YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: Looptree YES + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1},1->{1,2},2->{0},3->{0}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3] | `- p:[0,2,1] c: [2] | `- p:[1] c: [1] YES