MAYBE

Problem:
 tower(x) -> f(a(),x,s(0()))
 f(a(),0(),y) -> y
 f(a(),s(x),y) -> f(b(),y,s(x))
 f(b(),y,x) -> f(a(),half(x),exp(y))
 exp(0()) -> s(0())
 exp(s(x)) -> double(exp(x))
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 half(0()) -> double(0())
 half(s(0())) -> half(0())
 half(s(s(x))) -> s(half(x))

Proof:
 DP Processor:
  DPs:
   tower#(x) -> f#(a(),x,s(0()))
   f#(a(),s(x),y) -> f#(b(),y,s(x))
   f#(b(),y,x) -> exp#(y)
   f#(b(),y,x) -> half#(x)
   f#(b(),y,x) -> f#(a(),half(x),exp(y))
   exp#(s(x)) -> exp#(x)
   exp#(s(x)) -> double#(exp(x))
   double#(s(x)) -> double#(x)
   half#(0()) -> double#(0())
   half#(s(0())) -> half#(0())
   half#(s(s(x))) -> half#(x)
  TRS:
   tower(x) -> f(a(),x,s(0()))
   f(a(),0(),y) -> y
   f(a(),s(x),y) -> f(b(),y,s(x))
   f(b(),y,x) -> f(a(),half(x),exp(y))
   exp(0()) -> s(0())
   exp(s(x)) -> double(exp(x))
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   half(0()) -> double(0())
   half(s(0())) -> half(0())
   half(s(s(x))) -> s(half(x))
  Usable Rule Processor:
   DPs:
    tower#(x) -> f#(a(),x,s(0()))
    f#(a(),s(x),y) -> f#(b(),y,s(x))
    f#(b(),y,x) -> exp#(y)
    f#(b(),y,x) -> half#(x)
    f#(b(),y,x) -> f#(a(),half(x),exp(y))
    exp#(s(x)) -> exp#(x)
    exp#(s(x)) -> double#(exp(x))
    double#(s(x)) -> double#(x)
    half#(0()) -> double#(0())
    half#(s(0())) -> half#(0())
    half#(s(s(x))) -> half#(x)
   TRS:
    exp(0()) -> s(0())
    exp(s(x)) -> double(exp(x))
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    half(0()) -> double(0())
    half(s(0())) -> half(0())
    half(s(s(x))) -> s(half(x))
   Open