YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

0(P(x0)) → 1(P(x0))
1(P(x0)) → c(P(x0))
0(c(x0)) → 1(0(x0))
1(c(x0)) → c(0(x0))

Proof

1 Rule Removal

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

1.1 R is empty

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