(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
The set Q consists of the following terms:
s1(s1(s0(s0(x0))))
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
S1(s1(s0(s0(x)))) → S1(s1(s1(x)))
S1(s1(s0(s0(x)))) → S1(s1(x))
S1(s1(s0(s0(x)))) → S1(x)
The TRS R consists of the following rules:
s1(s1(s0(s0(x)))) → s0(s0(s0(s1(s1(s1(x))))))
The set Q consists of the following terms:
s1(s1(s0(s0(x0))))
We have to consider all minimal (P,Q,R)-chains.