YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,F,10,0,E) True (1,1) 1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] (?,1) 2. f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] (?,1) Signature: {(f0,5);(f19,5);(f7,5)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E) -> f7(F,F,10,0,E) True f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] Signature: {(f0,5);(f19,5);(f7,5)} Rule Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2] | `- p:[1] c: [1] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E) -> f7(F,F,10,0,E) True f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && C >= 1 + D] f7(A,B,C,D,E) -> f19(A,B,C,D,E) [D >= 0 && -10 + C + D >= 0 && 10 + -1*C + D >= 0 && 10 + -1*C >= 0 && -10 + C >= 0 && D >= C] Signature: {(f0,5);(f19,5);(f7,5)} Rule Graph: [0->{1},1->{1,2},2->{}] ,We construct a looptree: P: [0,1,2] | `- p:[1] c: [1]) + Applied Processor: CloseWith True + Details: () YES