NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f6(A,B,C,D) -> f7(A,B,C,D) [0 >= 1 + A] (?,1) 1. f6(A,B,C,D) -> f7(A,B,C,D) [A >= 1] (?,1) 2. f0(A,B,C,D) -> f4(A,B,C,1 + B) [B >= 0 && C >= B] (1,1) 3. f4(A,B,C,D) -> f6(E,B,C,D) [B >= 1 + D] (?,1) 4. f4(A,B,C,D) -> f6(E,B,C,D) [D >= 1 + B] (?,1) 5. f7(A,B,C,D) -> f4(A,B,C,1 + D) [C >= D] (?,1) 6. f7(A,B,C,D) -> f4(A,B,C,0) [D >= 1 + C] (?,1) 7. f6(A,B,C,D) -> f14(0,B,C,D) [A = 0] (?,1) 8. f4(A,B,C,D) -> f14(A,B,C,B) [B = D] (?,1) Signature: {(f0,4);(f14,4);(f4,4);(f6,4);(f7,4)} Flow Graph: [0->{5,6},1->{5,6},2->{3,4,8},3->{0,1,7},4->{0,1,7},5->{3,4,8},6->{3,4,8},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,3),(2,8)] * Step 2: FromIts NO + Considered Problem: Rules: 0. f6(A,B,C,D) -> f7(A,B,C,D) [0 >= 1 + A] (?,1) 1. f6(A,B,C,D) -> f7(A,B,C,D) [A >= 1] (?,1) 2. f0(A,B,C,D) -> f4(A,B,C,1 + B) [B >= 0 && C >= B] (1,1) 3. f4(A,B,C,D) -> f6(E,B,C,D) [B >= 1 + D] (?,1) 4. f4(A,B,C,D) -> f6(E,B,C,D) [D >= 1 + B] (?,1) 5. f7(A,B,C,D) -> f4(A,B,C,1 + D) [C >= D] (?,1) 6. f7(A,B,C,D) -> f4(A,B,C,0) [D >= 1 + C] (?,1) 7. f6(A,B,C,D) -> f14(0,B,C,D) [A = 0] (?,1) 8. f4(A,B,C,D) -> f14(A,B,C,B) [B = D] (?,1) Signature: {(f0,4);(f14,4);(f4,4);(f6,4);(f7,4)} Flow Graph: [0->{5,6},1->{5,6},2->{4},3->{0,1,7},4->{0,1,7},5->{3,4,8},6->{3,4,8},7->{},8->{}] + Applied Processor: FromIts + Details: () * Step 3: CloseWith NO + Considered Problem: Rules: f6(A,B,C,D) -> f7(A,B,C,D) [0 >= 1 + A] f6(A,B,C,D) -> f7(A,B,C,D) [A >= 1] f0(A,B,C,D) -> f4(A,B,C,1 + B) [B >= 0 && C >= B] f4(A,B,C,D) -> f6(E,B,C,D) [B >= 1 + D] f4(A,B,C,D) -> f6(E,B,C,D) [D >= 1 + B] f7(A,B,C,D) -> f4(A,B,C,1 + D) [C >= D] f7(A,B,C,D) -> f4(A,B,C,0) [D >= 1 + C] f6(A,B,C,D) -> f14(0,B,C,D) [A = 0] f4(A,B,C,D) -> f14(A,B,C,B) [B = D] Signature: {(f0,4);(f14,4);(f4,4);(f6,4);(f7,4)} Rule Graph: [0->{5,6},1->{5,6},2->{4},3->{0,1,7},4->{0,1,7},5->{3,4,8},6->{3,4,8},7->{},8->{}] + Applied Processor: CloseWith False + Details: () NO