(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
average(s(x), y) → average(x, s(y))
average(x, s(s(s(y)))) → s(average(s(x), y))
average(0, 0) → 0
average(0, s(0)) → 0
average(0, s(s(0))) → s(0)
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:
average(s(x), y) → average(x, s(y))
average(x, s(s(s(y)))) → s(average(s(x), y))
average(0, 0) → 0
average(0, s(0)) → 0
average(0, s(s(0))) → s(0)
The set Q consists of the following terms:
average(s(x0), x1)
average(x0, s(s(s(x1))))
average(0, 0)
average(0, s(0))
average(0, s(s(0)))
(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:
AVERAGE(s(x), y) → AVERAGE(x, s(y))
AVERAGE(x, s(s(s(y)))) → AVERAGE(s(x), y)
The TRS R consists of the following rules:
average(s(x), y) → average(x, s(y))
average(x, s(s(s(y)))) → s(average(s(x), y))
average(0, 0) → 0
average(0, s(0)) → 0
average(0, s(s(0))) → s(0)
The set Q consists of the following terms:
average(s(x0), x1)
average(x0, s(s(s(x1))))
average(0, 0)
average(0, s(0))
average(0, s(s(0)))
We have to consider all minimal (P,Q,R)-chains.