Term Rewriting System R:
[x, y, z]
not(and(x, y)) > or(not(x), not(y))
not(or(x, y)) > and(not(x), not(y))
and(x, or(y, z)) > or(and(x, y), and(x, z))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
NOT(and(x, y)) > NOT(x)
NOT(and(x, y)) > NOT(y)
NOT(or(x, y)) > AND(not(x), not(y))
NOT(or(x, y)) > NOT(x)
NOT(or(x, y)) > NOT(y)
AND(x, or(y, z)) > AND(x, y)
AND(x, or(y, z)) > AND(x, z)
Furthermore, R contains two SCCs.
R
↳DPs
→DP Problem 1
↳SizeChange Principle
→DP Problem 2
↳SCP
Dependency Pairs:
AND(x, or(y, z)) > AND(x, z)
AND(x, or(y, z)) > AND(x, y)
Rules:
not(and(x, y)) > or(not(x), not(y))
not(or(x, y)) > and(not(x), not(y))
and(x, or(y, z)) > or(and(x, y), and(x, z))
We number the DPs as follows:
 AND(x, or(y, z)) > AND(x, z)
 AND(x, or(y, z)) > AND(x, y)
and get the following SizeChange Graph(s):
which lead(s) to this/these maximal multigraph(s):
D_{P}: empty set
Oriented Rules: none
We used the order Homeomorphic Embedding Order with NonStrict Precedence.
trivial
with Argument Filtering System:
or(x_{1}, x_{2}) > or(x_{1}, x_{2})
We obtain no new DP problems.
R
↳DPs
→DP Problem 1
↳SCP
→DP Problem 2
↳SizeChange Principle
Dependency Pairs:
NOT(or(x, y)) > NOT(y)
NOT(or(x, y)) > NOT(x)
NOT(and(x, y)) > NOT(y)
NOT(and(x, y)) > NOT(x)
Rules:
not(and(x, y)) > or(not(x), not(y))
not(or(x, y)) > and(not(x), not(y))
and(x, or(y, z)) > or(and(x, y), and(x, z))
We number the DPs as follows:
 NOT(or(x, y)) > NOT(y)
 NOT(or(x, y)) > NOT(x)
 NOT(and(x, y)) > NOT(y)
 NOT(and(x, y)) > NOT(x)
and get the following SizeChange Graph(s): {4, 3, 2, 1}  ,  {4, 3, 2, 1} 

1  >  1 

which lead(s) to this/these maximal multigraph(s): {4, 3, 2, 1}  ,  {4, 3, 2, 1} 

1  >  1 

D_{P}: empty set
Oriented Rules: none
We used the order Homeomorphic Embedding Order with NonStrict Precedence.
trivial
with Argument Filtering System:
and(x_{1}, x_{2}) > and(x_{1}, x_{2})
or(x_{1}, x_{2}) > or(x_{1}, x_{2})
We obtain no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes