Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

implies2(not1(x), y) -> or2(x, y)
implies2(not1(x), or2(y, z)) -> implies2(y, or2(x, z))
implies2(x, or2(y, z)) -> or2(y, implies2(x, z))

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

implies2(not1(x), y) -> or2(x, y)
implies2(not1(x), or2(y, z)) -> implies2(y, or2(x, z))
implies2(x, or2(y, z)) -> or2(y, implies2(x, z))

Q is empty.

Q DP problem:
The TRS P consists of the following rules:

IMPLIES2(x, or2(y, z)) -> IMPLIES2(x, z)
IMPLIES2(not1(x), or2(y, z)) -> IMPLIES2(y, or2(x, z))

The TRS R consists of the following rules:

implies2(not1(x), y) -> or2(x, y)
implies2(not1(x), or2(y, z)) -> implies2(y, or2(x, z))
implies2(x, or2(y, z)) -> or2(y, implies2(x, z))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS
  ↳ DependencyPairsProof
QDP
      ↳ QDPAfsSolverProof

Q DP problem:
The TRS P consists of the following rules:

IMPLIES2(x, or2(y, z)) -> IMPLIES2(x, z)
IMPLIES2(not1(x), or2(y, z)) -> IMPLIES2(y, or2(x, z))

The TRS R consists of the following rules:

implies2(not1(x), y) -> or2(x, y)
implies2(not1(x), or2(y, z)) -> implies2(y, or2(x, z))
implies2(x, or2(y, z)) -> or2(y, implies2(x, z))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using an argument filtering and a montonic ordering, at least one Dependency Pair of this SCC can be strictly oriented.

IMPLIES2(x, or2(y, z)) -> IMPLIES2(x, z)
Used argument filtering: IMPLIES2(x1, x2)  =  x2
or2(x1, x2)  =  or1(x2)
Used ordering: Quasi Precedence: trivial


↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPAfsSolverProof
QDP

Q DP problem:
The TRS P consists of the following rules:

IMPLIES2(not1(x), or2(y, z)) -> IMPLIES2(y, or2(x, z))

The TRS R consists of the following rules:

implies2(not1(x), y) -> or2(x, y)
implies2(not1(x), or2(y, z)) -> implies2(y, or2(x, z))
implies2(x, or2(y, z)) -> or2(y, implies2(x, z))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.