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