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)))
  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)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [plus#](x0, x1) = x0 + 1,
      
      [false] = 0,
      
      [double](x0) = x0 + 1,
      
      [plus](x0, x1) = x0 + x1 + 1,
      
      [and](x0, x1) = x0 + 1,
      
      [s](x0) = 1,
      
      [0] = 0,
      
      [gt](x0, x1) = 0,
      
      [f](x0, x1, x2) = 0,
      
      [true] = 0
     orientation:
      plus#(plus(n,m),u) = m + n + 2 >= m + 1 = plus#(m,u)
      
      plus#(plus(n,m),u) = m + n + 2 >= n + 1 = plus#(n,plus(m,u))
      
      plus#(n,s(m)) = n + 1 >= n + 1 = plus#(n,m)
      
      f(true(),x,y) = 0 >= 0 = f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y))
      
      gt(0(),v) = 0 >= 0 = false()
      
      gt(s(u),0()) = 0 >= 0 = true()
      
      gt(s(u),s(v)) = 0 >= 0 = gt(u,v)
      
      and(x,true()) = x + 1 >= x = x
      
      and(x,false()) = x + 1 >= 0 = false()
      
      plus(n,0()) = n + 1 >= n = n
      
      plus(n,s(m)) = n + 2 >= 1 = s(plus(n,m))
      
      plus(plus(n,m),u) = m + n + u + 2 >= m + n + u + 2 = plus(n,plus(m,u))
      
      double(0()) = 1 >= 0 = 0()
      
      double(s(x)) = 2 >= 1 = s(s(double(x)))
     problem:
      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))
       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