/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex49_GM04_C.trs

The program

(VAR Y X X1 X2 X3)
(RULES 
active(minus(0,Y)) -> mark(0)
active(minus(s(X),s(Y))) -> mark(minus(X,Y))
active(geq(X,0)) -> mark(true)
active(geq(0,s(Y))) -> mark(false)
active(geq(s(X),s(Y))) -> mark(geq(X,Y))
active(div(0,s(Y))) -> mark(0)
active(div(s(X),s(Y))) -> mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0))
active(if(true,X,Y)) -> mark(X)
active(if(false,X,Y)) -> mark(Y)
active(s(X)) -> s(active(X))
active(div(X1,X2)) -> div(active(X1),X2)
active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
s(mark(X)) -> mark(s(X))
div(mark(X1),X2) -> mark(div(X1,X2))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
proper(minus(X1,X2)) -> minus(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(geq(X1,X2)) -> geq(proper(X1),proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(div(X1,X2)) -> div(proper(X1),proper(X2))
proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
minus(ok(X1),ok(X2)) -> ok(minus(X1,X2))
s(ok(X)) -> ok(s(X))
geq(ok(X1),ok(X2)) -> ok(geq(X1,X2))
div(ok(X1),ok(X2)) -> ok(div(X1,X2))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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