MAYBE

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

Proof:
 DP Processor:
  DPs:
   cond1#(s(x),y) -> gr#(s(x),y)
   cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y)
   cond2#(true(),x,y) -> cond1#(y,y)
   cond2#(false(),x,y) -> p#(x)
   cond2#(false(),x,y) -> cond1#(p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
   neq#(s(x),s(y)) -> neq#(x,y)
  TRS:
   cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
   cond2(true(),x,y) -> cond1(y,y)
   cond2(false(),x,y) -> cond1(p(x),y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   neq(0(),0()) -> false()
   neq(0(),s(x)) -> true()
   neq(s(x),0()) -> true()
   neq(s(x),s(y)) -> neq(x,y)
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond1#(s(x),y) -> gr#(s(x),y)
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y)
    cond2#(true(),x,y) -> cond1#(y,y)
    cond2#(false(),x,y) -> p#(x)
    cond2#(false(),x,y) -> cond1#(p(x),y)
    gr#(s(x),s(y)) -> gr#(x,y)
    neq#(s(x),s(y)) -> neq#(x,y)
   TRS:
    cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
    cond2(true(),x,y) -> cond1(y,y)
    cond2(false(),x,y) -> cond1(p(x),y)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    neq(0(),0()) -> false()
    neq(0(),s(x)) -> true()
    neq(s(x),0()) -> true()
    neq(s(x),s(y)) -> neq(x,y)
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    neq#(s(x),s(y)) -> neq#(x,y) ->
    neq#(s(x),s(y)) -> neq#(x,y)
    cond2#(false(),x,y) -> cond1#(p(x),y) ->
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y)
    cond2#(false(),x,y) -> cond1#(p(x),y) ->
    cond1#(s(x),y) -> gr#(s(x),y)
    cond2#(true(),x,y) -> cond1#(y,y) ->
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y)
    cond2#(true(),x,y) -> cond1#(y,y) -> cond1#(s(x),y) -> gr#(s(x),y)
    gr#(s(x),s(y)) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y) ->
    cond2#(false(),x,y) -> cond1#(p(x),y)
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y) ->
    cond2#(false(),x,y) -> p#(x)
    cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y) ->
    cond2#(true(),x,y) -> cond1#(y,y)
    cond1#(s(x),y) -> gr#(s(x),y) -> gr#(s(x),s(y)) -> gr#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 10/49
    DPs:
     cond2#(false(),x,y) -> cond1#(p(x),y)
     cond1#(s(x),y) -> cond2#(gr(s(x),y),s(x),y)
     cond2#(true(),x,y) -> cond1#(y,y)
    TRS:
     cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
     cond2(true(),x,y) -> cond1(y,y)
     cond2(false(),x,y) -> cond1(p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     neq(0(),0()) -> false()
     neq(0(),s(x)) -> true()
     neq(s(x),0()) -> true()
     neq(s(x),s(y)) -> neq(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Open
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
     cond2(true(),x,y) -> cond1(y,y)
     cond2(false(),x,y) -> cond1(p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     neq(0(),0()) -> false()
     neq(0(),s(x)) -> true()
     neq(s(x),0()) -> true()
     neq(s(x),s(y)) -> neq(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 1
     problem:
      DPs:
       
      TRS:
       cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
       cond2(true(),x,y) -> cond1(y,y)
       cond2(false(),x,y) -> cond1(p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       neq(0(),0()) -> false()
       neq(0(),s(x)) -> true()
       neq(s(x),0()) -> true()
       neq(s(x),s(y)) -> neq(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed
    
    DPs:
     neq#(s(x),s(y)) -> neq#(x,y)
    TRS:
     cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
     cond2(true(),x,y) -> cond1(y,y)
     cond2(false(),x,y) -> cond1(p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     neq(0(),0()) -> false()
     neq(0(),s(x)) -> true()
     neq(s(x),0()) -> true()
     neq(s(x),s(y)) -> neq(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(neq#) = 1
     problem:
      DPs:
       
      TRS:
       cond1(s(x),y) -> cond2(gr(s(x),y),s(x),y)
       cond2(true(),x,y) -> cond1(y,y)
       cond2(false(),x,y) -> cond1(p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       neq(0(),0()) -> false()
       neq(0(),s(x)) -> true()
       neq(s(x),0()) -> true()
       neq(s(x),s(y)) -> neq(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed