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:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            .#_A(x1,x2) = max{0, x1 - 8, x2 - 11}
            ._A(x1,x2) = max{7, x1 + 3, x2}
            .#!_A(x1,x2) = x1 + 4
            .!_A(x1,x2) = max{0, x1 - 1, x2 - 6}
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            .#_A(x1,x2) = max{0, x2 - 3}
            ._A(x1,x2) = 2
            .#!_A(x1,x2) = 0
            .!_A(x1,x2) = max{1, x2 - 3}
        
  
    partial status:
  
      pi(.#) = []
      pi(.) = [1]

The following rules are removed:

  p1



-- SCC decomposition.

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

p1: .#(.(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}


-- Reduction pair.

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

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

and R consists of:

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

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            .#_A(x1,x2) = 0
            ._A(x1,x2) = max{1, x1 - 3, x2 - 5}
            .#!_A(x1,x2) = 0
            .!_A(x1,x2) = 0
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            .#_A(x1,x2) = 0
            ._A(x1,x2) = 1
            .#!_A(x1,x2) = 1
            .!_A(x1,x2) = max{2, x2 - 2}
        
  
    partial status:
  
      pi(.#) = [1]
      pi(.) = [2]

The following rules are removed:

  p1

Then no dependency pair remains.