YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Rule Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2,7] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Rule Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2,7] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5]) + Applied Processor: CloseWith True + Details: () YES