Term Rewriting System R:
[x]
f(s(x)) -> s(f(f(p(s(x)))))
f(0) -> 0
p(s(x)) -> x
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(x)) -> F(f(p(s(x))))
F(s(x)) -> F(p(s(x)))
F(s(x)) -> P(s(x))
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pairs:
F(s(x)) -> F(p(s(x)))
F(s(x)) -> F(f(p(s(x))))
Rules:
f(s(x)) -> s(f(f(p(s(x)))))
f(0) -> 0
p(s(x)) -> x
Termination of R could not be shown.
Duration:
0:00 minutes