YES

Problem:
 .(1(),x) -> x
 .(x,1()) -> x
 .(i(x),x) -> 1()
 .(x,i(x)) -> 1()
 i(1()) -> 1()
 i(i(x)) -> x
 .(i(y),.(y,z)) -> z
 .(y,.(i(y),z)) -> z
 .(.(x,y),z) -> .(x,.(y,z))
 i(.(x,y)) -> .(i(y),i(x))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [.](x0, x1) = x0 + x1 + 2,
   
   [1] = 1,
   
   [i](x0) = x0
  orientation:
   .(1(),x) = x + 3 >= x = x
   
   .(x,1()) = x + 3 >= x = x
   
   .(i(x),x) = 2x + 2 >= 1 = 1()
   
   .(x,i(x)) = 2x + 2 >= 1 = 1()
   
   i(1()) = 1 >= 1 = 1()
   
   i(i(x)) = x >= x = x
   
   .(i(y),.(y,z)) = 2y + z + 4 >= z = z
   
   .(y,.(i(y),z)) = 2y + z + 4 >= z = z
   
   .(.(x,y),z) = x + y + z + 4 >= x + y + z + 4 = .(x,.(y,z))
   
   i(.(x,y)) = x + y + 2 >= x + y + 2 = .(i(y),i(x))
  problem:
   i(1()) -> 1()
   i(i(x)) -> x
   .(.(x,y),z) -> .(x,.(y,z))
   i(.(x,y)) -> .(i(y),i(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [.](x0, x1) = x0 + x1 + 2,
    
    [1] = 0,
    
    [i](x0) = 4x0
   orientation:
    i(1()) = 0 >= 0 = 1()
    
    i(i(x)) = 16x >= x = x
    
    .(.(x,y),z) = x + y + z + 4 >= x + y + z + 4 = .(x,.(y,z))
    
    i(.(x,y)) = 4x + 4y + 8 >= 4x + 4y + 2 = .(i(y),i(x))
   problem:
    i(1()) -> 1()
    i(i(x)) -> x
    .(.(x,y),z) -> .(x,.(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [.](x0, x1) = 4x0 + x1 + 4,
     
     [1] = 0,
     
     [i](x0) = 3x0 + 6
    orientation:
     i(1()) = 6 >= 0 = 1()
     
     i(i(x)) = 9x + 24 >= x = x
     
     .(.(x,y),z) = 16x + 4y + z + 20 >= 4x + 4y + z + 8 = .(x,.(y,z))
    problem:
     
    Qed