YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && E >= 0 && C >= 1 + B && 1022 >= E] 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && 0 >= 1 + E] (?,1) Signature: {(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3,4,5,6},1->{3,4,5,6},2->{3,4,5,6},3->{3,4,5,6},4->{},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6)] * Step 2: FromIts YES + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] (1,1) 1. f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] (1,1) 2. f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True (1,1) 3. f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && B >= C] (?,1) 4. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && E >= 0 && C >= 1 + B && 1022 >= E] 5. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && E >= 1023] (?,1) 6. f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && 0 >= 1 + E] (?,1) Signature: {(f0,5);(f21,5);(f7,5)} Flow Graph: [0->{3},1->{3},2->{3},3->{3,4,5,6},4->{},5->{},6->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && B >= C] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && E >= 0 && C >= 1 + B && 1022 >= E] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && E >= 1023] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && 0 >= 1 + E] Signature: {(f0,5);(f21,5);(f7,5)} Rule Graph: [0->{3},1->{3},2->{3},3->{3,4,5,6},4->{},5->{},6->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [3] * Step 4: CloseWith YES + Considered Problem: (Rules: f0(A,B,C,D,E) -> f7(F,0,0,D,E) [0 >= 1 + F] f0(A,B,C,D,E) -> f7(F,0,0,D,E) [F >= 1] f0(A,B,C,D,E) -> f7(0,1023,0,D,E) True f7(A,B,C,D,E) -> f7(A,B,1 + C,2 + D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && B >= C] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && E >= 0 && C >= 1 + B && 1022 >= E] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && E >= 1023] f7(A,B,C,D,E) -> f21(A,B,C,D,E) [C >= 0 && B + C >= 0 && 1023 + -1*B + C >= 0 && 1023 + -1*B >= 0 && B >= 0 && C >= 1 + B && 0 >= 1 + E] Signature: {(f0,5);(f21,5);(f7,5)} Rule Graph: [0->{3},1->{3},2->{3},3->{3,4,5,6},4->{},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[3] c: [3]) + Applied Processor: CloseWith True + Details: () YES