(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
1(0(x)) → 0(0(0(1(x))))
0(1(x)) → 1(x)
1(1(x)) → 0(0(0(0(x))))
0(0(x)) → 0(x)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
11 > 01
Status:
11: multiset
01: [1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
1(0(x)) → 0(0(0(1(x))))
0(1(x)) → 1(x)
1(1(x)) → 0(0(0(0(x))))
0(0(x)) → 0(x)
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE