MAYBE * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f1(A,B) -> f0(A,B) True (1,1) 1. f0(A,B) -> f0(A + B,B) [A >= 1 && B >= 1] (?,1) 2. f0(A,B) -> f0(A + B,B) [A >= 1 && 0 >= 1 + B] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(2,1)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f1(A,B) -> f0(A,B) True (1,1) 1. f0(A,B) -> f0(A + B,B) [A >= 1 && B >= 1] (?,1) 2. f0(A,B) -> f0(A + B,B) [A >= 1 && 0 >= 1 + B] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f1(A,B) -> f0(A,B) True f0(A,B) -> f0(A + B,B) [A >= 1 && B >= 1] f0(A,B) -> f0(A + B,B) [A >= 1 && 0 >= 1 + B] Signature: {(f0,2);(f1,2)} Rule Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f1.0(A,B) -> f0.1(A,B) True f1.0(A,B) -> f0.2(A,B) True f0.1(A,B) -> f0.1(A + B,B) [A >= 1 && B >= 1] f0.2(A,B) -> f0.2(A + B,B) [A >= 1 && 0 >= 1 + B] Signature: {(f0.1,2);(f0.2,2);(f1.0,2)} Rule Graph: [0->{2},1->{3},2->{2},3->{3}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f1.0(A,B) -> f0.1(A,B) True f1.0(A,B) -> f0.2(A,B) True f0.1(A,B) -> f0.1(A + B,B) [A >= 1 && B >= 1] f0.2(A,B) -> f0.2(A + B,B) [A >= 1 && 0 >= 1 + B] f0.2(A,B) -> exitus616(A,B) True f0.1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0.1,2);(f0.2,2);(f1.0,2)} Rule Graph: [0->{2},1->{3},2->{2,5},3->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3] c: [3] | `- p:[2] c: [] MAYBE