YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f18(A,B,C,D,E,F) -> f18(A,1 + B,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 1. f24(A,B,C,D,E,F) -> f24(A,1 + B,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 2. f31(A,B,C,D,E,F) -> f31(A,1 + B,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 3. f31(A,B,C,D,E,F) -> f39(A,B,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 4. f24(A,B,C,D,E,F) -> f31(A,0,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 5. f18(A,B,C,D,E,F) -> f24(A,0,C,D,E,F) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 6. f0(A,B,C,D,E,F) -> f18(10,0,10,G,10,H) True (1,1) Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{0,5}] + Applied Processor: ArgumentFilter [3,5] + Details: We remove following argument positions: [3,5]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f18(A,B,C,E) -> f18(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 1. f24(A,B,C,E) -> f24(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 2. f31(A,B,C,E) -> f31(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 3. f31(A,B,C,E) -> f39(A,B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 4. f24(A,B,C,E) -> f31(A,0,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 5. f18(A,B,C,E) -> f24(A,0,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 6. f0(A,B,C,E) -> f18(10,0,10,10) True (1,1) Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2,3},5->{1,4},6->{0,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,3),(5,4),(6,5)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f18(A,B,C,E) -> f18(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 1. f24(A,B,C,E) -> f24(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 2. f31(A,B,C,E) -> f31(A,1 + B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] 3. f31(A,B,C,E) -> f39(A,B,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 4. f24(A,B,C,E) -> f31(A,0,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 5. f18(A,B,C,E) -> f24(A,0,C,E) [10 + -1*E >= 0 (?,1) && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] 6. f0(A,B,C,E) -> f18(10,0,10,10) True (1,1) Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Flow Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2},5->{1},6->{0}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f18(A,B,C,E) -> f18(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f24(A,B,C,E) -> f24(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f31(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f39(A,B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f24(A,B,C,E) -> f31(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f18(A,B,C,E) -> f24(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f0(A,B,C,E) -> f18(10,0,10,10) True Signature: {(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Rule Graph: [0->{0,5},1->{1,4},2->{2,3},3->{},4->{2},5->{1},6->{0}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f18(A,B,C,E) -> f18(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f24(A,B,C,E) -> f24(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f31(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f39(A,B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f24(A,B,C,E) -> f31(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f18(A,B,C,E) -> f24(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f0(A,B,C,E) -> f18(10,0,10,10) True f39(A,B,C,E) -> exitus616(A,B,C,E) True Signature: {(exitus616,4);(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Rule Graph: [0->{0,5},1->{1,4},2->{2,3},3->{7},4->{2},5->{1},6->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[0] c: [0] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f18(A,B,C,E) -> f18(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f24(A,B,C,E) -> f24(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f31(A,1 + B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && A >= 1 + B] f31(A,B,C,E) -> f39(A,B,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f24(A,B,C,E) -> f31(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f18(A,B,C,E) -> f24(A,0,C,E) [10 + -1*E >= 0 && C + -1*E >= 0 && 20 + -1*C + -1*E >= 0 && 10 + B + -1*E >= 0 && A + -1*E >= 0 && 20 + -1*A + -1*E >= 0 && -10 + E >= 0 && -20 + C + E >= 0 && -1*C + E >= 0 && -10 + B + E >= 0 && -20 + A + E >= 0 && -1*A + E >= 0 && 10 + -1*C >= 0 && 10 + B + -1*C >= 0 && A + -1*C >= 0 && 20 + -1*A + -1*C >= 0 && -10 + C >= 0 && -10 + B + C >= 0 && -20 + A + C >= 0 && -1*A + C >= 0 && B >= 0 && -10 + A + B >= 0 && 10 + -1*A + B >= 0 && 10 + -1*A >= 0 && -10 + A >= 0 && B >= A] f0(A,B,C,E) -> f18(10,0,10,10) True f39(A,B,C,E) -> exitus616(A,B,C,E) True Signature: {(exitus616,4);(f0,6);(f18,6);(f24,6);(f31,6);(f39,6)} Rule Graph: [0->{0,5},1->{1,4},2->{2,3},3->{7},4->{2},5->{1},6->{0}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[0] c: [0] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,E,0.0,0.1,0.2] f18 ~> f18 [A <= A, B <= 10*K, C <= C, E <= E] f24 ~> f24 [A <= A, B <= 10*K, C <= C, E <= E] f31 ~> f31 [A <= A, B <= 10*K, C <= C, E <= E] f31 ~> f39 [A <= A, B <= B, C <= C, E <= E] f24 ~> f31 [A <= A, B <= 0*K, C <= C, E <= E] f18 ~> f24 [A <= A, B <= 0*K, C <= C, E <= E] f0 ~> f18 [A <= 10*K, B <= 0*K, C <= 10*K, E <= 10*K] f39 ~> exitus616 [A <= A, B <= B, C <= C, E <= E] + Loop: [0.0 <= K + A + B] f18 ~> f18 [A <= A, B <= 10*K, C <= C, E <= E] + Loop: [0.1 <= K + A + B] f24 ~> f24 [A <= A, B <= 10*K, C <= C, E <= E] + Loop: [0.2 <= K + A + B] f31 ~> f31 [A <= A, B <= 10*K, C <= C, E <= E] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,E,0.0,0.1,0.2] f18 ~> f18 [K ~=> B] f24 ~> f24 [K ~=> B] f31 ~> f31 [K ~=> B] f31 ~> f39 [] f24 ~> f31 [K ~=> B] f18 ~> f24 [K ~=> B] f0 ~> f18 [K ~=> A,K ~=> B,K ~=> C,K ~=> E] f39 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] f18 ~> f18 [K ~=> B] + Loop: [A ~+> 0.1,B ~+> 0.1,K ~+> 0.1] f24 ~> f24 [K ~=> B] + Loop: [A ~+> 0.2,B ~+> 0.2,K ~+> 0.2] f31 ~> f31 [K ~=> B] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + f18> [K ~=> B,A ~+> 0.0,A ~+> tick,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] + f24> [K ~=> B,A ~+> 0.1,A ~+> tick,B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] + f31> [K ~=> B,A ~+> 0.2,A ~+> tick,B ~+> 0.2,B ~+> tick,tick ~+> tick,K ~+> 0.2,K ~+> tick] YES(?,O(1))