MAYBE

Problem:
 f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
 gt(0(),v) -> false()
 gt(s(u),0()) -> true()
 gt(s(u),s(v)) -> gt(u,v)
 and(x,true()) -> x
 and(x,false()) -> false()
 plus(n,0()) -> n
 plus(n,s(m)) -> s(plus(n,m))
 plus(plus(n,m),u) -> plus(n,plus(m,u))
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))

Proof:
 DP Processor:
  DPs:
   f#(true(),x,y) -> double#(y)
   f#(true(),x,y) -> plus#(s(0()),x)
   f#(true(),x,y) -> gt#(y,s(s(0())))
   f#(true(),x,y) -> gt#(x,y)
   f#(true(),x,y) -> and#(gt(x,y),gt(y,s(s(0()))))
   f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
   gt#(s(u),s(v)) -> gt#(u,v)
   plus#(n,s(m)) -> plus#(n,m)
   plus#(plus(n,m),u) -> plus#(m,u)
   plus#(plus(n,m),u) -> plus#(n,plus(m,u))
   double#(s(x)) -> double#(x)
  TRS:
   f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
   gt(0(),v) -> false()
   gt(s(u),0()) -> true()
   gt(s(u),s(v)) -> gt(u,v)
   and(x,true()) -> x
   and(x,false()) -> false()
   plus(n,0()) -> n
   plus(n,s(m)) -> s(plus(n,m))
   plus(plus(n,m),u) -> plus(n,plus(m,u))
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
  TDG Processor:
   DPs:
    f#(true(),x,y) -> double#(y)
    f#(true(),x,y) -> plus#(s(0()),x)
    f#(true(),x,y) -> gt#(y,s(s(0())))
    f#(true(),x,y) -> gt#(x,y)
    f#(true(),x,y) -> and#(gt(x,y),gt(y,s(s(0()))))
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
    gt#(s(u),s(v)) -> gt#(u,v)
    plus#(n,s(m)) -> plus#(n,m)
    plus#(plus(n,m),u) -> plus#(m,u)
    plus#(plus(n,m),u) -> plus#(n,plus(m,u))
    double#(s(x)) -> double#(x)
   TRS:
    f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
    gt(0(),v) -> false()
    gt(s(u),0()) -> true()
    gt(s(u),s(v)) -> gt(u,v)
    and(x,true()) -> x
    and(x,false()) -> false()
    plus(n,0()) -> n
    plus(n,s(m)) -> s(plus(n,m))
    plus(plus(n,m),u) -> plus(n,plus(m,u))
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
   graph:
    gt#(s(u),s(v)) -> gt#(u,v) -> gt#(s(u),s(v)) -> gt#(u,v)
    plus#(plus(n,m),u) -> plus#(m,u) ->
    plus#(plus(n,m),u) -> plus#(n,plus(m,u))
    plus#(plus(n,m),u) -> plus#(m,u) ->
    plus#(plus(n,m),u) -> plus#(m,u)
    plus#(plus(n,m),u) -> plus#(m,u) ->
    plus#(n,s(m)) -> plus#(n,m)
    plus#(plus(n,m),u) -> plus#(n,plus(m,u)) ->
    plus#(plus(n,m),u) -> plus#(n,plus(m,u))
    plus#(plus(n,m),u) -> plus#(n,plus(m,u)) ->
    plus#(plus(n,m),u) -> plus#(m,u)
    plus#(plus(n,m),u) -> plus#(n,plus(m,u)) ->
    plus#(n,s(m)) -> plus#(n,m)
    plus#(n,s(m)) -> plus#(n,m) ->
    plus#(plus(n,m),u) -> plus#(n,plus(m,u))
    plus#(n,s(m)) -> plus#(n,m) -> plus#(plus(n,m),u) -> plus#(m,u)
    plus#(n,s(m)) -> plus#(n,m) -> plus#(n,s(m)) -> plus#(n,m)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    f#(true(),x,y) -> gt#(y,s(s(0()))) -> gt#(s(u),s(v)) -> gt#(u,v)
    f#(true(),x,y) -> gt#(x,y) -> gt#(s(u),s(v)) -> gt#(u,v)
    f#(true(),x,y) -> plus#(s(0()),x) ->
    plus#(plus(n,m),u) -> plus#(n,plus(m,u))
    f#(true(),x,y) -> plus#(s(0()),x) ->
    plus#(plus(n,m),u) -> plus#(m,u)
    f#(true(),x,y) -> plus#(s(0()),x) -> plus#(n,s(m)) -> plus#(n,m)
    f#(true(),x,y) -> double#(y) ->
    double#(s(x)) -> double#(x)
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> and#(gt(x,y),gt(y,s(s(0()))))
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> gt#(x,y)
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> gt#(y,s(s(0())))
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> plus#(s(0()),x)
    f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
    f#(true(),x,y) -> double#(y)
   EDG Processor:
    DPs:
     f#(true(),x,y) -> double#(y)
     f#(true(),x,y) -> plus#(s(0()),x)
     f#(true(),x,y) -> gt#(y,s(s(0())))
     f#(true(),x,y) -> gt#(x,y)
     f#(true(),x,y) -> and#(gt(x,y),gt(y,s(s(0()))))
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
     gt#(s(u),s(v)) -> gt#(u,v)
     plus#(n,s(m)) -> plus#(n,m)
     plus#(plus(n,m),u) -> plus#(m,u)
     plus#(plus(n,m),u) -> plus#(n,plus(m,u))
     double#(s(x)) -> double#(x)
    TRS:
     f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
     and(x,true()) -> x
     and(x,false()) -> false()
     plus(n,0()) -> n
     plus(n,s(m)) -> s(plus(n,m))
     plus(plus(n,m),u) -> plus(n,plus(m,u))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
    graph:
     gt#(s(u),s(v)) -> gt#(u,v) -> gt#(s(u),s(v)) -> gt#(u,v)
     plus#(plus(n,m),u) -> plus#(m,u) ->
     plus#(n,s(m)) -> plus#(n,m)
     plus#(plus(n,m),u) -> plus#(m,u) ->
     plus#(plus(n,m),u) -> plus#(m,u)
     plus#(plus(n,m),u) -> plus#(m,u) ->
     plus#(plus(n,m),u) -> plus#(n,plus(m,u))
     plus#(plus(n,m),u) -> plus#(n,plus(m,u)) ->
     plus#(n,s(m)) -> plus#(n,m)
     plus#(n,s(m)) -> plus#(n,m) -> plus#(n,s(m)) -> plus#(n,m)
     plus#(n,s(m)) -> plus#(n,m) -> plus#(plus(n,m),u) -> plus#(m,u)
     plus#(n,s(m)) -> plus#(n,m) ->
     plus#(plus(n,m),u) -> plus#(n,plus(m,u))
     double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
     f#(true(),x,y) -> gt#(y,s(s(0()))) -> gt#(s(u),s(v)) -> gt#(u,v)
     f#(true(),x,y) -> gt#(x,y) -> gt#(s(u),s(v)) -> gt#(u,v)
     f#(true(),x,y) -> plus#(s(0()),x) -> plus#(n,s(m)) -> plus#(n,m)
     f#(true(),x,y) -> double#(y) ->
     double#(s(x)) -> double#(x)
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> double#(y)
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> plus#(s(0()),x)
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> gt#(y,s(s(0())))
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> gt#(x,y)
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> and#(gt(x,y),gt(y,s(s(0()))))
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) ->
     f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
    SCC Processor:
     #sccs: 4
     #rules: 6
     #arcs: 19/121
     DPs:
      f#(true(),x,y) -> f#(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
     TRS:
      f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
      gt(0(),v) -> false()
      gt(s(u),0()) -> true()
      gt(s(u),s(v)) -> gt(u,v)
      and(x,true()) -> x
      and(x,false()) -> false()
      plus(n,0()) -> n
      plus(n,s(m)) -> s(plus(n,m))
      plus(plus(n,m),u) -> plus(n,plus(m,u))
      double(0()) -> 0()
      double(s(x)) -> s(s(double(x)))
     Open
     
     DPs:
      double#(s(x)) -> double#(x)
     TRS:
      f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
      gt(0(),v) -> false()
      gt(s(u),0()) -> true()
      gt(s(u),s(v)) -> gt(u,v)
      and(x,true()) -> x
      and(x,false()) -> false()
      plus(n,0()) -> n
      plus(n,s(m)) -> s(plus(n,m))
      plus(plus(n,m),u) -> plus(n,plus(m,u))
      double(0()) -> 0()
      double(s(x)) -> s(s(double(x)))
     Open
     
     DPs:
      plus#(plus(n,m),u) -> plus#(m,u)
      plus#(plus(n,m),u) -> plus#(n,plus(m,u))
      plus#(n,s(m)) -> plus#(n,m)
     TRS:
      f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
      gt(0(),v) -> false()
      gt(s(u),0()) -> true()
      gt(s(u),s(v)) -> gt(u,v)
      and(x,true()) -> x
      and(x,false()) -> false()
      plus(n,0()) -> n
      plus(n,s(m)) -> s(plus(n,m))
      plus(plus(n,m),u) -> plus(n,plus(m,u))
      double(0()) -> 0()
      double(s(x)) -> s(s(double(x)))
     Open
     
     DPs:
      gt#(s(u),s(v)) -> gt#(u,v)
     TRS:
      f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
      gt(0(),v) -> false()
      gt(s(u),0()) -> true()
      gt(s(u),s(v)) -> gt(u,v)
      and(x,true()) -> x
      and(x,false()) -> false()
      plus(n,0()) -> n
      plus(n,s(m)) -> s(plus(n,m))
      plus(plus(n,m),u) -> plus(n,plus(m,u))
      double(0()) -> 0()
      double(s(x)) -> s(s(double(x)))
     Open