Term Rewriting System R:
[x]
f(a, f(x, a)) -> f(x, f(f(a, a), a))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a, f(x, a)) -> F(x, f(f(a, a), a))
F(a, f(x, a)) -> F(f(a, a), a)
F(a, f(x, a)) -> F(a, a)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Forward Instantiation Transformation
Dependency Pair:
F(a, f(x, a)) -> F(x, f(f(a, a), a))
Rule:
f(a, f(x, a)) -> f(x, f(f(a, a), a))
On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule
F(a, f(x, a)) -> F(x, f(f(a, a), a))
one new Dependency Pair
is created:
F(a, f(a, a)) -> F(a, f(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(a, f(a, a)) -> F(a, f(f(a, a), a))
Rule:
f(a, f(x, a)) -> f(x, f(f(a, a), a))
On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule
F(a, f(a, a)) -> F(a, f(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