YES * Step 1: FromIts YES + Considered Problem: Rules: 0. f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] (?,1) 1. f0(A,B,C) -> f2(A,B,1) [A >= 1] (1,1) 2. f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] (?,1) 3. f0(A,B,C) -> f4(A,B,0) [0 >= A] (1,1) Signature: {(f0,3);(f2,3);(f4,3);(f5,3)} Flow Graph: [0->{},1->{},2->{0,2},3->{0,2}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] f0(A,B,C) -> f2(A,B,1) [A >= 1] f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] f0(A,B,C) -> f4(A,B,0) [0 >= A] Signature: {(f0,3);(f2,3);(f4,3);(f5,3)} Rule Graph: [0->{},1->{},2->{0,2},3->{0,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2] * Step 3: CloseWith YES + Considered Problem: (Rules: f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] f0(A,B,C) -> f2(A,B,1) [A >= 1] f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] f0(A,B,C) -> f4(A,B,0) [0 >= A] Signature: {(f0,3);(f2,3);(f4,3);(f5,3)} Rule Graph: [0->{},1->{},2->{0,2},3->{0,2}] ,We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2]) + Applied Processor: CloseWith True + Details: () YES