MAYBE * Step 1: ArgumentFilter 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) [-1*A >= 0 && A >= 0 && B >= C] (?,1) 2. f1(A,B,C,D) -> f2(1,1 + B,C,E) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] (?,1) 3. f1(A,B,C,D) -> f1(0,1 + B,1 + C,D) [-1*A >= 0 && A >= 0 && 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: ArgumentFilter [3] + Details: We remove following argument positions: [3]. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f3(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f2(A,B,C) [-1*A >= 0 && A >= 0 && B >= C] (?,1) 2. f1(A,B,C) -> f2(1,1 + B,C) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] (?,1) 3. f1(A,B,C) -> f1(0,1 + B,1 + C) [-1*A >= 0 && A >= 0 && 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: FromIts MAYBE + Considered Problem: Rules: 0. f3(A,B,C) -> f1(0,B,C) True (1,1) 1. f1(A,B,C) -> f2(A,B,C) [-1*A >= 0 && A >= 0 && B >= C] (?,1) 2. f1(A,B,C) -> f2(1,1 + B,C) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] (?,1) 3. f1(A,B,C) -> f1(0,1 + B,1 + C) [-1*A >= 0 && A >= 0 && 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: FromIts + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f3(A,B,C) -> f1(0,B,C) True f1(A,B,C) -> f2(A,B,C) [-1*A >= 0 && A >= 0 && B >= C] f1(A,B,C) -> f2(1,1 + B,C) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] f1(A,B,C) -> f1(0,1 + B,1 + C) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] Signature: {(f1,4);(f2,4);(f3,4)} Rule Graph: [0->{1,2,3},1->{},2->{},3->{3}] + Applied Processor: AddSinks + Details: () * Step 5: Failure MAYBE + Considered Problem: Rules: f3(A,B,C) -> f1(0,B,C) True f1(A,B,C) -> f2(A,B,C) [-1*A >= 0 && A >= 0 && B >= C] f1(A,B,C) -> f2(1,1 + B,C) [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0] f1(A,B,C) -> f1(0,1 + B,1 + C) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] f1(A,B,C) -> exitus616(A,B,C) True f2(A,B,C) -> exitus616(A,B,C) True f2(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f1,4);(f2,4);(f3,4)} Rule Graph: [0->{1,2,3},1->{6},2->{5},3->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [] MAYBE