YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,10),(1,9),(2,8),(3,7)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] (?,1) 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] (?,1) 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] (?,1) 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] (?,1) 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] (?,1) 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] (?,1) 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] (?,1) 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] (?,1) 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10},10->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E) -> f7(400,0,C,D,E) True f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10},10->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,9,8,7,4,3,2,5] c: [1,9] | `- p:[2,8,7,4,3,5] c: [2,8] | `- p:[3,7,4,5] c: [3,7] | `- p:[4,5] c: [5] | `- p:[4] c: [4] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E) -> f7(400,0,C,D,E) True f7(A,B,C,D,E) -> f10(A,B,0,D,E) [4 >= B] f10(A,B,C,D,E) -> f13(A,B,C,0,E) [4 >= C] f13(A,B,C,D,E) -> f16(A,B,C,D,0) [4 >= D] f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E && A >= 1 + F] f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [4 >= E] f16(A,B,C,D,E) -> f31(A,B,C,D,E) [4 >= E] f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 5] f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 5] f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 5] f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 5] Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[1,9,8,7,4,3,2,5] c: [1,9] | `- p:[2,8,7,4,3,5] c: [2,8] | `- p:[3,7,4,5] c: [3,7] | `- p:[4,5] c: [5] | `- p:[4] c: [4]) + Applied Processor: CloseWith True + Details: () YES