MAYBE

Problem:
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 min(x,0()) -> 0()
 min(0(),y) -> 0()
 min(s(x),s(y)) -> s(min(x,y))
 twice(0()) -> 0()
 twice(s(x)) -> s(s(twice(x)))
 f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
 f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   min#(s(x),s(y)) -> min#(x,y)
   twice#(s(x)) -> twice#(x)
   f#(s(x),s(y)) -> twice#(min(x,y))
   f#(s(x),s(y)) -> min#(x,y)
   f#(s(x),s(y)) -> -#(y,min(x,y))
   f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y))))
   f#(s(x),s(y)) -> -#(x,min(x,y))
   f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y))))
  TRS:
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   min(x,0()) -> 0()
   min(0(),y) -> 0()
   min(s(x),s(y)) -> s(min(x,y))
   twice(0()) -> 0()
   twice(s(x)) -> s(s(twice(x)))
   f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
   f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
  TDG Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    min#(s(x),s(y)) -> min#(x,y)
    twice#(s(x)) -> twice#(x)
    f#(s(x),s(y)) -> twice#(min(x,y))
    f#(s(x),s(y)) -> min#(x,y)
    f#(s(x),s(y)) -> -#(y,min(x,y))
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y))))
    f#(s(x),s(y)) -> -#(x,min(x,y))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y))))
   TRS:
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    min(x,0()) -> 0()
    min(0(),y) -> 0()
    min(s(x),s(y)) -> s(min(x,y))
    twice(0()) -> 0()
    twice(s(x)) -> s(s(twice(x)))
    f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
    f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
   graph:
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y))))
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> -#(x,min(x,y))
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y))))
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> -#(y,min(x,y))
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> min#(x,y)
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> twice#(min(x,y))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y))))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> -#(x,min(x,y))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y))))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> -#(y,min(x,y))
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> min#(x,y)
    f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y)))) ->
    f#(s(x),s(y)) -> twice#(min(x,y))
    f#(s(x),s(y)) -> twice#(min(x,y)) -> twice#(s(x)) -> twice#(x)
    f#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
    f#(s(x),s(y)) -> -#(y,min(x,y)) -> -#(s(x),s(y)) -> -#(x,y)
    f#(s(x),s(y)) -> -#(x,min(x,y)) -> -#(s(x),s(y)) -> -#(x,y)
    twice#(s(x)) -> twice#(x) -> twice#(s(x)) -> twice#(x)
    min#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
   SCC Processor:
    #sccs: 4
    #rules: 5
    #arcs: 19/81
    DPs:
     f#(s(x),s(y)) -> f#(-(y,min(x,y)),s(twice(min(x,y))))
     f#(s(x),s(y)) -> f#(-(x,min(x,y)),s(twice(min(x,y))))
    TRS:
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
     f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
    Open
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
     f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
       f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
     Qed
    
    DPs:
     min#(s(x),s(y)) -> min#(x,y)
    TRS:
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
     f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
    Subterm Criterion Processor:
     simple projection:
      pi(min#) = 1
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
       f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
     Qed
    
    DPs:
     twice#(s(x)) -> twice#(x)
    TRS:
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
     f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
    Subterm Criterion Processor:
     simple projection:
      pi(twice#) = 0
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       f(s(x),s(y)) -> f(-(y,min(x,y)),s(twice(min(x,y))))
       f(s(x),s(y)) -> f(-(x,min(x,y)),s(twice(min(x,y))))
     Qed