MAYBE

Problem:
 0(#()) -> #()
 +(#(),x) -> x
 +(x,#()) -> x
 +(0(x),0(y)) -> 0(+(x,y))
 +(0(x),1(y)) -> 1(+(x,y))
 +(1(x),0(y)) -> 1(+(x,y))
 +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
 +(+(x,y),z) -> +(x,+(y,z))
 -(#(),x) -> #()
 -(x,#()) -> x
 -(0(x),0(y)) -> 0(-(x,y))
 -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
 -(1(x),0(y)) -> 1(-(x,y))
 -(1(x),1(y)) -> 0(-(x,y))
 not(true()) -> false()
 not(false()) -> true()
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 ge(0(x),0(y)) -> ge(x,y)
 ge(0(x),1(y)) -> not(ge(y,x))
 ge(1(x),0(y)) -> ge(x,y)
 ge(1(x),1(y)) -> ge(x,y)
 ge(x,#()) -> true()
 ge(#(),0(x)) -> ge(#(),x)
 ge(#(),1(x)) -> false()
 log(x) -> -(log'(x),1(#()))
 log'(#()) -> #()
 log'(1(x)) -> +(log'(x),1(#()))
 log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#())

Proof:
 Open