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