YES

Problem:
 eq(0(),0()) -> true()
 eq(0(),s(Y)) -> false()
 eq(s(X),0()) -> false()
 eq(s(X),s(Y)) -> eq(X,Y)
 le(0(),Y) -> true()
 le(s(X),0()) -> false()
 le(s(X),s(Y)) -> le(X,Y)
 min(cons(0(),nil())) -> 0()
 min(cons(s(N),nil())) -> s(N)
 min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
 ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
 ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
 replace(N,M,nil()) -> nil()
 replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
 ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
 ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
 selsort(nil()) -> nil()
 selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
 ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
 ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))

Proof:
 DP Processor:
  DPs:
   eq#(s(X),s(Y)) -> eq#(X,Y)
   le#(s(X),s(Y)) -> le#(X,Y)
   min#(cons(N,cons(M,L))) -> le#(N,M)
   min#(cons(N,cons(M,L))) -> ifmin#(le(N,M),cons(N,cons(M,L)))
   ifmin#(true(),cons(N,cons(M,L))) -> min#(cons(N,L))
   ifmin#(false(),cons(N,cons(M,L))) -> min#(cons(M,L))
   replace#(N,M,cons(K,L)) -> eq#(N,K)
   replace#(N,M,cons(K,L)) -> ifrepl#(eq(N,K),N,M,cons(K,L))
   ifrepl#(false(),N,M,cons(K,L)) -> replace#(N,M,L)
   selsort#(cons(N,L)) -> min#(cons(N,L))
   selsort#(cons(N,L)) -> eq#(N,min(cons(N,L)))
   selsort#(cons(N,L)) -> ifselsort#(eq(N,min(cons(N,L))),cons(N,L))
   ifselsort#(true(),cons(N,L)) -> selsort#(L)
   ifselsort#(false(),cons(N,L)) -> replace#(min(cons(N,L)),N,L)
   ifselsort#(false(),cons(N,L)) -> selsort#(replace(min(cons(N,L)),N,L))
   ifselsort#(false(),cons(N,L)) -> min#(cons(N,L))
  TRS:
   eq(0(),0()) -> true()
   eq(0(),s(Y)) -> false()
   eq(s(X),0()) -> false()
   eq(s(X),s(Y)) -> eq(X,Y)
   le(0(),Y) -> true()
   le(s(X),0()) -> false()
   le(s(X),s(Y)) -> le(X,Y)
   min(cons(0(),nil())) -> 0()
   min(cons(s(N),nil())) -> s(N)
   min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
   ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
   ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
   replace(N,M,nil()) -> nil()
   replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
   ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
   ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
   selsort(nil()) -> nil()
   selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
   ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
   ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))
  Usable Rule Processor:
   DPs:
    eq#(s(X),s(Y)) -> eq#(X,Y)
    le#(s(X),s(Y)) -> le#(X,Y)
    min#(cons(N,cons(M,L))) -> le#(N,M)
    min#(cons(N,cons(M,L))) -> ifmin#(le(N,M),cons(N,cons(M,L)))
    ifmin#(true(),cons(N,cons(M,L))) -> min#(cons(N,L))
    ifmin#(false(),cons(N,cons(M,L))) -> min#(cons(M,L))
    replace#(N,M,cons(K,L)) -> eq#(N,K)
    replace#(N,M,cons(K,L)) -> ifrepl#(eq(N,K),N,M,cons(K,L))
    ifrepl#(false(),N,M,cons(K,L)) -> replace#(N,M,L)
    selsort#(cons(N,L)) -> min#(cons(N,L))
    selsort#(cons(N,L)) -> eq#(N,min(cons(N,L)))
    selsort#(cons(N,L)) -> ifselsort#(eq(N,min(cons(N,L))),cons(N,L))
    ifselsort#(true(),cons(N,L)) -> selsort#(L)
    ifselsort#(false(),cons(N,L)) -> replace#(min(cons(N,L)),N,L)
    ifselsort#(false(),cons(N,L)) -> selsort#(replace(min(cons(N,L)),N,L))
    ifselsort#(false(),cons(N,L)) -> min#(cons(N,L))
   TRS:
    le(0(),Y) -> true()
    le(s(X),0()) -> false()
    le(s(X),s(Y)) -> le(X,Y)
    eq(0(),0()) -> true()
    eq(0(),s(Y)) -> false()
    eq(s(X),0()) -> false()
    eq(s(X),s(Y)) -> eq(X,Y)
    min(cons(0(),nil())) -> 0()
    min(cons(s(N),nil())) -> s(N)
    min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
    ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
    ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
    replace(N,M,nil()) -> nil()
    replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
    ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
    ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     eq(0(),0()) -> true()
     eq(0(),s(Y)) -> false()
     eq(s(X),0()) -> false()
     eq(s(X),s(Y)) -> eq(X,Y)
     min(cons(0(),nil())) -> 0()
     min(cons(s(N),nil())) -> s(N)
     min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
     ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
     ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
     replace(N,M,nil()) -> nil()
     replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
     ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
     ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
    interpretation:
     [ifselsort#](x0, x1) = 2x0 + 4x1 + 2,
     
     [selsort#](x0) = 4x0 + 7,
     
     [ifrepl#](x0, x1, x2, x3) = x2 + 4x3,
     
     [replace#](x0, x1, x2) = x1 + 4x2 + 1,
     
     [ifmin#](x0, x1) = 2x1 + 6,
     
     [min#](x0) = 2x0 + 7,
     
     [le#](x0, x1) = x0,
     
     [eq#](x0, x1) = x1,
     
     [ifrepl](x0, x1, x2, x3) = 2x0 + x2 + x3,
     
     [replace](x0, x1, x2) = x1 + x2 + 2,
     
     [ifmin](x0, x1) = x1,
     
     [min](x0) = x0,
     
     [cons](x0, x1) = x0 + x1 + 4,
     
     [nil] = 5,
     
     [le](x0, x1) = 0,
     
     [false] = 1,
     
     [s](x0) = 2x0 + 1,
     
     [true] = 0,
     
     [eq](x0, x1) = 1,
     
     [0] = 1
    orientation:
     eq#(s(X),s(Y)) = 2Y + 1 >= Y = eq#(X,Y)
     
     le#(s(X),s(Y)) = 2X + 1 >= X = le#(X,Y)
     
     min#(cons(N,cons(M,L))) = 2L + 2M + 2N + 23 >= N = le#(N,M)
     
     min#(cons(N,cons(M,L))) = 2L + 2M + 2N + 23 >= 2L + 2M + 2N + 22 = ifmin#(le(N,M),cons(N,cons(M,L)))
     
     ifmin#(true(),cons(N,cons(M,L))) = 2L + 2M + 2N + 22 >= 2L + 2N + 15 = min#(cons(N,L))
     
     ifmin#(false(),cons(N,cons(M,L))) = 2L + 2M + 2N + 22 >= 2L + 2M + 15 = min#(cons(M,L))
     
     replace#(N,M,cons(K,L)) = 4K + 4L + M + 17 >= K = eq#(N,K)
     
     replace#(N,M,cons(K,L)) = 4K + 4L + M + 17 >= 4K + 4L + M + 16 = ifrepl#(eq(N,K),N,M,cons(K,L))
     
     ifrepl#(false(),N,M,cons(K,L)) = 4K + 4L + M + 16 >= 4L + M + 1 = replace#(N,M,L)
     
     selsort#(cons(N,L)) = 4L + 4N + 23 >= 2L + 2N + 15 = min#(cons(N,L))
     
     selsort#(cons(N,L)) = 4L + 4N + 23 >= L + N + 4 = eq#(N,min(cons(N,L)))
     
     selsort#(cons(N,L)) = 4L + 4N + 23 >= 4L + 4N + 20 = ifselsort#(eq(N,min(cons(N,L))),cons(N,L))
     
     ifselsort#(true(),cons(N,L)) = 4L + 4N + 18 >= 4L + 7 = selsort#(L)
     
     ifselsort#(false(),cons(N,L)) = 4L + 4N + 20 >= 4L + N + 1 = replace#(min(cons(N,L)),N,L)
     
     ifselsort#(false(),cons(N,L)) = 4L + 4N + 20 >= 4L + 4N + 15 = selsort#(replace(min(cons(N,L)),N,L))
     
     ifselsort#(false(),cons(N,L)) = 4L + 4N + 20 >= 2L + 2N + 15 = min#(cons(N,L))
     
     le(0(),Y) = 0 >= 0 = true()
     
     le(s(X),0()) = 0 >= 1 = false()
     
     le(s(X),s(Y)) = 0 >= 0 = le(X,Y)
     
     eq(0(),0()) = 1 >= 0 = true()
     
     eq(0(),s(Y)) = 1 >= 1 = false()
     
     eq(s(X),0()) = 1 >= 1 = false()
     
     eq(s(X),s(Y)) = 1 >= 1 = eq(X,Y)
     
     min(cons(0(),nil())) = 10 >= 1 = 0()
     
     min(cons(s(N),nil())) = 2N + 10 >= 2N + 1 = s(N)
     
     min(cons(N,cons(M,L))) = L + M + N + 8 >= L + M + N + 8 = ifmin(le(N,M),cons(N,cons(M,L)))
     
     ifmin(true(),cons(N,cons(M,L))) = L + M + N + 8 >= L + N + 4 = min(cons(N,L))
     
     ifmin(false(),cons(N,cons(M,L))) = L + M + N + 8 >= L + M + 4 = min(cons(M,L))
     
     replace(N,M,nil()) = M + 7 >= 5 = nil()
     
     replace(N,M,cons(K,L)) = K + L + M + 6 >= K + L + M + 6 = ifrepl(eq(N,K),N,M,cons(K,L))
     
     ifrepl(true(),N,M,cons(K,L)) = K + L + M + 4 >= L + M + 4 = cons(M,L)
     
     ifrepl(false(),N,M,cons(K,L)) = K + L + M + 6 >= K + L + M + 6 = cons(K,replace(N,M,L))
    problem:
     DPs:
      
     TRS:
      le(0(),Y) -> true()
      le(s(X),0()) -> false()
      le(s(X),s(Y)) -> le(X,Y)
      eq(0(),0()) -> true()
      eq(0(),s(Y)) -> false()
      eq(s(X),0()) -> false()
      eq(s(X),s(Y)) -> eq(X,Y)
      min(cons(0(),nil())) -> 0()
      min(cons(s(N),nil())) -> s(N)
      min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
      ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
      ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
      replace(N,M,nil()) -> nil()
      replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
      ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
      ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
    Qed