MAYBE * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,B,C) True (?,1) 1. f3(A,B,C) -> f3(A,-1 + B,C) [B >= 1] (?,1) 2. f5(A,B,C) -> f5(A,B,1) True (?,1) 3. f0(A,B,C) -> f2(0,B,C) [C >= 1] (1,1) 4. f0(A,B,C) -> f3(0,B,C) [0 >= C] (1,1) 5. f3(A,B,C) -> f5(0,B,C) [0 >= B] (?,1) Signature: {(f0,3);(f2,3);(f3,3);(f5,3)} Flow Graph: [0->{0},1->{1,5},2->{2},3->{0},4->{1,5},5->{2}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f2(A,B,C) -> f2(1 + A,B,C) True f3(A,B,C) -> f3(A,-1 + B,C) [B >= 1] f5(A,B,C) -> f5(A,B,1) True f0(A,B,C) -> f2(0,B,C) [C >= 1] f0(A,B,C) -> f3(0,B,C) [0 >= C] f3(A,B,C) -> f5(0,B,C) [0 >= B] Signature: {(f0,3);(f2,3);(f3,3);(f5,3)} Rule Graph: [0->{0},1->{1,5},2->{2},3->{0},4->{1,5},5->{2}] + Applied Processor: AddSinks + Details: () * Step 3: Failure MAYBE + Considered Problem: Rules: f2(A,B,C) -> f2(1 + A,B,C) True f3(A,B,C) -> f3(A,-1 + B,C) [B >= 1] f5(A,B,C) -> f5(A,B,1) True f0(A,B,C) -> f2(0,B,C) [C >= 1] f0(A,B,C) -> f3(0,B,C) [0 >= C] f3(A,B,C) -> f5(0,B,C) [0 >= B] f5(A,B,C) -> exitus616(A,B,C) True f2(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f2,3);(f3,3);(f5,3)} Rule Graph: [0->{0,7},1->{1,5},2->{2,6},3->{0},4->{1,5},5->{2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | +- p:[2] c: [] | `- p:[0] c: [] MAYBE