YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B) -> f1(3000,B) True (1,1) 1. f1(A,B) -> f1(A,1000 + B) [889 + B >= 0 && 1999 >= A] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{1},1->{1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1)] * Step 2: UnreachableRules YES + Considered Problem: Rules: 0. f0(A,B) -> f1(3000,B) True (1,1) 1. f1(A,B) -> f1(A,1000 + B) [889 + B >= 0 && 1999 >= A] (?,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{},1->{1}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [1] * Step 3: FromIts YES + Considered Problem: Rules: 0. f0(A,B) -> f1(3000,B) True (1,1) Signature: {(f0,2);(f1,2)} Flow Graph: [0->{}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: f0(A,B) -> f1(3000,B) True Signature: {(f0,2);(f1,2)} Rule Graph: [0->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0] * Step 5: CloseWith YES + Considered Problem: (Rules: f0(A,B) -> f1(3000,B) True Signature: {(f0,2);(f1,2)} Rule Graph: [0->{}] ,We construct a looptree: P: [0]) + Applied Processor: CloseWith True + Details: () YES