MAYBE * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f3(A,B) -> f0(0,B) True (1,1) 1. f0(A,B) -> f0(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f4(A,B) -> f4(A,B) [-1*B >= 0 && 1 + A + -1*B >= 0 && -1 + -1*A + -1*B >= 0 && -1 + -1*A >= 0 && 1 + A >= 0] (?,1) 3. f0(A,B) -> f4(-1,B) [-1*A >= 0 && A >= 0 && 0 >= B] (?,1) Signature: {(f0,2);(f3,2);(f4,2)} Flow Graph: [0->{1,3},1->{1,3},2->{2},3->{2}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f3(A,B) -> f0(0,B) True f0(A,B) -> f0(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] f4(A,B) -> f4(A,B) [-1*B >= 0 && 1 + A + -1*B >= 0 && -1 + -1*A + -1*B >= 0 && -1 + -1*A >= 0 && 1 + A >= 0] f0(A,B) -> f4(-1,B) [-1*A >= 0 && A >= 0 && 0 >= B] Signature: {(f0,2);(f3,2);(f4,2)} Rule Graph: [0->{1,3},1->{1,3},2->{2},3->{2}] + Applied Processor: AddSinks + Details: () * Step 3: Failure MAYBE + Considered Problem: Rules: f3(A,B) -> f0(0,B) True f0(A,B) -> f0(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] f4(A,B) -> f4(A,B) [-1*B >= 0 && 1 + A + -1*B >= 0 && -1 + -1*A + -1*B >= 0 && -1 + -1*A >= 0 && 1 + A >= 0] f0(A,B) -> f4(-1,B) [-1*A >= 0 && A >= 0 && 0 >= B] f4(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,2);(f3,2);(f4,2)} Rule Graph: [0->{1,3},1->{1,3},2->{2,4},3->{2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[2] c: [] MAYBE