My code compiles now, but my outputs RG (z1) and RN (z0) are incorrect and show up as X's in the simulation. I have no idea how to implement double JKFFs using "always @" code. I think I need to somehow fix my jkff module so that I do not get X's in my code.

The JKFFs I should be implementing is:

module main_file(
input r,
input x1,
input x0,
input clk,
output RN,
output RG
);
wire ss0, ss1, a1; 
jkff i_jkff
( 
.s0(ss0),  
.s1(ss1)
);  
assign a1=(!ss0||x1);
assign RN=(x0&&ss1&&a1);
assign RG=(x1&&ss1&&!ss0);
endmodule

Below is the jkff implementation:

module jkff(
input clk, r, x1, x0,
output reg s0,
output reg s1
);
 wire a1, a2, a3, a4, J1, K1, J0, K0;
 assign a1=(x1||s0);
 assign J1=(a1&&x0);
 assign a2=(x1||!s0);
 assign K1=(x0&&a2);
 assign a3=(x1||x0);
 assign J0=(a3&&!s1);
 assign a4=(x1||s1);
 assign K0=(a4&&x0);
 
 always @(posedge clk or posedge r)
 begin
    if (r) begin
        s1<=0;
        end
    else begin
    case ({J1,K1})
    2'b00: s1<=s1;
    2'b01: s1<=1'b0;
    2'b10: s1<=1'b1;
    2'b11: s1<=~s1;
    endcase
end
end
endmodule

Below is the test bench

module main_file_tb(
);

reg a;
reg b;
reg c;
reg d;
wire e;
wire f;

main_file main_file
(
.r(a),
.x1(b),
.x0(c),
.clk(d),
.RN(e),
.RG(f)
);

initial begin
a=0;b=1;c=1;d=1;
#10;
a=0;b=0;c=1;d=1;
#10;
a=0;b=1;c=1;d=1;
#10;
a=1;b=0;c=0;d=0;
#10;
a=0;b=0;c=1;d=1;
#10;
a=0;b=0;c=1;d=1;
#10;
a=0;b=0;c=1;d=1;
#10;
a=0;b=0;c=1;d=1;
#10;
a=1;b=0;c=0;d=0;
#10;
a=0;b=1;c=1;d=1;
#10;
a=1;b=0;c=0;d=0;
#10;
end
endmodule