MAYBE * Step 1: ArgumentFilter 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) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B,C) -> f4(A,B,D) [-1*A >= 0 && A >= 0 && 0 >= B] (?,1) 3. f4(A,B,C) -> f4(1,B,D) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f1(0,B) True (1,1) 1. f1(A,B) -> f1(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] (?,1) 2. f1(A,B) -> f4(A,B) [-1*A >= 0 && A >= 0 && 0 >= B] (?,1) 3. f4(A,B) -> f4(1,B) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f1,3);(f4,3)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks MAYBE + Considered Problem: Rules: f0(A,B) -> f1(0,B) True f1(A,B) -> f1(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] f1(A,B) -> f4(A,B) [-1*A >= 0 && A >= 0 && 0 >= B] f4(A,B) -> f4(1,B) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] Signature: {(f0,3);(f1,3);(f4,3)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: AddSinks + Details: () * Step 4: Failure MAYBE + Considered Problem: Rules: f0(A,B) -> f1(0,B) True f1(A,B) -> f1(A,-1 + B) [-1*A >= 0 && A >= 0 && B >= 1] f1(A,B) -> f4(A,B) [-1*A >= 0 && A >= 0 && 0 >= B] f4(A,B) -> f4(1,B) [-1*B >= 0 && A + -1*B >= 0 && A >= 0] f4(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,3);(f1,3);(f4,3)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[3] c: [] MAYBE