Term Rewriting System R:
[x]
a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))
Termination of R to be shown.
TRS
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
A(b(a(b(x)))) -> A(b(a(a(b(x)))))
A(b(a(b(x)))) -> A(a(b(x)))
Furthermore, R contains one SCC.
TRS
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pairs:
A(b(a(b(x)))) -> A(a(b(x)))
A(b(a(b(x)))) -> A(b(a(a(b(x)))))
Rule:
a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))
Found an infinite P-chain over R:
P =
A(b(a(b(x)))) -> A(a(b(x)))
A(b(a(b(x)))) -> A(b(a(a(b(x)))))
R =
a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))
s = A(b(a(a(b(a(b(x'')))))))
evaluates to t =A(b(a(a(b(a(b(a(a(b(x''))))))))))
Thus, s starts an infinite chain as s matches t.
Non-Termination of R could be shown.
Duration:
0:01 minutes