MAYBE

Problem:
 cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
 cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
 cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)
 p(0()) -> 0()
 p(s(x)) -> x
 eq(0(),0()) -> true()
 eq(s(x),0()) -> false()
 eq(0(),s(x)) -> false()
 eq(s(x),s(y)) -> eq(x,y)
 and(true(),true()) -> true()
 and(false(),x) -> false()
 and(x,false()) -> false()

Proof:
 DP Processor:
  DPs:
   cond1#(true(),x,y,z) -> gr#(y,z)
   cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
   cond2#(true(),x,y,z) -> p#(y)
   cond2#(true(),x,y,z) -> p#(x)
   cond2#(true(),x,y,z) -> gr#(y,z)
   cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z)
   cond2#(false(),x,y,z) -> gr#(x,z)
   cond2#(false(),x,y,z) -> eq#(x,y)
   cond2#(false(),x,y,z) -> and#(eq(x,y),gr(x,z))
   cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z)
   gr#(s(x),s(y)) -> gr#(x,y)
   eq#(s(x),s(y)) -> eq#(x,y)
  TRS:
   cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
   cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
   cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   p(0()) -> 0()
   p(s(x)) -> x
   eq(0(),0()) -> true()
   eq(s(x),0()) -> false()
   eq(0(),s(x)) -> false()
   eq(s(x),s(y)) -> eq(x,y)
   and(true(),true()) -> true()
   and(false(),x) -> false()
   and(x,false()) -> false()
  TDG Processor:
   DPs:
    cond1#(true(),x,y,z) -> gr#(y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
    cond2#(true(),x,y,z) -> p#(y)
    cond2#(true(),x,y,z) -> p#(x)
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z)
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond2#(false(),x,y,z) -> eq#(x,y)
    cond2#(false(),x,y,z) -> and#(eq(x,y),gr(x,z))
    cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z)
    gr#(s(x),s(y)) -> gr#(x,y)
    eq#(s(x),s(y)) -> eq#(x,y)
   TRS:
    cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
    cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
    cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    p(0()) -> 0()
    p(s(x)) -> x
    eq(0(),0()) -> true()
    eq(s(x),0()) -> false()
    eq(0(),s(x)) -> false()
    eq(s(x),s(y)) -> eq(x,y)
    and(true(),true()) -> true()
    and(false(),x) -> false()
    and(x,false()) -> false()
   graph:
    eq#(s(x),s(y)) -> eq#(x,y) -> eq#(s(x),s(y)) -> eq#(x,y)
    cond2#(false(),x,y,z) -> eq#(x,y) ->
    eq#(s(x),s(y)) -> eq#(x,y)
    cond2#(false(),x,y,z) -> gr#(x,z) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z) ->
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
    cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z) ->
    cond1#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(false(),x,y,z) -> and#(eq(x,y),gr(x,z))
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(false(),x,y,z) -> eq#(x,y)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(true(),x,y,z) -> p#(x)
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z) ->
    cond2#(true(),x,y,z) -> p#(y)
    cond2#(true(),x,y,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
    gr#(s(x),s(y)) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> and#(eq(x,y),gr(x,z))
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> eq#(x,y)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(false(),x,y,z) -> gr#(x,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> gr#(y,z)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> p#(x)
    cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z) ->
    cond2#(true(),x,y,z) -> p#(y)
    cond1#(true(),x,y,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 24/144
    DPs:
     cond2#(false(),x,y,z) -> cond1#(and(eq(x,y),gr(x,z)),x,y,z)
     cond1#(true(),x,y,z) -> cond2#(gr(y,z),x,y,z)
     cond2#(true(),x,y,z) -> cond2#(gr(y,z),p(x),p(y),z)
    TRS:
     cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
     cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
     cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(x)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     and(true(),true()) -> true()
     and(false(),x) -> false()
     and(x,false()) -> false()
    Open
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
     cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
     cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(x)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     and(true(),true()) -> true()
     and(false(),x) -> false()
     and(x,false()) -> false()
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(cond1) = 3
      pi(gr) = 0
      pi(cond2) = 3
      pi(p) = [0]
      pi(false) = []
      pi(eq) = []
      pi(and) = []
      pi(0) = []
      pi(s) = [0]
      pi(gr#) = 0
     weight function:
      w0 = 1
      w(gr#) = w(s) = w(0) = w(and) = w(eq) = w(false) = w(cond2) = w(
      gr) = w(true) = 1
      w(p) = w(cond1) = 0
     precedence:
      gr# ~ and ~ p > 0 ~ eq > s ~ false ~ cond2 ~ gr ~ cond1 ~ true
     problem:
      DPs:
       
      TRS:
       cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
       cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
       cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(x)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       and(true(),true()) -> true()
       and(false(),x) -> false()
       and(x,false()) -> false()
     Qed
    
    DPs:
     eq#(s(x),s(y)) -> eq#(x,y)
    TRS:
     cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
     cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
     cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(x)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     and(true(),true()) -> true()
     and(false(),x) -> false()
     and(x,false()) -> false()
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(cond1) = 3
      pi(gr) = 0
      pi(cond2) = 3
      pi(p) = [0]
      pi(false) = []
      pi(eq) = []
      pi(and) = []
      pi(0) = []
      pi(s) = [0]
      pi(eq#) = 0
     weight function:
      w0 = 1
      w(eq#) = w(s) = w(0) = w(and) = w(eq) = w(false) = w(cond2) = w(
      gr) = w(true) = 1
      w(p) = w(cond1) = 0
     precedence:
      eq# ~ and ~ p > 0 ~ eq > s ~ false ~ cond2 ~ gr ~ cond1 ~ true
     problem:
      DPs:
       
      TRS:
       cond1(true(),x,y,z) -> cond2(gr(y,z),x,y,z)
       cond2(true(),x,y,z) -> cond2(gr(y,z),p(x),p(y),z)
       cond2(false(),x,y,z) -> cond1(and(eq(x,y),gr(x,z)),x,y,z)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(x)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       and(true(),true()) -> true()
       and(false(),x) -> false()
       and(x,false()) -> false()
     Qed