MAYBE * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f6(E,0,C,D) True (1,1) 1. f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [A >= 1] (?,1) 2. f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [B >= 1] (?,1) 3. f14(A,B,C,D) -> f14(A,B,-1 + C,0) [C >= 1] (?,1) 4. f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && 0 >= 1 + E] (?,1) 5. f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && E >= 1] (?,1) 6. f14(A,B,C,D) -> f10(A,B,C,D) [0 >= C] (?,1) 7. f10(A,B,C,D) -> f6(A,B,C,D) [0 >= B] (?,1) 8. f6(A,B,C,D) -> f25(A,B,C,D) [0 >= A] (?,1) Signature: {(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Flow Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(E,0,C,D) True f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [A >= 1] f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [B >= 1] f14(A,B,C,D) -> f14(A,B,-1 + C,0) [C >= 1] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && 0 >= 1 + E] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && E >= 1] f14(A,B,C,D) -> f10(A,B,C,D) [0 >= C] f10(A,B,C,D) -> f6(A,B,C,D) [0 >= B] f6(A,B,C,D) -> f25(A,B,C,D) [0 >= A] Signature: {(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Rule Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},7->{1,8},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: Failure MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f6(E,0,C,D) True f6(A,B,C,D) -> f10(-1 + A,1 + B,C,D) [A >= 1] f10(A,B,C,D) -> f14(A,-1 + B,-1 + A,D) [B >= 1] f14(A,B,C,D) -> f14(A,B,-1 + C,0) [C >= 1] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && 0 >= 1 + E] f14(A,B,C,D) -> f14(-1 + A,1 + B,-1 + C,E) [C >= 1 && E >= 1] f14(A,B,C,D) -> f10(A,B,C,D) [0 >= C] f10(A,B,C,D) -> f6(A,B,C,D) [0 >= B] f6(A,B,C,D) -> f25(A,B,C,D) [0 >= A] f25(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f10,4);(f14,4);(f25,4);(f6,4)} Rule Graph: [0->{1,8},1->{2,7},2->{3,4,5,6},3->{3,4,5,6},4->{3,4,5,6},5->{3,4,5,6},6->{2,7},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:[1,7,6,2,3,4,5] c: [1,7] | `- p:[2,6,3,4,5] c: [] MAYBE