Term Rewriting System R:
[x, y, z]
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

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

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)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

A(a(x, y), z) -> A(y, z)
A(p(x, y), z) -> A(y, z)
A(p(x, y), z) -> A(x, z)
A(lambda(x), y) -> A(y, t)
A(lambda(x), y) -> A(x, p(1, a(y, t)))

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

Strategy:

innermost

Innermost Termination of R could not be shown.
Duration:
0:00 minutes