YES
We show the termination of the TRS R:

  cond(true(),x) -> cond(and(even(x),gr(x,|0|())),p(x))
  and(x,false()) -> false()
  and(false(),x) -> false()
  and(true(),true()) -> true()
  even(|0|()) -> true()
  even(s(|0|())) -> false()
  even(s(s(x))) -> even(x)
  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) -> cond#(and(even(x),gr(x,|0|())),p(x))
p2: cond#(true(),x) -> and#(even(x),gr(x,|0|()))
p3: cond#(true(),x) -> even#(x)
p4: cond#(true(),x) -> gr#(x,|0|())
p5: cond#(true(),x) -> p#(x)
p6: even#(s(s(x))) -> even#(x)
p7: gr#(s(x),s(y())) -> gr#(x,y())

and R consists of:

r1: cond(true(),x) -> cond(and(even(x),gr(x,|0|())),p(x))
r2: and(x,false()) -> false()
r3: and(false(),x) -> false()
r4: and(true(),true()) -> true()
r5: even(|0|()) -> true()
r6: even(s(|0|())) -> false()
r7: even(s(s(x))) -> even(x)
r8: gr(|0|(),x) -> false()
r9: gr(s(x),|0|()) -> true()
r10: gr(s(x),s(y())) -> gr(x,y())
r11: p(|0|()) -> |0|()
r12: p(s(x)) -> x

The estimated dependency graph contains the following SCCs:

  {p1}
  {p6}


-- Reduction pair.

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

p1: cond#(true(),x) -> cond#(and(even(x),gr(x,|0|())),p(x))

and R consists of:

r1: cond(true(),x) -> cond(and(even(x),gr(x,|0|())),p(x))
r2: and(x,false()) -> false()
r3: and(false(),x) -> false()
r4: and(true(),true()) -> true()
r5: even(|0|()) -> true()
r6: even(s(|0|())) -> false()
r7: even(s(s(x))) -> even(x)
r8: gr(|0|(),x) -> false()
r9: gr(s(x),|0|()) -> true()
r10: gr(s(x),s(y())) -> gr(x,y())
r11: p(|0|()) -> |0|()
r12: p(s(x)) -> x

The set of usable rules consists of

  r2, r3, r4, r6, r8, r9, r11, r12

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        cond#_A(x1,x2) = max{x1 + 60, x2 + 66}
        true_A = 17
        and_A(x1,x2) = max{4, x2 + 1}
        even_A(x1) = 8
        gr_A(x1,x2) = max{3, x1 - 22}
        |0|_A = 8
        p_A(x1) = max{10, x1 - 1}
        false_A = 2
        s_A(x1) = max{40, x1 + 21}
  
    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) = 0
            true_A() = 6
            and_A(x1,x2) = 6
            even_A(x1) = x1 + 1
            gr_A(x1,x2) = 6
            |0|_A() = 4
            p_A(x1) = x1 + 1
            false_A() = 1
            s_A(x1) = x1 + 4
            cond#!_A(x1,x2) = 10
            true!_A() = 5
            and!_A(x1,x2) = 11
            even!_A(x1) = x1
            gr!_A(x1,x2) = x1 + 4
            |0|!_A() = 8
            p!_A(x1) = 9
            false!_A() = 7
            s!_A(x1) = 6
  
    partial status:
  
      pi(cond#) = [2]
      pi(true) = []
      pi(and) = [2]
      pi(even) = []
      pi(gr) = []
      pi(|0|) = []
      pi(p) = []
      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: even#(s(s(x))) -> even#(x)

and R consists of:

r1: cond(true(),x) -> cond(and(even(x),gr(x,|0|())),p(x))
r2: and(x,false()) -> false()
r3: and(false(),x) -> false()
r4: and(true(),true()) -> true()
r5: even(|0|()) -> true()
r6: even(s(|0|())) -> false()
r7: even(s(s(x))) -> even(x)
r8: gr(|0|(),x) -> false()
r9: gr(s(x),|0|()) -> true()
r10: gr(s(x),s(y())) -> gr(x,y())
r11: p(|0|()) -> |0|()
r12: 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:
      
        even#_A(x1) = 3
        s_A(x1) = max{2, x1 - 12}
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            even#_A(x1) = 0
            s_A(x1) = x1 + 5
            even#!_A(x1) = x1 + 4
            s!_A(x1) = 3
  
    partial status:
  
      pi(even#) = []
      pi(s) = []

The following rules are removed:

  p1

Then no dependency pair remains.