(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
A(lambda(x), y) → A(x, p(1, a(y, t)))
A(lambda(x), y) → A(y, t)
A(p(x, y), z) → A(x, z)
A(p(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
A(a(x, y), z) → A(y, z)
The TRS R consists of the following rules:
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
Q is empty.
We have to consider all minimal (P,Q,R)-chains.