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