MAYBE * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f4(0,B,C,D) True (1,1) 1. f4(A,B,C,D) -> f8(1 + A,B,0,D) [B >= 1 + A] (?,1) 2. f8(A,B,C,D) -> f16(A,B,C,0) [B >= 1 + A] (?,1) 3. f8(A,B,C,D) -> f16(A,B,C,D) [A >= B] (?,1) 4. f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && 0 >= 1 + E] (?,1) 5. f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && E >= 1] (?,1) 6. f16(A,B,C,D) -> f4(A,B,C,D) [0 >= C] (?,1) 7. f16(A,B,C,D) -> f4(-1 + A,B,C,D) [C >= 1] (?,1) 8. f4(A,B,C,D) -> f20(A,B,C,D) [A >= B] (?,1) Signature: {(f0,4);(f16,4);(f20,4);(f4,4);(f8,4)} Flow Graph: [0->{1,8},1->{2,3,4,5},2->{6,7},3->{6,7},4->{2,3,4,5},5->{2,3,4,5},6->{1,8},7->{1,8},8->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f4(0,B,C,D) True f4(A,B,C,D) -> f8(1 + A,B,0,D) [B >= 1 + A] f8(A,B,C,D) -> f16(A,B,C,0) [B >= 1 + A] f8(A,B,C,D) -> f16(A,B,C,D) [A >= B] f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && 0 >= 1 + E] f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && E >= 1] f16(A,B,C,D) -> f4(A,B,C,D) [0 >= C] f16(A,B,C,D) -> f4(-1 + A,B,C,D) [C >= 1] f4(A,B,C,D) -> f20(A,B,C,D) [A >= B] Signature: {(f0,4);(f16,4);(f20,4);(f4,4);(f8,4)} Rule Graph: [0->{1,8},1->{2,3,4,5},2->{6,7},3->{6,7},4->{2,3,4,5},5->{2,3,4,5},6->{1,8},7->{1,8},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: Failure MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f4(0,B,C,D) True f4(A,B,C,D) -> f8(1 + A,B,0,D) [B >= 1 + A] f8(A,B,C,D) -> f16(A,B,C,0) [B >= 1 + A] f8(A,B,C,D) -> f16(A,B,C,D) [A >= B] f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && 0 >= 1 + E] f8(A,B,C,D) -> f8(1 + A,B,1 + C,E) [B >= 1 + A && E >= 1] f16(A,B,C,D) -> f4(A,B,C,D) [0 >= C] f16(A,B,C,D) -> f4(-1 + A,B,C,D) [C >= 1] f4(A,B,C,D) -> f20(A,B,C,D) [A >= B] f20(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f16,4);(f20,4);(f4,4);(f8,4)} Rule Graph: [0->{1,8},1->{2,3,4,5},2->{6,7},3->{6,7},4->{2,3,4,5},5->{2,3,4,5},6->{1,8},7->{1,8},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[1,6,2,4,5,3,7] c: [4,5] | `- p:[1,6,2,3,7] c: [] MAYBE