YES
We show the termination of the TRS R:

  cond(true(),x,y) -> cond(gr(x,y),p(x),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),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),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),y)

and R consists of:

r1: cond(true(),x,y) -> cond(gr(x,y),p(x),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:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          cond#_A(x1,x2,x3) = x1 + 1
          true_A() = 1
          gr_A(x1,x2) = 1
          p_A(x1) = x1 + 3
          |0|_A() = 2
          false_A() = 0
          s_A(x1) = x1 + 2
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          cond#_A(x1,x2,x3) = max{1, x2 - 1, x3 - 1}
          true_A = 8
          gr_A(x1,x2) = x1 + 2
          p_A(x1) = max{2, x1 - 1}
          |0|_A = 0
          false_A = 1
          s_A(x1) = max{6, x1 + 1}
          cond#!_A(x1,x2,x3) = max{x1 - 3, x2 + 2}
          true!_A = 8
          gr!_A(x1,x2) = x1 + 3
          p!_A(x1) = max{10, x1 - 1}
          |0|!_A = 9
          false!_A = 4
          s!_A(x1) = max{0, x1 - 1}
  
    partial status:
  
      pi(cond#) = [1]
      pi(true) = []
      pi(gr) = []
      pi(p) = []
      pi(|0|) = []
      pi(false) = []
      pi(s) = [1]

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),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:
  
      matrix interpretation with standard point-wise order:
      
        carrier: N^1
        order: standard order
        interpretations:
          gr#_A(x1,x2) = x1 + 5
          s_A(x1) = x1 + 4
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        max/plus interpretation on natural numbers:
        
          gr#_A(x1,x2) = max{x1, x2}
          s_A(x1) = x1
          gr#!_A(x1,x2) = max{3, x1 - 1, x2 - 1}
          s!_A(x1) = max{2, x1 - 2}
  
    partial status:
  
      pi(gr#) = [1]
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.