >= 0 && -100 + G + I >= 0 && -100 + F + I >= 0 && -100 + E + I >= 0 && -100 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 10. f75(A,B,C,D,E,F,G,H,I) -> f83(0,B,C,D,E,F,G,H,I) [I >= 0 (?,1) && -50 + H + I >= 0 && -50 + G + I >= 0 && -50 + F + I >= 0 && -50 + E + I >= 0 && -50 + D + I >= 0 && -50 + A + I >= 0 && -50 + H >= 0 && -100 + G + H >= 0 && -100 + F + H >= 0 && -100 + E + H >= 0 && -100 + D + H >= 0 && -100 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && I >= 50] 11. f65(A,B,C,D,E,F,G,H,I) -> f75(A,B,C,D,E,F,G,H,0) [H >= 0 (?,1) && -50 + G + H >= 0 && -50 + F + H >= 0 && -50 + E + H >= 0 && -50 + D + H >= 0 && -50 + A + H >= 0 && -50 + G >= 0 && -100 + F + G >= 0 && -100 + E + G >= 0 && -100 + D + G >= 0 && -100 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && H >= 50] 12. f55(A,B,C,D,E,F,G,H,I) -> f65(A,B,C,D,E,F,G,0,I) [G >= 0 (?,1) && -50 + F + G >= 0 && -50 + E + G >= 0 && -50 + D + G >= 0 && -50 + A + G >= 0 && -50 + F >= 0 && -100 + E + F >= 0 && -100 + D + F >= 0 && -100 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -100 + A + E >= 0 && -50 + D >= 0 && -100 + A + D >= 0 && -50 + A >= 0 && G >= 50] 13. f45(A,B,C,D,E,F,G,H,I) -> f55(A,B,C,D,E,F,0,H,I) [-50 + F >= 0 (?,1) && -100 + E + F >= 0 && -100 + D + F >= 0 && -50 + A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && A >= 0 && A >= 50] 14. f37(A,B,C,D,E,F,G,H,I) -> f45(0,B,C,D,E,F,G,H,I) [F >= 0 (?,1) && -50 + E + F >= 0 && -50 + D + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -50 + E >= 0 && -100 + D + E >= 0 && -50 + A + E >= 0 && -50 + -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && F >= 50] 15. f27(A,B,C,D,E,F,G,H,I) -> f37(A,B,C,D,E,0,G,H,I) [E >= 0 (?,1) && -50 + D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && -50 + D >= 0 && -50 + A + D >= 0 && -50 + -1*A + D >= 0 && -1*A >= 0 && A >= 0 && E >= 50] 16. f17(A,B,C,D,E,F,G,H,I) -> f27(A,B,C,D,0,F,G,H,I) [D >= 0 && A + D >= 0 && -1*A + D >= 0 && -1*A >= 0 && A >= 0 && D >= 50] (?,1) 17. f83(A,B,C,D,E,F,G,H,I) -> exitus616(A,B,C,D,E,F,G,H,I) True (?,1) Signature: {(exitus616,9);(f0,9);(f17,9);(f27,9);(f37,9);(f45,9);(f55,9);(f65,9);(f75,9);(f83,9);(f93,9)} Flow Graph: [0->{1},1->{1,16},2->{2,15},3->{3,14},4->{4,13},5->{5,12},6->{6,11},7->{7,10},8->{8,9,17},9->{},10->{8,17} ,11->{7},12->{6},13->{5},14->{4},15->{3},16->{2},17->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | +- p:[1] c: [1] | +- p:[2] c: [2] | +- p:[3] c: [3] | +- p:[4] c: [4] | +- p:[5] c: [5] | +- p:[6] c: [6] | +- p:[7] c: [7] | `- p:[8] c: [8]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,I,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7] f0 ~> f17 [A <= 0*K, B <= unknown, C <= unknown, D <= 0*K, E <= E, F <= F, G <= G, H <= H, I <= I] f17 ~> f17 [A <= A, B <= B, C <= C, D <= 50*K, E <= E, F <= F, G <= G, H <= H, I <= I] f27 ~> f27 [A <= A, B <= B, C <= C, D <= D, E <= 50*K, F <= F, G <= G, H <= H, I <= I] f37 ~> f37 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 50*K, G <= G, H <= H, I <= I] f45 ~> f45 [A <= 50*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] f55 ~> f55 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 50*K, H <= H, I <= I] f65 ~> f65 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= 50*K, I <= I] f75 ~> f75 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= 50*K] f83 ~> f83 [A <= 50*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] f83 ~> f93 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] f75 ~> f83 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] f65 ~> f75 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= 0*K] f55 ~> f65 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= 0*K, I <= I] f45 ~> f55 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 0*K, H <= H, I <= I] f37 ~> f45 [A <= 0*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] f27 ~> f37 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G, H <= H, I <= I] f17 ~> f27 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G, H <= H, I <= I] f83 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] + Loop: [0.0 <= 50*K + D] f17 ~> f17 [A <= A, B <= B, C <= C, D <= 50*K, E <= E, F <= F, G <= G, H <= H, I <= I] + Loop: [0.1 <= 50*K + E] f27 ~> f27 [A <= A, B <= B, C <= C, D <= D, E <= 50*K, F <= F, G <= G, H <= H, I <= I] + Loop: [0.2 <= 50*K + F] f37 ~> f37 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 50*K, G <= G, H <= H, I <= I] + Loop: [0.3 <= 50*K + A] f45 ~> f45 [A <= 50*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] + Loop: [0.4 <= 50*K + G] f55 ~> f55 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 50*K, H <= H, I <= I] + Loop: [0.5 <= 50*K + H] f65 ~> f65 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= 50*K, I <= I] + Loop: [0.6 <= 50*K + I] f75 ~> f75 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= 50*K] + Loop: [0.7 <= 50*K + A] f83 ~> f83 [A <= 50*K, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,I,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7] f0 ~> f17 [K ~=> A,K ~=> D,huge ~=> B,huge ~=> C] f17 ~> f17 [K ~=> D] f27 ~> f27 [K ~=> E] f37 ~> f37 [K ~=> F] f45 ~> f45 [K ~=> A] f55 ~> f55 [K ~=> G] f65 ~> f65 [K ~=> H] f75 ~> f75 [K ~=> I] f83 ~> f83 [K ~=> A] f83 ~> f93 [] f75 ~> f83 [K ~=> A] f65 ~> f75 [K ~=> I] f55 ~> f65 [K ~=> H] f45 ~> f55 [K ~=> G] f37 ~> f45 [K ~=> A] f27 ~> f37 [K ~=> F] f17 ~> f27 [K ~=> E] f83 ~> exitus616 [] + Loop: [D ~+> 0.0,K ~*> 0.0] f17 ~> f17 [K ~=> D] + Loop: [E ~+> 0.1,K ~*> 0.1] f27 ~> f27 [K ~=> E] + Loop: [F ~+> 0.2,K ~*> 0.2] f37 ~> f37 [K ~=> F] + Loop: [A ~+> 0.3,K ~*> 0.3] f45 ~> f45 [K ~=> A] + Loop: [G ~+> 0.4,K ~*> 0.4] f55 ~> f55 [K ~=> G] + Loop: [H ~+> 0.5,K ~*> 0.5] f65 ~> f65 [K ~=> H] + Loop: [I ~+> 0.6,K ~*> 0.6] f75 ~> f75 [K ~=> I] + Loop: [A ~+> 0.7,K ~*> 0.7] f83 ~> f83 [K ~=> A] + Applied Processor: LareProcessor + Details: f0 ~> f93 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,K ~=> H ,K ~=> I ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> 0.3 ,K ~+> 0.4 ,K ~+> 0.5 ,K ~+> 0.6 ,K ~+> 0.7 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> 0.3 ,K ~*> 0.4 ,K ~*> 0.5 ,K ~*> 0.6 ,K ~*> 0.7 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,K ~=> H ,K ~=> I ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> 0.3 ,K ~+> 0.4 ,K ~+> 0.5 ,K ~+> 0.6 ,K ~+> 0.7 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> 0.3 ,K ~*> 0.4 ,K ~*> 0.5 ,K ~*> 0.6 ,K ~*> 0.7 ,K ~*> tick] + f17> [K ~=> D,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f27> [K ~=> E,E ~+> 0.1,E ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] + f37> [K ~=> F,F ~+> 0.2,F ~+> tick,tick ~+> tick,K ~*> 0.2,K ~*> tick] + f45> [K ~=> A,A ~+> 0.3,A ~+> tick,tick ~+> tick,K ~*> 0.3,K ~*> tick] + f55> [K ~=> G,G ~+> 0.4,G ~+> tick,tick ~+> tick,K ~*> 0.4,K ~*> tick] + f65> [K ~=> H,H ~+> 0.5,H ~+> tick,tick ~+> tick,K ~*> 0.5,K ~*> tick] + f75> [K ~=> I,I ~+> 0.6,I ~+> tick,tick ~+> tick,K ~*> 0.6,K ~*> tick] + f83> [K ~=> A,A ~+> 0.7,A ~+> tick,tick ~+> tick,K ~*> 0.7,K ~*> tick] YES(?,O(1))