YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,4),(9,4)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [C + -1*D >= 0 (?,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && 9 >= A] 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 10] (1,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [C + -1*D >= 0 && -1*C + D >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 9 >= A] (1,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [C + -1*D >= 0 (1,1) && -1*C + D >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 10] 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && C = 0] (1,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[1,3,2] c: [3] | `- p:[5,6] c: [6] | `- p:[5] c: [5] YES