YES * Step 1: FromIts YES + Considered Problem: Rules: 0. f2(A,B,C) -> f2(-1 + A,B,C) [A >= 31] (?,1) 1. f2(A,B,C) -> f300(A,-1 + B,C) [30 >= A] (?,1) 2. f300(A,B,C) -> f2(A,B,C) [B >= 21] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [20 >= B] (?,1) 4. f3(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: f2(A,B,C) -> f2(-1 + A,B,C) [A >= 31] f2(A,B,C) -> f300(A,-1 + B,C) [30 >= A] f300(A,B,C) -> f2(A,B,C) [B >= 21] f300(A,B,C) -> f1(A,B,D) [20 >= B] f3(A,B,C) -> f300(A,B,C) True Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[0,2,1] c: [1,2] | `- p:[0] c: [0] * Step 3: CloseWith YES + Considered Problem: (Rules: f2(A,B,C) -> f2(-1 + A,B,C) [A >= 31] f2(A,B,C) -> f300(A,-1 + B,C) [30 >= A] f300(A,B,C) -> f2(A,B,C) [B >= 21] f300(A,B,C) -> f1(A,B,D) [20 >= B] f3(A,B,C) -> f300(A,B,C) True Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[0,2,1] c: [1,2] | `- p:[0] c: [0]) + Applied Processor: CloseWith True + Details: () YES