MAYBE * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [C >= 2 + B && C >= 1 + B && A = 0] (?,1) Signature: {(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,2,3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [B >= C] (1,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [1 + B = C && A = 0] (1,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [C >= 2 + B && C >= 1 + B && A = 0] (?,1) Signature: {(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,1),(3,2)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [B >= C] (1,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [1 + B = C && A = 0] (1,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [C >= 2 + B && C >= 1 + B && A = 0] (?,1) Signature: {(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{3}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [C >= 2 + B && C >= 1 + B && A = 0] (?,1) 4. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{1,2,3,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,1),(3,2)] * Step 5: Failure MAYBE + Considered Problem: Rules: 0. f3(A,B,C,D) -> f1(0,B,C,D) True (1,1) 1. f1(A,B,C,D) -> f2(A,B,C,E) [B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [C >= 2 + B && C >= 1 + B && A = 0] (?,1) 4. f1(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(exitus616,4);(f1,4);(f2,4);(f3,4)} Flow Graph: [0->{1,2,3,4},1->{},2->{},3->{3,4},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[3] c: [] MAYBE