YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1,15},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{} ,10->{},11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13}] + 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) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (1,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (1,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (1,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (1,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1,15},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{} ,10->{},11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,15) ,(1,14) ,(3,7) ,(4,6) ,(15,8) ,(15,9) ,(15,10) ,(15,11) ,(15,12) ,(15,13)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (1,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (1,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (1,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (1,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (1,1) Signature: {(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1},1->{2},2->{2,14},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13},8->{},9->{},10->{},11->{} ,12->{},13->{},14->{1,15},15->{3}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 16. f23(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1,15},1->{2,14},2->{2,14},3->{4,7},4->{5,6},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13,16},8->{},9->{} ,10->{},11->{},12->{},13->{},14->{1,15},15->{3,8,9,10,11,12,13,16},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,15) ,(1,14) ,(3,7) ,(4,6) ,(15,8) ,(15,9) ,(15,10) ,(15,11) ,(15,12) ,(15,13)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 16. f23(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1},1->{2},2->{2,14},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13,16},8->{},9->{},10->{} ,11->{},12->{},13->{},14->{1,15},15->{3,16},16->{}] + 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] | +- p:[1,14,2] c: [1] | | | `- p:[2] c: [2] | `- p:[3,7,6,5,4] c: [3] | `- p:[4,6,5] c: [4] | `- p:[5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f12(2,H,I,0,E,F,G) True (1,1) 1. f12(A,B,C,D,E,F,G) -> f15(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 2. f15(A,B,C,D,E,F,G) -> f15(A,B,C,D,1 + E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 3. f23(A,B,C,D,E,F,G) -> f26(A,B,C,D,0,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + D] (?,1) 4. f26(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,0,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + E] 5. f30(A,B,C,D,E,F,G) -> f30(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && A >= 1 + F] 6. f30(A,B,C,D,E,F,G) -> f26(A,B,C,D,1 + E,F,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -2 + A + F >= 0 && 2 + -1*A + F >= 0 && E >= 0 && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && F >= A] 7. f26(A,B,C,D,E,F,G) -> f23(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 8. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,0) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 9. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 49 >= H] (?,1) 10. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 11. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 42 >= H] (?,1) 12. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 21 >= H] (?,1) 13. f23(A,B,C,D,E,F,G) -> f52(A,B,C,D,E,F,1) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A && 18 >= H] (?,1) 14. f15(A,B,C,D,E,F,G) -> f12(A,B,C,1 + D,E,F,G) [E >= 0 (?,1) && D + E >= 0 && -2 + A + E >= 0 && 2 + -1*A + E >= 0 && D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && E >= A] 15. f12(A,B,C,D,E,F,G) -> f23(A,B,C,0,E,F,G) [D >= 0 && -2 + A + D >= 0 && 2 + -1*A + D >= 0 && 2 + -1*A >= 0 && -2 + A >= 0 && D >= A] (?,1) 16. f23(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f12,7);(f15,7);(f23,7);(f26,7);(f30,7);(f52,7)} Flow Graph: [0->{1},1->{2},2->{2,14},3->{4},4->{5},5->{5,6},6->{4,7},7->{3,8,9,10,11,12,13,16},8->{},9->{},10->{} ,11->{},12->{},13->{},14->{1,15},15->{3,16},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | +- p:[1,14,2] c: [1] | | | `- p:[2] c: [2] | `- p:[3,7,6,5,4] c: [3] | `- p:[4,6,5] c: [4] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0 ~> f12 [A <= 2*K, B <= unknown, C <= unknown, D <= 0*K, E <= E, F <= F, G <= G] f12 ~> f15 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f15 ~> f15 [A <= A, B <= B, C <= C, D <= D, E <= 2*K, F <= F, G <= G] f23 ~> f26 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f26 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 2*K, G <= G] f30 ~> f26 [A <= A, B <= B, C <= C, D <= D, E <= E + F, F <= F, G <= G] f26 ~> f23 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= 0*K] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f23 ~> f52 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= K] f15 ~> f12 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G] f12 ~> f23 [A <= A, B <= B, C <= C, D <= 0*K, E <= E, F <= F, G <= G] f23 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= 2*K + A + D] f12 ~> f15 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f15 ~> f12 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G] f15 ~> f15 [A <= A, B <= B, C <= C, D <= D, E <= 2*K, F <= F, G <= G] + Loop: [0.0.0 <= A + E] f15 ~> f15 [A <= A, B <= B, C <= C, D <= D, E <= 2*K, F <= F, G <= G] + Loop: [0.1 <= 2*K + A + D] f23 ~> f26 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f26 ~> f23 [A <= A, B <= B, C <= C, D <= D + E, E <= E, F <= F, G <= G] f30 ~> f26 [A <= A, B <= B, C <= C, D <= D, E <= E + F, F <= F, G <= G] f30 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 2*K, G <= G] f26 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] + Loop: [0.1.0 <= 2*K + A + E] f26 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f30 ~> f26 [A <= A, B <= B, C <= C, D <= D, E <= E + F, F <= F, G <= G] f30 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 2*K, G <= G] + Loop: [0.1.0.0 <= A + F] f30 ~> f30 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 2*K, G <= G] + 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,0.0,0.0.0,0.1,0.1.0,0.1.0.0] f0 ~> f12 [K ~=> A,K ~=> D,huge ~=> B,huge ~=> C] f12 ~> f15 [K ~=> E] f15 ~> f15 [K ~=> E] f23 ~> f26 [K ~=> E] f26 ~> f30 [K ~=> F] f30 ~> f30 [K ~=> F] f30 ~> f26 [E ~+> E,F ~+> E] f26 ~> f23 [D ~+> D,E ~+> D] f23 ~> f52 [K ~=> G] f23 ~> f52 [K ~=> G] f23 ~> f52 [K ~=> G] f23 ~> f52 [K ~=> G] f23 ~> f52 [K ~=> G] f23 ~> f52 [K ~=> G] f15 ~> f12 [D ~+> D,E ~+> D] f12 ~> f23 [K ~=> D] f23 ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,K ~*> 0.0] f12 ~> f15 [K ~=> E] f15 ~> f12 [D ~+> D,E ~+> D] f15 ~> f15 [K ~=> E] + Loop: [A ~+> 0.0.0,E ~+> 0.0.0] f15 ~> f15 [K ~=> E] + Loop: [A ~+> 0.1,D ~+> 0.1,K ~*> 0.1] f23 ~> f26 [K ~=> E] f26 ~> f23 [D ~+> D,E ~+> D] f30 ~> f26 [E ~+> E,F ~+> E] f30 ~> f30 [K ~=> F] f26 ~> f30 [K ~=> F] + Loop: [A ~+> 0.1.0,E ~+> 0.1.0,K ~*> 0.1.0] f26 ~> f30 [K ~=> F] f30 ~> f26 [E ~+> E,F ~+> E] f30 ~> f30 [K ~=> F] + Loop: [A ~+> 0.1.0.0,F ~+> 0.1.0.0] f30 ~> f30 [K ~=> F] + Applied Processor: LareProcessor + Details: f0 ~> f52 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> D ,K ~*> E ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> D ,K ~^> E] f0 ~> exitus616 [K ~=> A ,K ~=> D ,K ~=> E ,K ~=> F ,huge ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,K ~*> D ,K ~*> E ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,K ~^> D ,K ~^> E] + f12> [K ~=> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> D ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> D ,A ~*> tick ,D ~*> D ,D ~*> tick ,K ~*> D ,K ~*> 0.0 ,K ~*> tick] + f15> [K ~=> E,A ~+> 0.0.0,A ~+> tick,E ~+> 0.0.0,E ~+> tick,tick ~+> tick] + f23> [K ~=> E ,K ~=> F ,A ~+> 0.1 ,A ~+> 0.1.0 ,A ~+> 0.1.0.0 ,A ~+> tick ,D ~+> D ,D ~+> 0.1 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> D ,A ~*> E ,A ~*> 0.1.0 ,A ~*> tick ,D ~*> D ,D ~*> E ,D ~*> tick ,K ~*> D ,K ~*> E ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> tick ,A ~^> D ,A ~^> E ,D ~^> D ,D ~^> E ,K ~^> D ,K ~^> E] + f26> [K ~=> F ,A ~+> 0.1.0 ,A ~+> 0.1.0.0 ,A ~+> tick ,E ~+> E ,E ~+> 0.1.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> 0.1.0.0 ,K ~+> tick ,A ~*> E ,A ~*> tick ,E ~*> E ,E ~*> tick ,K ~*> E ,K ~*> 0.1.0 ,K ~*> tick] + f30> [K ~=> F,A ~+> 0.1.0.0,A ~+> tick,F ~+> 0.1.0.0,F ~+> tick,tick ~+> tick] YES(?,O(1))