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