YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

2(1(x0)) → 4(1(x0))
3(4(x0)) → 4(2(x0))
2(4(x0)) → 3(2(x0))

Proof

1 Rule Removal

Using the Knuth Bendix order with w0 = 1 and the following precedence and weight function
prec(3) = 1 weight(3) = 1
prec(4) = 0 weight(4) = 1
prec(2) = 3 weight(2) = 1
prec(1) = 0 weight(1) = 1
all rules could be removed.

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.