YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(1,2),(2,1)] * Step 2: UnreachableRules YES + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) 2. f1(A) -> f1(-1 + A) [100 >= A] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1},2->{2}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [2] * Step 3: FromIts YES + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [A >= 102] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: f0(A) -> f1(300) True f1(A) -> f1(-1 + A) [A >= 102] Signature: {(f0,1);(f1,1)} Rule Graph: [0->{1},1->{1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1] | `- p:[1] c: [1] * Step 5: CloseWith YES + Considered Problem: (Rules: f0(A) -> f1(300) True f1(A) -> f1(-1 + A) [A >= 102] Signature: {(f0,1);(f1,1)} Rule Graph: [0->{1},1->{1}] ,We construct a looptree: P: [0,1] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES