(0) Obligation:

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

*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic path order with status [LPO].
Precedence:
*2 > 1
*2 > 0

Status:
*2: [1,2]
i1: [1]
1: []
0: []
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

*(i(x), x) → 1
*(1, y) → y
*(x, 0) → 0
*(*(x, y), z) → *(x, *(y, z))


(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