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:
0:01 minutes