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(x, y) -> x
a(x, y) -> y
lambda(x) -> x
p(x, y) -> x
p(x, y) -> y

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

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

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