MAYBE

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

Proof:
 DP Processor:
  DPs:
   +#(s(x),y) -> +#(x,y)
   *#(x,s(y)) -> *#(x,y)
   *#(x,s(y)) -> +#(x,*(x,y))
   twice#(s(x)) -> twice#(x)
   -#(s(x),s(y)) -> -#(x,y)
   f#(s(x)) -> *#(s(x),s(s(x)))
   f#(s(x)) -> +#(*(s(x),s(s(x))),s(s(0())))
   f#(s(x)) -> *#(s(s(x)),s(s(x)))
   f#(s(x)) -> -#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
   f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
  TRS:
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   *(x,0()) -> 0()
   *(x,s(y)) -> +(x,*(x,y))
   twice(0()) -> 0()
   twice(s(x)) -> s(s(twice(x)))
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
  TDG Processor:
   DPs:
    +#(s(x),y) -> +#(x,y)
    *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(x,*(x,y))
    twice#(s(x)) -> twice#(x)
    -#(s(x),s(y)) -> -#(x,y)
    f#(s(x)) -> *#(s(x),s(s(x)))
    f#(s(x)) -> +#(*(s(x),s(s(x))),s(s(0())))
    f#(s(x)) -> *#(s(s(x)),s(s(x)))
    f#(s(x)) -> -#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
   TRS:
    +(0(),y) -> y
    +(s(x),y) -> s(+(x,y))
    *(x,0()) -> 0()
    *(x,s(y)) -> +(x,*(x,y))
    twice(0()) -> 0()
    twice(s(x)) -> s(s(twice(x)))
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
   graph:
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))) ->
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))) ->
    f#(s(x)) -> -#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))) ->
    f#(s(x)) -> *#(s(s(x)),s(s(x)))
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))) ->
    f#(s(x)) -> +#(*(s(x),s(s(x))),s(s(0())))
    f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))) ->
    f#(s(x)) -> *#(s(x),s(s(x)))
    f#(s(x)) -> -#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))) ->
    -#(s(x),s(y)) -> -#(x,y)
    f#(s(x)) -> *#(s(s(x)),s(s(x))) -> *#(x,s(y)) -> +#(x,*(x,y))
    f#(s(x)) -> *#(s(s(x)),s(s(x))) -> *#(x,s(y)) -> *#(x,y)
    f#(s(x)) -> *#(s(x),s(s(x))) -> *#(x,s(y)) -> +#(x,*(x,y))
    f#(s(x)) -> *#(s(x),s(s(x))) -> *#(x,s(y)) -> *#(x,y)
    f#(s(x)) -> +#(*(s(x),s(s(x))),s(s(0()))) -> +#(s(x),y) -> +#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    twice#(s(x)) -> twice#(x) -> twice#(s(x)) -> twice#(x)
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> +#(x,*(x,y))
    *#(x,s(y)) -> *#(x,y) -> *#(x,s(y)) -> *#(x,y)
    *#(x,s(y)) -> +#(x,*(x,y)) -> +#(s(x),y) -> +#(x,y)
    +#(s(x),y) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 5
    #arcs: 17/100
    DPs:
     twice#(s(x)) -> twice#(x)
    TRS:
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(x,*(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    Subterm Criterion Processor:
     simple projection:
      pi(twice#) = 0
     problem:
      DPs:
       
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(x,*(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
     Qed
    
    DPs:
     f#(s(x)) -> f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    TRS:
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(x,*(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    Open
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(x,*(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     problem:
      DPs:
       
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(x,*(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
     Qed
    
    DPs:
     *#(x,s(y)) -> *#(x,y)
    TRS:
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(x,*(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 1
     problem:
      DPs:
       
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(x,*(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
     Qed
    
    DPs:
     +#(s(x),y) -> +#(x,y)
    TRS:
     +(0(),y) -> y
     +(s(x),y) -> s(+(x,y))
     *(x,0()) -> 0()
     *(x,s(y)) -> +(x,*(x,y))
     twice(0()) -> 0()
     twice(s(x)) -> s(s(twice(x)))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 0
     problem:
      DPs:
       
      TRS:
       +(0(),y) -> y
       +(s(x),y) -> s(+(x,y))
       *(x,0()) -> 0()
       *(x,s(y)) -> +(x,*(x,y))
       twice(0()) -> 0()
       twice(s(x)) -> s(s(twice(x)))
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
       f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
     Qed