MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [B >= 1 && D >= 1] (?,1) 2. f1(A,B,C) -> f1(A,-2 + B,D) [B >= 1 && 0 >= D] (?,1) 3. f1(A,B,C) -> f4(A,B,D) [0 >= B] (?,1) 4. f4(A,B,C) -> f4(1,B,D) [C >= 1] (?,1) 5. f4(A,B,C) -> f4(2,B,D) [0 >= C] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4,5},4->{4,5},5->{4,5}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [B >= 1 && D >= 1] (?,1) 2. f1(A,B,C) -> f1(A,-2 + B,D) [B >= 1 && 0 >= D] (?,1) 3. f1(A,B,C) -> f4(A,B,D) [0 >= B] (1,1) 4. f4(A,B,C) -> f4(1,B,D) [C >= 1] (?,1) 5. f4(A,B,C) -> f4(2,B,D) [0 >= C] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4,5},4->{4,5},5->{4,5}] + Applied Processor: AddSinks + Details: () * Step 3: Failure MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f1(A,-1 + B,D) [B >= 1 && D >= 1] (?,1) 2. f1(A,B,C) -> f1(A,-2 + B,D) [B >= 1 && 0 >= D] (?,1) 3. f1(A,B,C) -> f4(A,B,D) [0 >= B] (?,1) 4. f4(A,B,C) -> f4(1,B,D) [C >= 1] (?,1) 5. f4(A,B,C) -> f4(2,B,D) [0 >= C] (?,1) 6. f4(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{4,5,6},4->{4,5,6},5->{4,5,6},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | +- p:[1,2] c: [2] | | | `- p:[1] c: [1] | `- p:[4,5] c: [] MAYBE