YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [A >= 1] (?,1) 1. f1(A,B,C,D,E,F) -> f0(-1 + A,B,-1 + C,D,C,A) [A >= 1 && C >= 1] (?,1) 2. f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [0 >= A && C >= 1] (?,1) 3. f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] (1,1) Signature: {(f0,6);(f1,6);(f3,6)} Flow Graph: [0->{0,2},1->{0,2},2->{0,2},3->{0,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,2),(3,2)] * Step 2: UnreachableRules YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [A >= 1] (?,1) 1. f1(A,B,C,D,E,F) -> f0(-1 + A,B,-1 + C,D,C,A) [A >= 1 && C >= 1] (?,1) 2. f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [0 >= A && C >= 1] (?,1) 3. f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] (1,1) Signature: {(f0,6);(f1,6);(f3,6)} Flow Graph: [0->{0,2},1->{0,2},2->{0},3->{0}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [1] * Step 3: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [A >= 1] (?,1) 2. f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [0 >= A && C >= 1] (?,1) 3. f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] (1,1) Signature: {(f0,6);(f1,6);(f3,6)} Flow Graph: [0->{0,2},2->{0},3->{0}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [A >= 1] f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [0 >= A && C >= 1] f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] Signature: {(f0,6);(f1,6);(f3,6)} Rule Graph: [0->{0,2},2->{0},3->{0}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,2,3] | `- p:[0,2] c: [2] | `- p:[0] c: [0] * Step 5: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E,F) -> f0(-1 + A,C,-1 + C,A,E,F) [A >= 1] f0(A,B,C,D,E,F) -> f0(5000,B,C,D,E,F) [0 >= A && C >= 1] f3(A,B,C,D,E,F) -> f0(5000,B,G,D,E,F) [G >= 1] Signature: {(f0,6);(f1,6);(f3,6)} Rule Graph: [0->{0,2},2->{0},3->{0}] ,We construct a looptree: P: [0,2,3] | `- p:[0,2] c: [2] | `- p:[0] c: [0]) + Applied Processor: CloseWith True + Details: () YES