MAYBE

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           MAYBE
Input Problem:    innermost relative runtime-complexity with respect to
  Strict Rules:
    {  RAo(R()) -> R()
     , RAn(R()) -> R()
     , WAo(W()) -> W()
     , WAn(W()) -> W()}
  Weak Rules:
    {  Rw() -> RIn(Rw())
     , Ww() -> WIn(Ww())
     , top(ok(sys_r(read(r, RIo(x)), write(W(), Ww())))) ->
       top(check(sys_r(read(RAo(r), x), write(W(), Ww()))))
     , top(ok(sys_w(read(r, RIo(x)), write(W(), Ww())))) ->
       top(check(sys_w(read(RAo(r), x), write(W(), Ww()))))
     , top(ok(sys_r(read(r, RIn(x)), write(W(), Ww())))) ->
       top(check(sys_r(read(RAn(r), x), write(W(), Ww()))))
     , top(ok(sys_w(read(r, RIn(x)), write(W(), Ww())))) ->
       top(check(sys_w(read(RAn(r), x), write(W(), Ww()))))
     , top(ok(sys_r(read(R(), Rw()), write(W(), WIn(y))))) ->
       top(check(sys_r(read(R(), Rw()), write(WAn(W()), y))))
     , top(ok(sys_w(read(R(), Rw()), write(W(), WIn(y))))) ->
       top(check(sys_w(read(R(), Rw()), write(WAn(W()), y))))
     , top(ok(sys_r(read(R(), Rw()), write(W(), WIo(y))))) ->
       top(check(sys_r(read(R(), Rw()), write(WAo(W()), y))))
     , top(ok(sys_w(read(R(), Rw()), write(W(), WIo(y))))) ->
       top(check(sys_w(read(R(), Rw()), write(WAo(W()), y))))
     , top(ok(sys_r(read(r, RIo(x)), write(W(), y)))) ->
       top(check(sys_w(read(RAo(r), x), write(W(), y))))
     , top(ok(sys_r(read(r, RIn(x)), write(W(), y)))) ->
       top(check(sys_w(read(RAn(r), x), write(W(), y))))
     , top(ok(sys_w(read(R(), x), write(W(), WIo(y))))) ->
       top(check(sys_r(read(R(), x), write(WAo(W()), y))))
     , top(ok(sys_w(read(R(), x), write(W(), WIn(y))))) ->
       top(check(sys_r(read(R(), x), write(WAn(W()), y))))
     , check(RIo(x)) -> ok(RIo(x))
     , check(RAo(x)) -> RAo(check(x))
     , check(RAn(x)) -> RAn(check(x))
     , check(WAo(x)) -> WAo(check(x))
     , check(WAn(x)) -> WAn(check(x))
     , check(RIo(x)) -> RIo(check(x))
     , check(RIn(x)) -> RIn(check(x))
     , check(WIo(x)) -> WIo(check(x))
     , check(WIn(x)) -> WIn(check(x))
     , check(sys_r(x, y)) -> sys_r(check(x), y)
     , check(sys_r(x, y)) -> sys_r(x, check(y))
     , check(sys_w(x, y)) -> sys_w(check(x), y)
     , check(sys_w(x, y)) -> sys_w(x, check(y))
     , RAo(ok(x)) -> ok(RAo(x))
     , RAn(ok(x)) -> ok(RAn(x))
     , WAo(ok(x)) -> ok(WAo(x))
     , WAn(ok(x)) -> ok(WAn(x))
     , RIn(ok(x)) -> ok(RIn(x))
     , WIo(ok(x)) -> ok(WIo(x))
     , WIn(ok(x)) -> ok(WIn(x))
     , sys_r(ok(x), y) -> ok(sys_r(x, y))
     , sys_r(x, ok(y)) -> ok(sys_r(x, y))
     , sys_w(ok(x), y) -> ok(sys_w(x, y))
     , sys_w(x, ok(y)) -> ok(sys_w(x, y))}

Proof Output:    
  The input cannot be shown compatible