YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{},4->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,0),(0,2),(0,3),(1,0),(1,2),(2,1)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) 1. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [A >= 0] (?,1) 4. f2(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300(A,B,C) -> f1(A,B,D) [A >= 0] f2(A,B,C) -> f300(A,B,C) True Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[2] c: [2] | `- p:[1] c: [1] * Step 4: CloseWith YES + Considered Problem: (Rules: f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] f300(A,B,C) -> f1(A,B,D) [A >= 0] f2(A,B,C) -> f300(A,B,C) True Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1},1->{1,3},2->{0,2,3},3->{},4->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4] | +- p:[2] c: [2] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES