Term Rewriting System R:
[]
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(0)) -> F(p(s(0)))
F(s(0)) -> P(s(0))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pair:
F(s(0)) -> F(p(s(0)))
Rules:
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Strategy:
innermost
The following dependency pair can be strictly oriented:
F(s(0)) -> F(p(s(0)))
The following usable rule for innermost w.r.t. to the AFS can be oriented:
p(s(0)) -> 0
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
{0, p}
resulting in one new DP problem.
Used Argument Filtering System: F(x1) -> F(x1)
s(x1) -> s(x1)
p(x1) -> p
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes