/home/nowonder/forschung/aprove/TPDB05/TRS/AProVE/JFP_Ex51.trs

The program

(VAR x y z)
(RULES
minus_active(0,y) -> 0 
mark(0) -> 0 
minus_active(s(x),s(y)) -> minus_active(x,y) 
mark(s(x)) -> s(mark(x)) 
ge_active(x,0) -> true 
mark(minus(x,y)) -> minus_active(x,y) 
ge_active(0,s(y)) -> false 
mark(ge(x,y)) -> ge_active(x,y) 
ge_active(s(x),s(y)) -> ge_active(x,y) 
mark(div(x,y)) -> div_active(mark(x),y) 
div_active(0,s(y)) -> 0 
mark(if(x,y,z)) -> if_active(mark(x),y,z) 
div_active(s(x),s(y)) -> if_active(ge_active(x,y),s(div(minus(x,y),s(y))),0)
if_active(true,x,y) -> mark(x) 
minus_active(x,y) -> minus(x,y) 
if_active(false,x,y) -> mark(y) 
ge_active(x,y) -> ge(x,y) 
if_active(x,y,z) -> if(x,y,z)  
div_active(x,y) -> div(x,y)
)

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