NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= G && A >= 1 && A >= 1 + B] 2. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && A >= 1 && G >= 1] 3. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= A] 4. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 4 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -4 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,6);(f12,6);(f22,6)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= G && A >= 1 && A >= 1 + B] 2. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && A >= 1 && G >= 1] 3. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (1,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= A] 4. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 4 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -4 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,6);(f12,6);(f22,6)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 3: Looptree NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f12(4,G,0,D,G,4) [G >= 1] (1,1) 1. f12(A,B,C,D,E,F) -> f12(-1 + A,B,C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= G && A >= 1 && A >= 1 + B] 2. f12(A,B,C,D,E,F) -> f12(-1 + A,-1 + B,1 + C,G,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && A >= 1 && G >= 1] 3. f12(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (1,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 8 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && 3 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && 4 + -1*A + C >= 0 && 4 + -1*A >= 0 && 0 >= A] 4. f22(A,B,C,D,E,F) -> f22(A,B,C,D,E,F) [4 + -1*F >= 0 (?,1) && 3 + E + -1*F >= 0 && 4 + C + -1*F >= 0 && 4 + -1*A + -1*F >= 0 && -4 + F >= 0 && -5 + E + F >= 0 && -4 + C + F >= 0 && -4 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && 4 + -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,6);(f12,6);(f22,6)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4},4->{4}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1,2] c: [2] | | | `- p:[1] c: [1] | `- p:[4] c: [] NO