MAYBE

Problem:
 cond(true(),x,y) -> cond(gr(x,y),y,x)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)

Proof:
 DP Processor:
  DPs:
   cond#(true(),x,y) -> gr#(x,y)
   cond#(true(),x,y) -> cond#(gr(x,y),y,x)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y) -> cond(gr(x,y),y,x)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
  TDG Processor:
   DPs:
    cond#(true(),x,y) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),y,x)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y) -> cond(gr(x,y),y,x)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
   graph:
    gr#(s(x),s(y)) -> gr#(x,y) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(gr(x,y),y,x) ->
    cond#(true(),x,y) -> cond#(gr(x,y),y,x)
    cond#(true(),x,y) -> cond#(gr(x,y),y,x) -> cond#(true(),x,y) -> gr#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     cond#(true(),x,y) -> cond#(gr(x,y),y,x)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),y,x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
    Open
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond(true(),x,y) -> cond(gr(x,y),y,x)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(cond) = []
      pi(gr) = 0
      pi(0) = []
      pi(false) = []
      pi(s) = [0]
      pi(gr#) = 1
     weight function:
      w0 = 1
      w(gr#) = w(s) = w(false) = w(0) = w(gr) = w(cond) = w(true) = 1
     precedence:
      gr# ~ s ~ 0 ~ cond ~ true > false ~ gr
     problem:
      DPs:
       
      TRS:
       cond(true(),x,y) -> cond(gr(x,y),y,x)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
     Qed