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