YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B) -> f0(A,A) [0 >= 1 + A && B = 0] (?,1) 1. f0(A,B) -> f0(A,A) [A >= 1 && B = 0] (?,1) 2. start(A,B) -> f0(A,B) True (1,1) Signature: {(f0,2);(start,2)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0),(0,1),(1,0),(1,1)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B) -> f0(A,A) [0 >= 1 + A && B = 0] (?,1) 1. f0(A,B) -> f0(A,A) [A >= 1 && B = 0] (?,1) 2. start(A,B) -> f0(A,B) True (1,1) Signature: {(f0,2);(start,2)} Flow Graph: [0->{},1->{},2->{0,1}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B) -> f0(A,A) [0 >= 1 + A && B = 0] f0(A,B) -> f0(A,A) [A >= 1 && B = 0] start(A,B) -> f0(A,B) True Signature: {(f0,2);(start,2)} Rule Graph: [0->{},1->{},2->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B) -> f0(A,A) [0 >= 1 + A && B = 0] f0(A,B) -> f0(A,A) [A >= 1 && B = 0] start(A,B) -> f0(A,B) True Signature: {(f0,2);(start,2)} Rule Graph: [0->{},1->{},2->{0,1}] ,We construct a looptree: P: [0,1,2]) + Applied Processor: CloseWith True + Details: () YES