(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Quasi-Precedence:
[D1, -2] > 1 > *2
[D1, -2] > 0 > *2
[D1, -2] > +2 > *2
t > *2
constant > *2
Status:
constant: []
t: []
-2: [1,2]
D1: [1]
*2: [2,1]
0: []
1: []
+2: [1,2]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
(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