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, r10, r11, r12

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        cond#_A(x1,x2) = max{x1 - 2, x2 + 16}
        true_A = 25
        and_A(x1,x2) = x2 + 11
        even_A(x1) = 24
        gr_A(x1,x2) = max{3, x1 - 12}
        |0|_A = 5
        p_A(x1) = max{6, x1 - 17}
        false_A = 2
        s_A(x1) = x1 + 38
        y_A = 4
  
    base order 2:
  
      precedence:
      
        cond# > p > and = |0| > false > gr > true > s > even = y
      
  
    partial status:
  
      pi(cond#) = []
      pi(true) = []
      pi(and) = [2]
      pi(even) = []
      pi(gr) = []
      pi(|0|) = []
      pi(p) = []
      pi(false) = []
      pi(s) = [1]
      pi(y) = []

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

  r2, r3, r4, r5, r6, r8, r10, r12

Take the reduction pair:

  generalized weighted path order (>=MG, >MG)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        even#_A(x1) = max{1, x1 - 1}
        s_A(x1) = x1 + 12
        and_A(x1,x2) = max{5, x1 - 6, x2 - 6}
        false_A = 2
        true_A = 4
        even_A(x1) = max{5, x1 - 25}
        |0|_A = 5
        gr_A(x1,x2) = max{11, x1 - 18}
        y_A = 10
        p_A(x1) = max{12, x1 - 11}
  
    base order 2:
  
      precedence:
      
        gr = p > even# = s > and = even = |0| > false = true = y
      
  
    partial status:
  
      pi(even#) = []
      pi(s) = [1]
      pi(and) = []
      pi(false) = []
      pi(true) = []
      pi(even) = []
      pi(|0|) = []
      pi(gr) = []
      pi(y) = []
      pi(p) = []

The following rules are removed:

  p1

Then no dependency pair remains.