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 reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = max{14, x1 + 7}
        +_A(x1,x2) = max{x1 + 16, x2 + 27}
        -_A(x1,x2) = max{59, x1 + 48, x2 + 13}
        *_A(x1,x2) = max{14, x1 + 8, x2 + 9}
        D_A(x1) = max{10, x1 - 37}
        t_A = 1
        |1|_A = 0
        constant_A = 36
        |0|_A = 0
  
    base order 2:
  
      precedence:
      
        + = - > * = D = t = constant > D# = |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(+) = []
      pi(-) = [2]
      pi(*) = [1]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p6



-- 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)

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#(x)
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 set of usable rules consists of

  r1, r2

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = max{1, x1 - 11}
        +_A(x1,x2) = max{x1 + 13, x2 - 8}
        *_A(x1,x2) = max{7, x1 + 3, x2 + 2}
        -_A(x1,x2) = max{10, x1 + 5, x2}
        D_A(x1) = max{4, x1 - 18}
        t_A = 17
        |1|_A = 0
        constant_A = 1
        |0|_A = 0
  
    base order 2:
  
      precedence:
      
        + = * = - > D# = D = t = constant > |1| = |0|
      
  
    partial status:
  
      pi(D#) = []
      pi(+) = []
      pi(*) = [2]
      pi(-) = [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)
p3: D#(-(x,y)) -> D#(x)
p4: 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}


-- 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)

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:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = max{20, x1 + 10}
        *_A(x1,x2) = max{32, x1 + 19, x2 + 11}
        -_A(x1,x2) = max{21, x1 + 19, x2 + 15}
        D_A(x1) = x1 + 10
        t_A = 9
        |1|_A = 8
        constant_A = 9
        |0|_A = 8
  
    base order 2:
  
      precedence:
      
        - > * = D = t = constant > D# = |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(*) = [2]
      pi(-) = [2]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

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)
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 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#(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 set of usable rules consists of

  r1, r2

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = x1 + 4
        *_A(x1,x2) = max{x1 + 32, x2 + 17}
        -_A(x1,x2) = max{56, x1 + 5, x2 - 2}
        D_A(x1) = max{6, x1 - 49}
        t_A = 48
        |1|_A = 5
        constant_A = 1
        |0|_A = 0
  
    base order 2:
  
      precedence:
      
        * > - > D# = D = t = constant > |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(*) = [2]
      pi(-) = [1]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p3



-- 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

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = max{5, x1 + 2}
        *_A(x1,x2) = max{x1 + 6, x2 + 12}
        D_A(x1) = max{2, x1 - 24}
        t_A = 23
        |1|_A = 0
        constant_A = 23
        |0|_A = 0
  
    base order 2:
  
      precedence:
      
        * > D# = D = t = constant > |1| = |0|
      
  
    partial status:
  
      pi(D#) = [1]
      pi(*) = [2]
      pi(D) = []
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

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:
  
      max/plus interpretation on natural numbers:
      
        D#_A(x1) = x1 + 11
        *_A(x1,x2) = max{15, x1 + 12, x2 - 9}
        D_A(x1) = max{5, x1 + 1}
        t_A = 7
        |1|_A = 6
        constant_A = 7
        |0|_A = 6
  
    base order 2:
  
      precedence:
      
        constant > D# = * = D = t = |0| > |1|
      
  
    partial status:
  
      pi(D#) = []
      pi(*) = [1]
      pi(D) = [1]
      pi(t) = []
      pi(|1|) = []
      pi(constant) = []
      pi(|0|) = []

The following rules are removed:

  p1

Then no dependency pair remains.