(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

eqtrue
eqeq
eqfalse
inf(X) → cons
take(0, X) → nil
take(s, cons) → cons
length(nil) → 0
length(cons) → s

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:
eq > true
eq > false
inf1 > cons > s
take2 > nil
length1 > 0 > nil
length1 > s
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

eqtrue
eqfalse
inf(X) → cons
take(0, X) → nil
take(s, cons) → cons
length(nil) → 0
length(cons) → s


(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

eqeq

Q is empty.