YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] (?,1) 1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1) 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,0)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] (?,1) 1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1) 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0,1},2->{1}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] f0(A,B,C) -> f4(0,0,C) [C >= 1] Signature: {(f0,3);(f4,3)} Rule Graph: [0->{0,1},1->{0,1},2->{1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2] | `- p:[0,1] c: [1] | `- p:[0] c: [0] * Step 4: CloseWith YES + Considered Problem: (Rules: f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] f0(A,B,C) -> f4(0,0,C) [C >= 1] Signature: {(f0,3);(f4,3)} Rule Graph: [0->{0,1},1->{0,1},2->{1}] ,We construct a looptree: P: [0,1,2] | `- p:[0,1] c: [1] | `- p:[0] c: [0]) + Applied Processor: CloseWith True + Details: () YES