YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && 35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && B >= 36] (?,1) Signature: {(f0,3);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,3},2->{2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && 35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && B >= 36] (?,1) Signature: {(f0,3);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2},2->{2,3},3->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C) -> f5(A,0,C) [A >= 128] f0(A,B,C) -> f7(A,0,D) [127 >= A] f7(A,B,C) -> f7(A,1 + B,1 + C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && 35 >= B] f7(A,B,C) -> f5(A,B,C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && B >= 36] Signature: {(f0,3);(f5,3);(f7,3)} Rule Graph: [0->{},1->{2},2->{2,3},3->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C) -> f5(A,0,C) [A >= 128] f0(A,B,C) -> f7(A,0,D) [127 >= A] f7(A,B,C) -> f7(A,1 + B,1 + C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && 35 >= B] f7(A,B,C) -> f5(A,B,C) [B >= 0 && 127 + -1*A + B >= 0 && 127 + -1*A >= 0 && B >= 36] Signature: {(f0,3);(f5,3);(f7,3)} Rule Graph: [0->{},1->{2},2->{2,3},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES