Term Rewriting System R:
[X, Y]
f(0, 1, X) -> h(X, X)
h(0, X) -> f(0, X, X)
g(X, Y) -> X
g(X, Y) -> Y

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(0, 1, X) -> H(X, X)
H(0, X) -> F(0, X, X)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Non Termination


Dependency Pairs:

H(0, X) -> F(0, X, X)
F(0, 1, X) -> H(X, X)


Rules:


f(0, 1, X) -> h(X, X)
h(0, X) -> f(0, X, X)
g(X, Y) -> X
g(X, Y) -> Y





Found an infinite P-chain over R:
P =

H(0, X) -> F(0, X, X)
F(0, 1, X) -> H(X, X)

R =

f(0, 1, X) -> h(X, X)
h(0, X) -> f(0, X, X)
g(X, Y) -> X
g(X, Y) -> Y

s = F(0, g(1, 0), g(1, 0))
evaluates to t =F(0, g(1, 0), g(1, 0))

Thus, s starts an infinite chain.

Non-Termination of R could be shown.
Duration:
0:00 minutes