YES * Step 1: FromIts YES + Considered Problem: Rules: 0. start(A,B,C,D) -> stop1(A,B,C,D) [A + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D = 0] 1. start(A,B,C,D) -> cont1(A,B,C,D) [A + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 && A >= D] 2. cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && C = 0] 3. cont1(A,B,C,D) -> a(A,B,-1 + C,D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 && D >= 1 && A >= D] 4. a(A,B,C,D) -> b(A,B,E,-1 + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && D >= 1] 5. b(A,B,C,D) -> start(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 0 && A >= 1 + D] 6. b(A,B,C,D) -> stop3(A,B,C,D) [-1 + A + -1*D >= 0 (?,1) && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 0 >= 1 + C && A >= 1 + D] 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 + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D = 0] start(A,B,C,D) -> cont1(A,B,C,D) [A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 && A >= D] cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && C = 0] cont1(A,B,C,D) -> a(A,B,-1 + C,D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 && D >= 1 && A >= D] a(A,B,C,D) -> b(A,B,E,-1 + D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && D >= 1] b(A,B,C,D) -> start(A,B,C,D) [-1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 0 && A >= 1 + D] b(A,B,C,D) -> stop3(A,B,C,D) [-1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 0 >= 1 + C && 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 + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D = 0] start(A,B,C,D) -> cont1(A,B,C,D) [A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 && A >= D] cont1(A,B,C,D) -> stop2(A,B,1,-1 + D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && D >= 1 && A >= D && C = 0] cont1(A,B,C,D) -> a(A,B,-1 + C,D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 1 && D >= 1 && A >= D] a(A,B,C,D) -> b(A,B,E,-1 + D) [A + -1*D >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && D >= 1] b(A,B,C,D) -> start(A,B,C,D) [-1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && C >= 0 && A >= 1 + D] b(A,B,C,D) -> stop3(A,B,C,D) [-1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && 0 >= 1 + C && 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