YES * Step 1: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] (?,1) 1. start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] (?,1) 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] (?,1) 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] (?,1) 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] (?,1) 5. b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 6. b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] (?,1) 7. start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] (1,1) Signature: {(a,4);(b,4);(cont1,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Flow Graph: [0->{},1->{2,3},2->{},3->{4},4->{5,6},5->{0,1},6->{},7->{0,1}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] Signature: {(a,4);(b,4);(cont1,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Rule Graph: [0->{},1->{2,3},2->{},3->{4},4->{5,6},5->{0,1},6->{},7->{0,1}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[1,5,4,3] c: [1,3,4,5] * Step 3: CloseWith YES + Considered Problem: (Rules: start(A,B,C,D) -> stop1(A,B,C,D) [A >= 0 && B >= 0 && C >= 0 && D = 0] start(A,B,C,D) -> cont1(A,B,C,D) [D >= 1 && A >= 0 && B >= 0 && C >= 0 && D >= 0 && A >= D] cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [D >= 1 && B >= 0 && A >= D && C = 0] cont1(A,B,C,D) -> a(A,B,-1 + C,D) [C >= 1 && D >= 1 && C >= 0 && B >= 0 && A >= D] a(A,B,C,D) -> b(A,B,E,-1 + D) [A >= D && B >= 0 && C >= 0 && D >= 1] b(A,B,C,D) -> start(A,B,C,D) [C >= 0 && D >= 0 && B >= 0 && A >= 1 + D] b(A,B,C,D) -> stop3(A,B,C,D) [0 >= 1 + C && D >= 0 && B >= 0 && A >= 1 + D] start0(A,B,C,D) -> start(A,B,B,A) [A >= 0 && B >= 0] Signature: {(a,4);(b,4);(cont1,4);(start,4);(start0,4);(stop1,4);(stop2,4);(stop3,4)} Rule Graph: [0->{},1->{2,3},2->{},3->{4},4->{5,6},5->{0,1},6->{},7->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[1,5,4,3] c: [1,3,4,5]) + Applied Processor: CloseWith True + Details: () YES