NO * Step 1: TrivialSCCs NO + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f14(1 + 2*I,H,0,D,H,1 + 2*I,I) [H >= 1 && 2*I >= 0] (1,1) 1. f14(A,B,C,D,E,F,G) -> f14(-1 + A,B,C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= H && A >= 1 && A >= 1 + B] 2. f14(A,B,C,D,E,F,G) -> f14(-1 + A,-1 + B,1 + C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && A >= 1 && H >= 1] 3. f14(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= A] 4. f24(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1*A + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,7);(f14,7);(f24,7)} 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,G) -> f14(1 + 2*I,H,0,D,H,1 + 2*I,I) [H >= 1 && 2*I >= 0] (1,1) 1. f14(A,B,C,D,E,F,G) -> f14(-1 + A,B,C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= H && A >= 1 && A >= 1 + B] 2. f14(A,B,C,D,E,F,G) -> f14(-1 + A,-1 + B,1 + C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && A >= 1 && H >= 1] 3. f14(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (1,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= A] 4. f24(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1*A + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,7);(f14,7);(f24,7)} 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,G) -> f14(1 + 2*I,H,0,D,H,1 + 2*I,I) [H >= 1 && 2*I >= 0] (1,1) 1. f14(A,B,C,D,E,F,G) -> f14(-1 + A,B,C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= H && A >= 1 && A >= 1 + B] 2. f14(A,B,C,D,E,F,G) -> f14(-1 + A,-1 + B,1 + C,H,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && A >= 1 && H >= 1] 3. f14(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (1,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && C >= 0 && 0 >= A] 4. f24(A,B,C,D,E,F,G) -> f24(A,B,C,D,E,F,G) [G >= 0 (?,1) && -1 + F + G >= 0 && -1 + E + G >= 0 && C + G >= 0 && -1*A + G >= 0 && -1 + F >= 0 && -2 + E + F >= 0 && -1 + C + F >= 0 && -1 + -1*A + F >= 0 && -1 + E >= 0 && -1 + C + E >= 0 && -1 + -1*A + E >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0] Signature: {(f0,7);(f14,7);(f24,7)} 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