Term Rewriting System R:
[x, y, z]
xor(x, F) -> x
xor(x, neg(x)) -> F
xor(x, x) -> F
and(x, T) -> x
and(x, F) -> F
and(x, x) -> x
and(xor(x, y), z) -> xor(and(x, z), and(y, z))
impl(x, y) -> xor(and(x, y), xor(x, T))
or(x, y) -> xor(and(x, y), xor(x, y))
equiv(x, y) -> xor(x, xor(y, T))
neg(x) -> xor(x, T)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

AND(xor(x, y), z) -> XOR(and(x, z), and(y, z))
AND(xor(x, y), z) -> AND(x, z)
AND(xor(x, y), z) -> AND(y, z)
IMPL(x, y) -> XOR(and(x, y), xor(x, T))
IMPL(x, y) -> AND(x, y)
IMPL(x, y) -> XOR(x, T)
OR(x, y) -> XOR(and(x, y), xor(x, y))
OR(x, y) -> AND(x, y)
OR(x, y) -> XOR(x, y)
EQUIV(x, y) -> XOR(x, xor(y, T))
EQUIV(x, y) -> XOR(y, T)
NEG(x) -> XOR(x, T)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

AND(xor(x, y), z) -> AND(y, z)
AND(xor(x, y), z) -> AND(x, z)


Rules:


xor(x, F) -> x
xor(x, neg(x)) -> F
xor(x, x) -> F
and(x, T) -> x
and(x, F) -> F
and(x, x) -> x
and(xor(x, y), z) -> xor(and(x, z), and(y, z))
impl(x, y) -> xor(and(x, y), xor(x, T))
or(x, y) -> xor(and(x, y), xor(x, y))
equiv(x, y) -> xor(x, xor(y, T))
neg(x) -> xor(x, T)




Termination of R could not be shown.
Duration:
0:00 minutes