YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f12(A,B,C,D,E) -> f12(1 + A,B,C,D,E) [9 >= A] (?,1) 1. f25(A,B,C,D,E) -> f25(A,1 + B,C,D,E) [9 >= B] (?,1) 2. f25(A,B,C,D,E) -> f36(A,B,C,D,E) [B >= 10] (?,1) 3. f12(A,B,C,D,E) -> f25(A,0,F,D,E) [A >= 10] (?,1) 4. f0(A,B,C,D,E) -> f12(0,B,C,F,G) True (1,1) Signature: {(f0,5);(f12,5);(f25,5);(f36,5)} Flow Graph: [0->{0,3},1->{1,2},2->{},3->{1,2},4->{0,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,2),(4,3)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f12(A,B,C,D,E) -> f12(1 + A,B,C,D,E) [9 >= A] (?,1) 1. f25(A,B,C,D,E) -> f25(A,1 + B,C,D,E) [9 >= B] (?,1) 2. f25(A,B,C,D,E) -> f36(A,B,C,D,E) [B >= 10] (?,1) 3. f12(A,B,C,D,E) -> f25(A,0,F,D,E) [A >= 10] (?,1) 4. f0(A,B,C,D,E) -> f12(0,B,C,F,G) True (1,1) Signature: {(f0,5);(f12,5);(f25,5);(f36,5)} Flow Graph: [0->{0,3},1->{1,2},2->{},3->{1},4->{0}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f12(A,B,C,D,E) -> f12(1 + A,B,C,D,E) [9 >= A] f25(A,B,C,D,E) -> f25(A,1 + B,C,D,E) [9 >= B] f25(A,B,C,D,E) -> f36(A,B,C,D,E) [B >= 10] f12(A,B,C,D,E) -> f25(A,0,F,D,E) [A >= 10] f0(A,B,C,D,E) -> f12(0,B,C,F,G) True Signature: {(f0,5);(f12,5);(f25,5);(f36,5)} Rule Graph: [0->{0,3},1->{1,2},2->{},3->{1},4->{0}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[0] c: [0] | `- p:[1] c: [1] * Step 4: CloseWith YES + Considered Problem: (Rules: f12(A,B,C,D,E) -> f12(1 + A,B,C,D,E) [9 >= A] f25(A,B,C,D,E) -> f25(A,1 + B,C,D,E) [9 >= B] f25(A,B,C,D,E) -> f36(A,B,C,D,E) [B >= 10] f12(A,B,C,D,E) -> f25(A,0,F,D,E) [A >= 10] f0(A,B,C,D,E) -> f12(0,B,C,F,G) True Signature: {(f0,5);(f12,5);(f25,5);(f36,5)} Rule Graph: [0->{0,3},1->{1,2},2->{},3->{1},4->{0}] ,We construct a looptree: P: [0,1,2,3,4] | +- p:[0] c: [0] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES