YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f1(A,1 + B,D,Q,D,R,B,H,I,J,K,L,M,N,O,P) [-2 + H >= 0 && -4 + B + H >= 0 && -2 + B >= 0 && A >= 1 + B && B >= 0] (?,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(R,S,U,X,W,F,G,Q,T,V,Y,Z,C,N,O,P) [-2 + H >= 0 && -4 + B + H >= 0 && -2 + B >= 0 && B >= A && B >= 0 && S >= Q && Q >= 2] (?,1) 2. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(T,V,S,Y,X,F,G,R,U,W,Z,B1,O,Q,O,P) [0 >= R && 0 >= A1] (1,1) 3. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f1(R,2,U,S,U,F,G,R,T,U,K,L,M,Q,T,V) [R >= 2] (1,1) 4. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(R,S,U,Y,X,F,G,1,T,W,Z,B1,D,Q,V,P) True (1,1) Signature: {(f1,16);(f3,16);(f4,16)} Flow Graph: [0->{0,1},1->{},2->{},3->{0,1},4->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f1(A,1 + B,D,Q,D,R,B,H,I,J,K,L,M,N,O,P) [-2 + H >= 0 && -4 + B + H >= 0 && -2 + B >= 0 && A >= 1 + B && B >= 0] (?,1) 1. f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(R,S,U,X,W,F,G,Q,T,V,Y,Z,C,N,O,P) [-2 + H >= 0 && -4 + B + H >= 0 && -2 + B >= 0 && B >= A && B >= 0 && S >= Q && Q >= 2] (1,1) 2. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(T,V,S,Y,X,F,G,R,U,W,Z,B1,O,Q,O,P) [0 >= R && 0 >= A1] (1,1) 3. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f1(R,2,U,S,U,F,G,R,T,U,K,L,M,Q,T,V) [R >= 2] (1,1) 4. f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P) -> f4(R,S,U,Y,X,F,G,1,T,W,Z,B1,D,Q,V,P) True (1,1) Signature: {(f1,16);(f3,16);(f4,16)} Flow Graph: [0->{0,1},1->{},2->{},3->{0,1},4->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[0] c: [0] YES