MAYBE

Problem:
 cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
 cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
 cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
 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) -> gr#(y,0())
   cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
   cond2#(true(),x,y) -> p#(y)
   cond2#(true(),x,y) -> p#(x)
   cond2#(true(),x,y) -> gr#(y,0())
   cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y))
   cond2#(false(),x,y) -> gr#(x,0())
   cond2#(false(),x,y) -> eq#(x,y)
   cond2#(false(),x,y) -> and#(eq(x,y),gr(x,0()))
   cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
   gr#(s(x),s(y)) -> gr#(x,y)
   eq#(s(x),s(y)) -> eq#(x,y)
  TRS:
   cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
   cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
   cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
   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) -> gr#(y,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
    cond2#(true(),x,y) -> p#(y)
    cond2#(true(),x,y) -> p#(x)
    cond2#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y))
    cond2#(false(),x,y) -> gr#(x,0())
    cond2#(false(),x,y) -> eq#(x,y)
    cond2#(false(),x,y) -> and#(eq(x,y),gr(x,0()))
    cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
    gr#(s(x),s(y)) -> gr#(x,y)
    eq#(s(x),s(y)) -> eq#(x,y)
   TRS:
    cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
    cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
    cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
    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) -> eq#(x,y) -> eq#(s(x),s(y)) -> eq#(x,y)
    cond2#(false(),x,y) -> gr#(x,0()) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y) ->
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
    cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y) ->
    cond1#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(false(),x,y) -> and#(eq(x,y),gr(x,0()))
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(false(),x,y) -> eq#(x,y)
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(false(),x,y) -> gr#(x,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y))
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(true(),x,y) -> p#(x)
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y)) ->
    cond2#(true(),x,y) -> p#(y)
    cond2#(true(),x,y) -> gr#(y,0()) -> 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) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> and#(eq(x,y),gr(x,0()))
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> eq#(x,y)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> gr#(x,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y))
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> gr#(y,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> p#(x)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> p#(y)
    cond1#(true(),x,y) -> gr#(y,0()) -> gr#(s(x),s(y)) -> gr#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 24/144
    DPs:
     cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
     cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
     cond2#(true(),x,y) -> cond2#(gr(y,0()),p(x),p(y))
    TRS:
     cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
     cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
     cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
     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()
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [cond2#](x0, x1, x2) = x0 + x1 + 1x2,
      
      [cond1#](x0, x1, x2) = -9x0 + x1 + 1x2 + -7,
      
      [s](x0) = 2x0 + 2,
      
      [and](x0, x1) = 1x0 + x1 + 0,
      
      [eq](x0, x1) = x0 + 3x1 + 0,
      
      [false] = 0,
      
      [p](x0) = -1x0 + 0,
      
      [cond2](x0, x1, x2) = 2x0 + 4x1 + 4x2 + 0,
      
      [gr](x0, x1) = x0 + -8x1,
      
      [0] = 0,
      
      [cond1](x0, x1, x2) = x0 + 4x1 + 4x2 + 0,
      
      [true] = 2
     orientation:
      cond2#(false(),x,y) = x + 1y + 0 >= x + 1y + -7 = cond1#(and(eq(x,y),gr(x,0())),x,y)
      
      cond1#(true(),x,y) = x + 1y + -7 >= x + 1y + -8 = cond2#(gr(y,0()),x,y)
      
      cond2#(true(),x,y) = x + 1y + 2 >= -1x + y + 1 = cond2#(gr(y,0()),p(x),p(y))
      
      cond1(true(),x,y) = 4x + 4y + 2 >= 4x + 4y + 0 = cond2(gr(y,0()),x,y)
      
      cond2(true(),x,y) = 4x + 4y + 4 >= 3x + 3y + 4 = cond2(gr(y,0()),p(x),p(y))
      
      cond2(false(),x,y) = 4x + 4y + 2 >= 4x + 4y + 1 = cond1(and(eq(x,y),gr(x,0())),x,y)
      
      gr(0(),x) = -8x + 0 >= 0 = false()
      
      gr(s(x),0()) = 2x + 2 >= 2 = true()
      
      gr(s(x),s(y)) = 2x + -6y + 2 >= x + -8y = gr(x,y)
      
      p(0()) = 0 >= 0 = 0()
      
      p(s(x)) = 1x + 1 >= x = x
      
      eq(0(),0()) = 3 >= 2 = true()
      
      eq(s(x),0()) = 2x + 3 >= 0 = false()
      
      eq(0(),s(x)) = 5x + 5 >= 0 = false()
      
      eq(s(x),s(y)) = 2x + 5y + 5 >= x + 3y + 0 = eq(x,y)
      
      and(true(),true()) = 3 >= 2 = true()
      
      and(false(),x) = x + 1 >= 0 = false()
      
      and(x,false()) = 1x + 0 >= 0 = false()
     problem:
      DPs:
       cond2#(false(),x,y) -> cond1#(and(eq(x,y),gr(x,0())),x,y)
       cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
       cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
       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) -> cond2(gr(y,0()),x,y)
     cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
     cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
     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()
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 1
     problem:
      DPs:
       
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
       cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
       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) -> cond2(gr(y,0()),x,y)
     cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
     cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
     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()
    Subterm Criterion Processor:
     simple projection:
      pi(eq#) = 1
     problem:
      DPs:
       
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
       cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
       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