Term Rewriting System R:
[x]
f(a, x) -> f(g(x), 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, x) -> F(g(x), x)
F(a, 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, x) -> F(g(x), x)
Rules:
f(a, x) -> f(g(x), 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, x) -> F(g(x), x)
one new Dependency Pair
is created:
F(a, h(x'')) -> F(g(x''), h(x''))
The transformation is resulting in one new DP problem:
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
Dependency Pair:
F(a, h(x'')) -> F(g(x''), h(x''))
Rules:
f(a, x) -> f(g(x), 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''))
no new Dependency Pairs
are created.
The transformation is resulting in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes