YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,1 + B,C) [1 >= A] (?,1) 1. f2(A,B,C) -> f2(1 + A,1 + B,C) [2 >= B && A >= 2] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [B >= 3 && A >= 2] (?,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2},1->{0,1,2},2->{},3->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,0)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f2(A,B,C) -> f2(1 + A,1 + B,C) [1 >= A] (?,1) 1. f2(A,B,C) -> f2(1 + A,1 + B,C) [2 >= B && A >= 2] (?,1) 2. f2(A,B,C) -> f300(A,B,D) [B >= 3 && A >= 2] (?,1) 3. f1(A,B,C) -> f2(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2},1->{1,2},2->{},3->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f2(A,B,C) -> f2(1 + A,1 + B,C) [1 >= A] f2(A,B,C) -> f2(1 + A,1 + B,C) [2 >= B && A >= 2] f2(A,B,C) -> f300(A,B,D) [B >= 3 && A >= 2] f1(A,B,C) -> f2(A,B,C) True Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{0,1,2},1->{1,2},2->{},3->{0,1,2}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3] | +- p:[0] c: [0] | `- p:[1] c: [1] * Step 4: CloseWith YES + Considered Problem: (Rules: f2(A,B,C) -> f2(1 + A,1 + B,C) [1 >= A] f2(A,B,C) -> f2(1 + A,1 + B,C) [2 >= B && A >= 2] f2(A,B,C) -> f300(A,B,D) [B >= 3 && A >= 2] f1(A,B,C) -> f2(A,B,C) True Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{0,1,2},1->{1,2},2->{},3->{0,1,2}] ,We construct a looptree: P: [0,1,2,3] | +- p:[0] c: [0] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES