YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] (1,1) 1. f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && A >= 1] (?,1) 2. f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && 0 >= A && C >= 1] (?,1) Signature: {(f0,6);(f3,6)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(2,2)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] (1,1) 1. f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && A >= 1] (?,1) 2. f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && 0 >= A && C >= 1] (?,1) Signature: {(f0,6);(f3,6)} Flow Graph: [0->{1},1->{1,2},2->{1}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && A >= 1] f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && 0 >= A && C >= 1] Signature: {(f0,6);(f3,6)} Rule Graph: [0->{1},1->{1,2},2->{1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2] | `- p:[1,2] c: [2] | `- p:[1] c: [1] * Step 4: CloseWith YES + Considered Problem: (Rules: f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && A >= 1] f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [4999 + -1*A + C >= 0 && 5000 + -1*A >= 0 && 0 >= A && C >= 1] Signature: {(f0,6);(f3,6)} Rule Graph: [0->{1},1->{1,2},2->{1}] ,We construct a looptree: P: [0,1,2] | `- p:[1,2] c: [2] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES