(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
active(fact(X)) → mark(if(zero(X), s(0), prod(X, fact(p(X)))))
active(add(0, X)) → mark(X)
active(add(s(X), Y)) → mark(s(add(X, Y)))
active(prod(0, X)) → mark(0)
active(prod(s(X), Y)) → mark(add(Y, prod(X, Y)))
active(if(true, X, Y)) → mark(X)
active(if(false, X, Y)) → mark(Y)
active(zero(0)) → mark(true)
active(zero(s(X))) → mark(false)
active(p(s(X))) → mark(X)
mark(fact(X)) → active(fact(mark(X)))
mark(if(X1, X2, X3)) → active(if(mark(X1), X2, X3))
mark(zero(X)) → active(zero(mark(X)))
mark(s(X)) → active(s(mark(X)))
mark(0) → active(0)
mark(prod(X1, X2)) → active(prod(mark(X1), mark(X2)))
mark(p(X)) → active(p(mark(X)))
mark(add(X1, X2)) → active(add(mark(X1), mark(X2)))
mark(true) → active(true)
mark(false) → active(false)
fact(mark(X)) → fact(X)
fact(active(X)) → fact(X)
if(mark(X1), X2, X3) → if(X1, X2, X3)
if(X1, mark(X2), X3) → if(X1, X2, X3)
if(X1, X2, mark(X3)) → if(X1, X2, X3)
if(active(X1), X2, X3) → if(X1, X2, X3)
if(X1, active(X2), X3) → if(X1, X2, X3)
if(X1, X2, active(X3)) → if(X1, X2, X3)
zero(mark(X)) → zero(X)
zero(active(X)) → zero(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
prod(mark(X1), X2) → prod(X1, X2)
prod(X1, mark(X2)) → prod(X1, X2)
prod(active(X1), X2) → prod(X1, X2)
prod(X1, active(X2)) → prod(X1, X2)
p(mark(X)) → p(X)
p(active(X)) → p(X)
add(mark(X1), X2) → add(X1, X2)
add(X1, mark(X2)) → add(X1, X2)
add(active(X1), X2) → add(X1, X2)
add(X1, active(X2)) → add(X1, X2)
Q is empty.