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:

a2(lambda1(x), y) -> lambda1(a2(x, 1))
a2(lambda1(x), y) -> lambda1(a2(x, a2(y, t)))
a2(a2(x, y), z) -> a2(x, a2(y, z))
lambda1(x) -> x
a2(x, y) -> x
a2(x, y) -> y

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

a2(lambda1(x), y) -> lambda1(a2(x, 1))
a2(lambda1(x), y) -> lambda1(a2(x, a2(y, t)))
a2(a2(x, y), z) -> a2(x, a2(y, z))
lambda1(x) -> x
a2(x, y) -> x
a2(x, y) -> y

Q is empty.

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

A2(lambda1(x), y) -> A2(y, t)
A2(a2(x, y), z) -> A2(x, a2(y, z))
A2(lambda1(x), y) -> A2(x, a2(y, t))
A2(a2(x, y), z) -> A2(y, z)
A2(lambda1(x), y) -> A2(x, 1)
A2(lambda1(x), y) -> LAMBDA1(a2(x, a2(y, t)))
A2(lambda1(x), y) -> LAMBDA1(a2(x, 1))

The TRS R consists of the following rules:

a2(lambda1(x), y) -> lambda1(a2(x, 1))
a2(lambda1(x), y) -> lambda1(a2(x, a2(y, t)))
a2(a2(x, y), z) -> a2(x, a2(y, z))
lambda1(x) -> x
a2(x, y) -> x
a2(x, y) -> y

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof

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

A2(lambda1(x), y) -> A2(y, t)
A2(a2(x, y), z) -> A2(x, a2(y, z))
A2(lambda1(x), y) -> A2(x, a2(y, t))
A2(a2(x, y), z) -> A2(y, z)
A2(lambda1(x), y) -> A2(x, 1)
A2(lambda1(x), y) -> LAMBDA1(a2(x, a2(y, t)))
A2(lambda1(x), y) -> LAMBDA1(a2(x, 1))

The TRS R consists of the following rules:

a2(lambda1(x), y) -> lambda1(a2(x, 1))
a2(lambda1(x), y) -> lambda1(a2(x, a2(y, t)))
a2(a2(x, y), z) -> a2(x, a2(y, z))
lambda1(x) -> x
a2(x, y) -> x
a2(x, y) -> y

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 1 SCC with 2 less nodes.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
        ↳ QDP

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

A2(lambda1(x), y) -> A2(y, t)
A2(a2(x, y), z) -> A2(x, a2(y, z))
A2(lambda1(x), y) -> A2(x, a2(y, t))
A2(a2(x, y), z) -> A2(y, z)
A2(lambda1(x), y) -> A2(x, 1)

The TRS R consists of the following rules:

a2(lambda1(x), y) -> lambda1(a2(x, 1))
a2(lambda1(x), y) -> lambda1(a2(x, a2(y, t)))
a2(a2(x, y), z) -> a2(x, a2(y, z))
lambda1(x) -> x
a2(x, y) -> x
a2(x, y) -> y

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