YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f27(A,B,C,D,B,B,K,L,L,L) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (?,1) Signature: {(f0,10);(f27,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + 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,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f27(A,B,C,D,B,B,K,L,L,L) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (1,1) Signature: {(f0,10);(f27,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 3: Looptree YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f27(A,B,C,D,B,B,K,L,L,L) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (1,1) Signature: {(f0,10);(f27,10);(f5,10)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1,2] c: [2] | `- p:[1] c: [1] YES