YES
We show the termination of the TRS R:

  .(.(x,y),z) -> .(x,.(y,z))


-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: .#(.(x,y),z) -> .#(x,.(y,z))
p2: .#(.(x,y),z) -> .#(y,z)

and R consists of:

r1: .(.(x,y),z) -> .(x,.(y,z))

The estimated dependency graph contains the following SCCs:

  {p1, p2}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: .#(.(x,y),z) -> .#(x,.(y,z))
p2: .#(.(x,y),z) -> .#(y,z)

and R consists of:

r1: .(.(x,y),z) -> .(x,.(y,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          .#_A(x1,x2) = x1 + x2 + 2
          ._A(x1,x2) = x1 + x2 + 1
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          .#_A(x1,x2) = max{0, x1 - 4, x2 - 5}
          ._A(x1,x2) = max{3, x1 + 1, x2}
          .#!_A(x1,x2) = max{2, x1 - 4, x2 - 5}
          .!_A(x1,x2) = max{1, x1 - 5, x2 - 9}
  
    partial status:
  
      pi(.#) = []
      pi(.) = [1, 2]

The following rules are removed:

  p2



-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: .#(.(x,y),z) -> .#(x,.(y,z))

and R consists of:

r1: .(.(x,y),z) -> .(x,.(y,z))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: .#(.(x,y),z) -> .#(x,.(y,z))

and R consists of:

r1: .(.(x,y),z) -> .(x,.(y,z))

The set of usable rules consists of

  r1

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          .#_A(x1,x2) = x1 + x2 + 1
          ._A(x1,x2) = x1 + x2 + 1
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          .#_A(x1,x2) = max{0, x1 - 3, x2 - 7}
          ._A(x1,x2) = max{2, x1 + 1, x2 - 3}
          .#!_A(x1,x2) = max{1, x1 - 3, x2 - 7}
          .!_A(x1,x2) = max{1, x1 - 7, x2 - 11}
  
    partial status:
  
      pi(.#) = [1]
      pi(.) = [1, 2]

The following rules are removed:

  p1

Then no dependency pair remains.