MAYBE * Step 1: ArgumentFilter MAYBE + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,0,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,2 + B,D + E) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) 2. f5(A,B,C) -> f16(A,B,C) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f16,3);(f5,3)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B) -> f5(0,0) True (1,1) 1. f5(A,B) -> f5(1 + A,2 + B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) 2. f5(A,B) -> f16(A,B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] (?,1) Signature: {(f0,3);(f16,3);(f5,3)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks MAYBE + Considered Problem: Rules: f0(A,B) -> f5(0,0) True f5(A,B) -> f5(1 + A,2 + B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] f5(A,B) -> f16(A,B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] Signature: {(f0,3);(f16,3);(f5,3)} Rule Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 4: Failure MAYBE + Considered Problem: Rules: f0(A,B) -> f5(0,0) True f5(A,B) -> f5(1 + A,2 + B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] f5(A,B) -> f16(A,B) [B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0] f16(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,3);(f16,3);(f5,3)} Rule Graph: [0->{1,2},1->{1,2},2->{3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [] MAYBE