Term Rewriting System R:
[x]
f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(h(x)) -> F(i(x))
F(h(x)) -> I(x)
G(i(x)) -> G(h(x))
G(i(x)) -> H(x)
Furthermore, R contains two SCCs.
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
→DP Problem 2
↳Nar
Dependency Pair:
F(h(x)) -> F(i(x))
Rules:
f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b
On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule
F(h(x)) -> F(i(x))
one new Dependency Pair
is created:
F(h(a)) -> F(b)
The transformation is resulting in no new DP problems.
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
Dependency Pair:
G(i(x)) -> G(h(x))
Rules:
f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b
On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule
G(i(x)) -> G(h(x))
one new Dependency Pair
is created:
G(i(a)) -> G(b)
The transformation is resulting in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes