YES
We show the termination of the TRS R:

  D(t()) -> |1|()
  D(constant()) -> |0|()
  D(+(x,y)) -> +(D(x),D(y))
  D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
  D(-(x,y)) -> -(D(x),D(y))


-- SCC decomposition.

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

p1: D#(+(x,y)) -> D#(x)
p2: D#(+(x,y)) -> D#(y)
p3: D#(*(x,y)) -> D#(x)
p4: D#(*(x,y)) -> D#(y)
p5: D#(-(x,y)) -> D#(x)
p6: D#(-(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4, p5, p6}


-- Reduction pair.

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

p1: D#(+(x,y)) -> D#(x)
p2: D#(-(x,y)) -> D#(y)
p3: D#(-(x,y)) -> D#(x)
p4: D#(*(x,y)) -> D#(y)
p5: D#(*(x,y)) -> D#(x)
p6: D#(+(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2

Take the monotone reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          +_A(x1,x2) = x1 + x2 + 2
          -_A(x1,x2) = x1 + x2 + 2
          *_A(x1,x2) = x1 + x2 + 2
          D_A(x1) = x1 + 1
          t_A() = 1
          |1|_A() = 0
          constant_A() = 1
          |0|_A() = 0
  
    base order 2:
  
      precedence:
      
        + > - = * > D# = D = t = constant > |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(+) = [1, 2]
      pi(-) = [1, 2]
      pi(*) = [1, 2]
      pi(D) = [1]
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1



-- SCC decomposition.

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

p1: D#(-(x,y)) -> D#(y)
p2: D#(-(x,y)) -> D#(x)
p3: D#(*(x,y)) -> D#(y)
p4: D#(*(x,y)) -> D#(x)
p5: D#(+(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4, p5}


-- Reduction pair.

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

p1: D#(-(x,y)) -> D#(y)
p2: D#(+(x,y)) -> D#(y)
p3: D#(*(x,y)) -> D#(x)
p4: D#(*(x,y)) -> D#(y)
p5: D#(-(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2

Take the monotone reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          -_A(x1,x2) = x1 + x2 + 2
          +_A(x1,x2) = x1 + x2 + 2
          *_A(x1,x2) = x1 + x2 + 2
          D_A(x1) = x1 + 1
          t_A() = 1
          |1|_A() = 0
          constant_A() = 1
          |0|_A() = 0
  
    base order 2:
  
      precedence:
      
        + > - = * > D# = D = t = constant > |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(-) = [1, 2]
      pi(+) = [1, 2]
      pi(*) = [1, 2]
      pi(D) = [1]
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1



-- SCC decomposition.

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

p1: D#(+(x,y)) -> D#(y)
p2: D#(*(x,y)) -> D#(x)
p3: D#(*(x,y)) -> D#(y)
p4: D#(-(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4}


-- Reduction pair.

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

p1: D#(+(x,y)) -> D#(y)
p2: D#(-(x,y)) -> D#(x)
p3: D#(*(x,y)) -> D#(y)
p4: D#(*(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          +_A(x1,x2) = x1 + x2 + 2
          -_A(x1,x2) = x1 + 2
          *_A(x1,x2) = x1 + x2 + 2
          D_A(x1) = x1 + 1
          t_A() = 1
          |1|_A() = 0
          constant_A() = 1
          |0|_A() = 0
  
    base order 2:
  
      precedence:
      
        * > + = D = constant > D# = - = |1| = |0| > t
      
  
    partial status:
  
      pi(D#) = []
      pi(+) = []
      pi(-) = [1]
      pi(*) = [1, 2]
      pi(D) = [1]
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1



-- SCC decomposition.

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

p1: D#(-(x,y)) -> D#(x)
p2: D#(*(x,y)) -> D#(y)
p3: D#(*(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3}


-- Reduction pair.

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

p1: D#(-(x,y)) -> D#(x)
p2: D#(*(x,y)) -> D#(x)
p3: D#(*(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          -_A(x1,x2) = x1 + 1
          *_A(x1,x2) = x1 + x2 + 3
          D_A(x1) = x1 + 2
          t_A() = 1
          |1|_A() = 2
          constant_A() = 1
          |0|_A() = 0
  
    base order 2:
  
      precedence:
      
        * > D = t = constant > - = |1| = |0| > D#
      
  
    partial status:
  
      pi(D#) = []
      pi(-) = [1]
      pi(*) = [1, 2]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1



-- SCC decomposition.

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

p1: D#(*(x,y)) -> D#(x)
p2: D#(*(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1, p2}


-- Reduction pair.

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

p1: D#(*(x,y)) -> D#(x)
p2: D#(*(x,y)) -> D#(y)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2, r5

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          *_A(x1,x2) = x1 + x2 + 3
          D_A(x1) = 2
          t_A() = 1
          |1|_A() = 0
          constant_A() = 1
          |0|_A() = 0
          -_A(x1,x2) = 1
  
    base order 2:
  
      precedence:
      
        * = D = t = constant > D# = |1| = |0| = -
      
  
    partial status:
  
      pi(D#) = []
      pi(*) = [2]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []
      pi(-) = []

The following rules are removed:

  p2



-- SCC decomposition.

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

p1: D#(*(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

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

p1: D#(*(x,y)) -> D#(x)

and R consists of:

r1: D(t()) -> |1|()
r2: D(constant()) -> |0|()
r3: D(+(x,y)) -> +(D(x),D(y))
r4: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
r5: D(-(x,y)) -> -(D(x),D(y))

The set of usable rules consists of

  r1, r2

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          D#_A(x1) = x1
          *_A(x1,x2) = x1 + 2
          D_A(x1) = x1 + 1
          t_A() = 1
          |1|_A() = 0
          constant_A() = 1
          |0|_A() = 0
  
    base order 2:
  
      precedence:
      
        * = D = t = constant > D# = |1| = |0|
      
  
    partial status:
  
      pi(D#) = []
      pi(*) = [1]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1

Then no dependency pair remains.