NO * Step 1: UnsatPaths NO + Considered Problem: Rules: 0. f0(A,B) -> f0(A + B,B) [A >= 1 && 0 >= 1 + B] (?,1) 1. f0(A,B) -> f0(A + B,B) [A >= 1 && B >= 1] (?,1) 2. f1(A,B) -> f0(A,B) True (1,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(1,0)] * Step 2: Looptree NO + Considered Problem: Rules: 0. f0(A,B) -> f0(A + B,B) [A >= 1 && 0 >= 1 + B] (?,1) 1. f0(A,B) -> f0(A + B,B) [A >= 1 && B >= 1] (?,1) 2. f1(A,B) -> f0(A,B) True (1,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{0},1->{1},2->{0,1}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2] | +- p:[1] c: [] | `- p:[0] c: [0] NO