YES * Step 1: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] (?,1) 2. lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] 3. lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 (?,1) && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] 4. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl32,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(lbl32,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[3] c: [3] * Step 3: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 1 >= A && B = C && D = A] start(A,B,C,D) -> lbl32(A,B,C,-1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 2 && B = C && D = A] lbl32(A,B,C,D) -> stop(A,B,C,D) [-1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && A >= 2 && D = 1 && B = C] lbl32(A,B,C,D) -> lbl32(A,B,C,-1 + D) [-1 + A + -1*D >= 0 && -1 + D >= 0 && -3 + A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && -2 + A >= 0 && D >= 2 && D >= 1 && A >= 1 + D && B = C] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(lbl32,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{2,3},2->{},3->{2,3},4->{0,1}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[3] c: [3]) + Applied Processor: CloseWith True + Details: () YES