YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (?,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (1,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (1,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (1,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (1,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (1,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (1,1) Signature: {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8} ,10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [7] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H) -> f10(I,0,C,D,E,F,G,H) True (1,1) 1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [B >= 0 && C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && D >= 1 + G] 5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && D >= 2 + E] 6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [-1 + G >= 0 (?,1) && -1 + F + G >= 0 && -1 + -1*F + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -3 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && F >= 0 && E + F >= 0 && -1*E + F >= 0 && -2 + D + F >= 0 && -2 + C + F >= 0 && -2 + B + F >= 0 && -2 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -4 + C + D >= 0 && -1*C + D >= 0 && -4 + B + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -2 + B >= 0 && G >= D] 8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H) [B + -1*E >= 0 (?,1) && E >= 0 && B + E >= 0 && C + -1*D >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && B + -1*C >= 0 && B >= 0 && 1 + E >= D] 9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H) [B >= 0 && B >= C] (?,1) 10. f34(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [7] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [A <= unknown, B <= 0*K, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f10 ~> f10 [A <= A, B <= C, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= E, G <= C, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= B, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= B, H <= H] f34 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F, G <= G, H <= H] f34 ~> f43 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] f22 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F, G <= G, H <= unknown] f18 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G, H <= H] f10 ~> f18 [A <= A, B <= B, C <= C, D <= C, E <= 0*K, F <= F, G <= G, H <= H] f34 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= B + C] f10 ~> f10 [A <= A, B <= C, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.1 <= C + E] f18 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= E, G <= C, H <= H] f22 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F, G <= G, H <= unknown] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= B, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= B, H <= H] + Loop: [0.1.0 <= D + G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= B, H <= H] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= G, G <= B, H <= H] + Loop: [0.1.0.0 <= D + G] f22 ~> f22 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= B, H <= H] + Loop: [0.2 <= K + D + E] f34 ~> f34 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F, G <= G, H <= H] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [K ~=> B,huge ~=> A] f10 ~> f10 [C ~=> B] f18 ~> f22 [C ~=> G,E ~=> F] f22 ~> f22 [B ~=> G] f22 ~> f22 [B ~=> G,G ~=> F] f34 ~> f34 [C ~=> E] f34 ~> f43 [] f22 ~> f18 [C ~=> E,huge ~=> H] f18 ~> f34 [K ~=> E] f10 ~> f18 [C ~=> D,K ~=> E] f34 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] f10 ~> f10 [C ~=> B] + Loop: [C ~+> 0.1,E ~+> 0.1] f18 ~> f22 [C ~=> G,E ~=> F] f22 ~> f18 [C ~=> E,huge ~=> H] f22 ~> f22 [B ~=> G] f22 ~> f22 [B ~=> G,G ~=> F] + Loop: [D ~+> 0.1.0,G ~+> 0.1.0] f22 ~> f22 [B ~=> G] f22 ~> f22 [B ~=> G,G ~=> F] + Loop: [D ~+> 0.1.0.0,G ~+> 0.1.0.0] f22 ~> f22 [B ~=> G] + Loop: [D ~+> 0.2,E ~+> 0.2,K ~+> 0.2] f34 ~> f34 [C ~=> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [C ~=> B ,C ~=> D ,C ~=> E ,C ~=> F ,C ~=> G ,K ~=> B ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> A ,huge ~=> H ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> 0.2 ,K ~*> tick] f0 ~> f43 [C ~=> B ,C ~=> D ,C ~=> E ,C ~=> F ,C ~=> G ,K ~=> B ,K ~=> E ,K ~=> F ,K ~=> G ,huge ~=> A ,huge ~=> H ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> 0.2 ,K ~*> tick] + f10> [C ~=> B,B ~+> 0.0,B ~+> tick,C ~+> 0.0,C ~+> tick,tick ~+> tick] + f18> [B ~=> F ,B ~=> G ,C ~=> E ,C ~=> F ,C ~=> G ,E ~=> F ,huge ~=> H ,B ~+> 0.1.0 ,B ~+> 0.1.0.0 ,B ~+> tick ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> tick ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,E ~+> 0.1 ,E ~+> tick ,tick ~+> tick ,B ~*> tick ,C ~*> tick ,D ~*> tick ,E ~*> tick] + f22> [B ~=> F ,B ~=> G ,G ~=> F ,B ~+> 0.1.0.0 ,B ~+> tick ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,G ~+> 0.1.0 ,G ~+> 0.1.0.0 ,G ~+> tick ,tick ~+> tick ,B ~*> tick ,D ~*> tick ,G ~*> tick] + f22> [B ~=> G,D ~+> 0.1.0.0,D ~+> tick,G ~+> 0.1.0.0,G ~+> tick,tick ~+> tick] + f34> [C ~=> E,D ~+> 0.2,D ~+> tick,E ~+> 0.2,E ~+> tick,tick ~+> tick,K ~+> 0.2,K ~+> tick] YES(?,POLY)