NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,E) [A = 0] (?,1) 1. f2(A,B,C) -> f300(0,B,E) [A >= 1] (?,1) 2. f2(A,B,C) -> f300(0,B,E) [0 >= 1 + A] (?,1) 3. f2(A,B,C) -> f2(1 + E,B,C) [D >= 0 && A >= 1] (?,1) 4. f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && 0 >= B] (?,1) 5. f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && B >= 1] (?,1) 6. f2(A,B,C) -> f2(1 + E,B,C) [D >= 2 && 0 >= 1 + A] (?,1) 7. f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && 0 >= B] (?,1) 8. f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && B >= 1] (?,1) 9. f3(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{},1->{},2->{},3->{0,1,2,3,4,5,6,7,8},4->{0,1,2,3,4,5,6,7,8},5->{0,1,2,3,4,5,6,7,8},6->{0,1,2,3,4,5,6 ,7,8},7->{0,1,2,3,4,5,6,7,8},8->{0,1,2,3,4,5,6,7,8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,5),(4,8),(5,4),(5,7),(7,5),(7,8),(8,4),(8,7)] * Step 2: FromIts NO + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,E) [A = 0] (?,1) 1. f2(A,B,C) -> f300(0,B,E) [A >= 1] (?,1) 2. f2(A,B,C) -> f300(0,B,E) [0 >= 1 + A] (?,1) 3. f2(A,B,C) -> f2(1 + E,B,C) [D >= 0 && A >= 1] (?,1) 4. f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && 0 >= B] (?,1) 5. f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && B >= 1] (?,1) 6. f2(A,B,C) -> f2(1 + E,B,C) [D >= 2 && 0 >= 1 + A] (?,1) 7. f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && 0 >= B] (?,1) 8. f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && B >= 1] (?,1) 9. f3(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{},1->{},2->{},3->{0,1,2,3,4,5,6,7,8},4->{0,1,2,3,4,6,7},5->{0,1,2,3,5,6,8},6->{0,1,2,3,4,5,6,7,8} ,7->{0,1,2,3,4,6,7},8->{0,1,2,3,5,6,8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: FromIts + Details: () * Step 3: CloseWith NO + Considered Problem: Rules: f2(A,B,C) -> f300(A,B,E) [A = 0] f2(A,B,C) -> f300(0,B,E) [A >= 1] f2(A,B,C) -> f300(0,B,E) [0 >= 1 + A] f2(A,B,C) -> f2(1 + E,B,C) [D >= 0 && A >= 1] f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && 0 >= B] f2(A,B,C) -> f2(-1 + E,B,C) [A >= 1 && 0 >= 2 + D && B >= 1] f2(A,B,C) -> f2(1 + E,B,C) [D >= 2 && 0 >= 1 + A] f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && 0 >= B] f2(A,B,C) -> f2(-1 + E,B,C) [0 >= 1 + A && 0 >= D && B >= 1] f3(A,B,C) -> f2(A,B,C) True Signature: {(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{},1->{},2->{},3->{0,1,2,3,4,5,6,7,8},4->{0,1,2,3,4,6,7},5->{0,1,2,3,5,6,8},6->{0,1,2,3,4,5,6,7,8} ,7->{0,1,2,3,4,6,7},8->{0,1,2,3,5,6,8},9->{0,1,2,3,4,5,6,7,8}] + Applied Processor: CloseWith False + Details: () NO