YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{4,5,6,7},9->{4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,4),(9,4)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True (1,1) 1. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] (?,1) 2. f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] (?,1) 3. f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] (?,1) 4. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] (?,1) 5. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] (?,1) 6. f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] (?,1) 7. f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] (?,1) 8. f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] (?,1) 9. f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] (?,1) Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Flow Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Rule Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[1,3,2] c: [1,2,3] | `- p:[5,6] c: [6] | `- p:[5] c: [5] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F,G) -> f9(0,0,H,D,E,F,G) True f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [0 >= 1 + C] f9(A,B,C,D,E,F,G) -> f10(A,B,C,C,E,F,G) [C >= 1] f10(A,B,C,D,E,F,G) -> f9(1 + A,1 + A,H,D,E,F,G) [9 >= A] f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,E,F,G) [A >= 10] f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && 0 >= 1 + H] f16(A,B,C,D,E,F,G) -> f16(1 + A,B,C,D,A,H,H) [9 >= A && H >= 1] f16(A,B,C,D,E,F,G) -> f28(A,B,C,D,A,0,0) [9 >= A] f10(A,B,C,D,E,F,G) -> f16(0,B,C,D,E,F,G) [A >= 10] f9(A,B,C,D,E,F,G) -> f16(0,B,0,0,E,F,G) [C = 0] Signature: {(f0,7);(f10,7);(f16,7);(f28,7);(f9,7)} Rule Graph: [0->{1,2,9},1->{3,8},2->{3,8},3->{1,2,9},4->{},5->{4,5,6,7},6->{4,5,6,7},7->{},8->{5,6,7},9->{5,6,7}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[1,3,2] c: [1,2,3] | `- p:[5,6] c: [6] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES