YES
We show the termination of the TRS R:

  cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
  gr(|0|(),x) -> false()
  gr(s(x),|0|()) -> true()
  gr(s(x),s(y)) -> gr(x,y)
  p(|0|()) -> |0|()
  p(s(x)) -> x


-- SCC decomposition.

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

p1: cond#(true(),x,y) -> cond#(gr(x,y),p(x),s(y))
p2: cond#(true(),x,y) -> gr#(x,y)
p3: cond#(true(),x,y) -> p#(x)
p4: gr#(s(x),s(y)) -> gr#(x,y)

and R consists of:

r1: cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
r2: gr(|0|(),x) -> false()
r3: gr(s(x),|0|()) -> true()
r4: gr(s(x),s(y)) -> gr(x,y)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The estimated dependency graph contains the following SCCs:

  {p1}
  {p4}


-- Reduction pair.

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

p1: cond#(true(),x,y) -> cond#(gr(x,y),p(x),s(y))

and R consists of:

r1: cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
r2: gr(|0|(),x) -> false()
r3: gr(s(x),|0|()) -> true()
r4: gr(s(x),s(y)) -> gr(x,y)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The set of usable rules consists of

  r2, r3, r4, r5, r6

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        cond#_A(x1,x2,x3) = max{x1 - 5, x2 + 5}
        true_A = 11
        gr_A(x1,x2) = max{4, x1 - 3}
        p_A(x1) = max{0, x1 - 6}
        s_A(x1) = x1 + 15
        |0|_A = 0
        false_A = 0
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            cond#_A(x1,x2,x3) = 0
            true_A() = 1
            gr_A(x1,x2) = x1 + 1
            p_A(x1) = x1 + 1
            s_A(x1) = x1 + 1
            |0|_A() = 1
            false_A() = 2
            cond#!_A(x1,x2,x3) = 3
            true!_A() = 1
            gr!_A(x1,x2) = x1 + x2
            p!_A(x1) = 2
            s!_A(x1) = 4
            |0|!_A() = 2
            false!_A() = 0
  
    partial status:
  
      pi(cond#) = []
      pi(true) = []
      pi(gr) = []
      pi(p) = []
      pi(s) = [1]
      pi(|0|) = []
      pi(false) = []

The following rules are removed:

  p1

Then no dependency pair remains.

-- Reduction pair.

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

p1: gr#(s(x),s(y)) -> gr#(x,y)

and R consists of:

r1: cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
r2: gr(|0|(),x) -> false()
r3: gr(s(x),|0|()) -> true()
r4: gr(s(x),s(y)) -> gr(x,y)
r5: p(|0|()) -> |0|()
r6: p(s(x)) -> x

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        gr#_A(x1,x2) = max{3, x1 - 6, x2 - 11}
        s_A(x1) = max{10, x1 + 5}
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            gr#_A(x1,x2) = x1 + x2
            s_A(x1) = x1 + 1
            gr#!_A(x1,x2) = 6
            s!_A(x1) = 6
  
    partial status:
  
      pi(gr#) = []
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.