YES

TRS:

  and(false(),false()) -> false()
  and(true(),false()) -> false()
  and(false(),true()) -> false()
  and(true(),true()) -> true()
  eq(nil(),nil()) -> true()
  eq(cons(T,L),nil()) -> false()
  eq(nil(),cons(T,L)) -> false()
  eq(cons(T,L),cons(Tp,Lp)) -> and(eq(T,Tp),eq(L,Lp))
  eq(var(L),var(Lp)) -> eq(L,Lp)
  eq(var(L),apply(T,S)) -> false()
  eq(var(L),lambda(X,T)) -> false()
  eq(apply(T,S),var(L)) -> false()
  eq(apply(T,S),apply(Tp,Sp)) -> and(eq(T,Tp),eq(S,Sp))
  eq(apply(T,S),lambda(X,Tp)) -> false()
  eq(lambda(X,T),var(L)) -> false()
  eq(lambda(X,T),apply(Tp,Sp)) -> false()
  eq(lambda(X,T),lambda(Xp,Tp)) -> and(eq(T,Tp),eq(X,Xp))
  if(true(),var(K),var(L)) -> var(K)
  if(false(),var(K),var(L)) -> var(L)
  ren(var(L),var(K),var(Lp)) -> if(eq(L,Lp),var(K),var(Lp))
  ren(X,Y,apply(T,S)) -> apply(ren(X,Y,T),ren(X,Y,S))
  ren(X,Y,lambda(Z,T)) -> lambda(var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),ren(X,Y,ren(Z,var(cons(X,cons(Y,cons(lambda(Z,T),nil())))),T)))

max/plus interpretations on N:

  and_A(x1,x2) = max{2, 0, -67}
  and#_A(x1,x2) = max{0, 8 + x1, 5 + x2}
  false_A = 1
  false#_A = 8
  true_A = 2
  true#_A = 23
  eq_A(x1,x2) = max{13, -68, -6}
  eq#_A(x1,x2) = max{22, 1, 4}
  nil_A = 1
  nil#_A = 127
  cons_A(x1,x2) = max{1, 1, 1}
  cons#_A(x1,x2) = max{147, 2, 127}
  var_A(x1) = max{0, -10}
  var#_A(x1) = max{10, 7}
  apply_A(x1,x2) = max{82, 41 + x1, 61 + x2}
  apply#_A(x1,x2) = max{4, 0, -17 + x2}
  lambda_A(x1,x2) = max{22, 124 + x1, 103 + x2}
  lambda#_A(x1,x2) = max{4, 6, 3}
  if_A(x1,x2,x3) = max{1, -12 + x1, -9 + x2, -70 + x3}
  if#_A(x1,x2,x3) = max{4, -9 + x1, 14 + x2, 8}
  ren_A(x1,x2,x3) = max{21, -19, -80, x3}
  ren#_A(x1,x2,x3) = max{9, 5, 6, 23 + x3}

precedence:

  ren > nil > true = lambda > eq = cons = if > and = var > false > apply