(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
zero(0) → true
zero(s(x)) → false
id(0) → 0
id(s(x)) → s(id(x))
minus(x, 0) → x
minus(s(x), s(y)) → minus(x, y)
mod(x, y) → if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
if_mod(true, b1, b2, x, y) → 0
if_mod(false, b1, b2, x, y) → if2(b1, b2, x, y)
if2(true, b2, x, y) → 0
if2(false, b2, x, y) → if3(b2, x, y)
if3(true, x, y) → mod(minus(x, y), s(y))
if3(false, x, y) → x
Q is empty.