(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
not(x) → xor(x, true)
implies(x, y) → xor(and(x, y), xor(x, true))
or(x, y) → xor(and(x, y), xor(x, y))
=(x, y) → xor(x, xor(y, true))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Quasi-Precedence:
not1 > xor2
not1 > true
implies2 > xor2
implies2 > true
implies2 > and2
or2 > xor2
or2 > and2
=2 > xor2
=2 > true
Status:
not1: [1]
xor2: [2,1]
true: []
implies2: [2,1]
and2: [2,1]
or2: [2,1]
=2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
not(x) → xor(x, true)
implies(x, y) → xor(and(x, y), xor(x, true))
or(x, y) → xor(and(x, y), xor(x, y))
=(x, y) → xor(x, xor(y, true))
(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