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, r5, r6, r7, r8, r9, r11, r12

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            cond#_A(x1,x2) = max{1, x2 - 1}
            true_A = 35
            and_A(x1,x2) = max{29, x2 + 15}
            even_A(x1) = x1 + 69
            gr_A(x1,x2) = max{16, x1 - 34}
            |0|_A = 0
            p_A(x1) = max{2, x1 - 58}
            false_A = 16
            s_A(x1) = max{69, x1 + 68}
            cond#!_A(x1,x2) = max{x1 + 25, x2 + 57}
            true!_A = 53
            and!_A(x1,x2) = max{61, x1 + 46}
            even!_A(x1) = max{135, x1 + 67}
            gr!_A(x1,x2) = max{66, x1 - 1, x2 + 61}
            |0|!_A = 64
            p!_A(x1) = max{66, x1 + 2}
            false!_A = 63
            s!_A(x1) = max{134, x1 - 70}
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            cond#_A(x1,x2) = max{54, x1 + 6, x2 + 52}
            true_A = 12
            and_A(x1,x2) = max{46, x2 - 1}
            even_A(x1) = x1 + 20
            gr_A(x1,x2) = max{14, x2 - 6}
            |0|_A = 0
            p_A(x1) = max{2, x1 - 33}
            false_A = 5
            s_A(x1) = x1 + 33
            cond#!_A(x1,x2) = x1 + 18
            true!_A = 10
            and!_A(x1,x2) = max{3, x1 - 1, x2 - 11}
            even!_A(x1) = x1 + 33
            gr!_A(x1,x2) = max{5, x1 - 5, x2 - 3}
            |0|!_A = 31
            p!_A(x1) = max{33, x1 - 1}
            false!_A = 3
            s!_A(x1) = max{5, x1 - 4}
        
  
    partial status:
  
      pi(cond#) = []
      pi(true) = []
      pi(and) = [1, 2]
      pi(even) = [1]
      pi(gr) = [1, 2]
      pi(|0|) = []
      pi(p) = [1]
      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:
  
      trivial reduction triple (T x T, T x T, Φ)
  
    base order 2:
  
      lexicographic combination of reduction triples:
      
        1. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            even#_A(x1) = x1
            s_A(x1) = max{7, x1}
            even#!_A(x1) = max{2, x1 - 10}
            s!_A(x1) = max{2, x1 - 10}
        
        2. marked-algebra reduction triple (>=A, >=A!, >A!):
        
          max/plus interpretation on natural numbers:
          
            even#_A(x1) = x1
            s_A(x1) = max{17, x1 + 9}
            even#!_A(x1) = max{5, x1 - 19}
            s!_A(x1) = max{6, x1 - 19}
        
  
    partial status:
  
      pi(even#) = [1]
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.