Term Rewriting System R:
[x, y, z]
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(a), s(b), x) -> F(x, x, x)
G(f(s(x), s(y), z)) -> G(f(x, y, z))
G(f(s(x), s(y), z)) -> F(x, y, z)
Furthermore, R contains two SCCs.
R
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(s(a), s(b), x) -> F(x, x, x)
Rules:
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y
Found an infinite P-chain over R:
P =
F(s(a), s(b), x) -> F(x, x, x)
R =
f(s(a), s(b), x) -> f(x, x, x)
g(f(s(x), s(y), z)) -> g(f(x, y, z))
cons(x, y) -> x
cons(x, y) -> y
s = F(cons(s(b), s(a)), cons(s(b), s(a)), cons(s(b), s(a)))
evaluates to t =F(cons(s(b), s(a)), cons(s(b), s(a)), cons(s(b), s(a)))
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:00 minutes