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))
 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)
   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))
   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)
    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))
    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#(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#(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)
   SCC Processor:
    #sccs: 4
    #rules: 4
    #arcs: 13/81
    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))
     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))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(double#) = 0
     problem:
      DPs:
       
      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))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
     Qed
    
    DPs:
     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))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 1
     problem:
      DPs:
       
      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))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
     Qed
    
    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))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(gt#) = 1
     problem:
      DPs:
       
      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))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
     Qed