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