YES * Step 1: FromIts YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(A,1 + B,D,O,D,P,B,H,I,J,K,L,M,N) [A >= 1 + B && B >= 0] (?,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,O,S,V,W,C,M,N) [B >= A && B >= 0 && Q >= O && O >= 2] (?,1) 2. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(R,S,Q,V,U,F,G,P,T,W,Y,0,O,N) [0 >= P && 0 >= X] (1,1) 3. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(P,2,R,Q,R,F,G,P,R,J,K,L,O,S) [P >= 2] (1,1) 4. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,1,S,V,W,D,O,N) True (1,1) Signature: {(f1,14);(f3,14);(f4,14)} Flow Graph: [0->{0,1},1->{},2->{},3->{0,1},4->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(A,1 + B,D,O,D,P,B,H,I,J,K,L,M,N) [A >= 1 + B && B >= 0] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,O,S,V,W,C,M,N) [B >= A && B >= 0 && Q >= O && O >= 2] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(R,S,Q,V,U,F,G,P,T,W,Y,0,O,N) [0 >= P && 0 >= X] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(P,2,R,Q,R,F,G,P,R,J,K,L,O,S) [P >= 2] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,1,S,V,W,D,O,N) True Signature: {(f1,14);(f3,14);(f4,14)} Rule Graph: [0->{0,1},1->{},2->{},3->{0,1},4->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[0] c: [0] * Step 3: CloseWith YES + Considered Problem: (Rules: f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(A,1 + B,D,O,D,P,B,H,I,J,K,L,M,N) [A >= 1 + B && B >= 0] f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,O,S,V,W,C,M,N) [B >= A && B >= 0 && Q >= O && O >= 2] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(R,S,Q,V,U,F,G,P,T,W,Y,0,O,N) [0 >= P && 0 >= X] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f1(P,2,R,Q,R,F,G,P,R,J,K,L,O,S) [P >= 2] f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> f4(P,Q,R,U,T,F,G,1,S,V,W,D,O,N) True Signature: {(f1,14);(f3,14);(f4,14)} Rule Graph: [0->{0,1},1->{},2->{},3->{0,1},4->{}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[0] c: [0]) + Applied Processor: CloseWith True + Details: () YES