(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → X
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Quasi-Precedence:
tail1 > activate1 > zeros > cons2
tail1 > activate1 > zeros > 0
tail1 > activate1 > zeros > nzeros
Status:
cons2: [2,1]
tail1: [1]
zeros: []
nzeros: []
activate1: [1]
0: []
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → 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