a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
↳ QTRS
↳ DependencyPairsProof
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
A(a(x, y), z) → A(y, z)
A(lambda(x), y) → A(y, t)
A(lambda(x), y) → LAMBDA(a(x, 1))
A(lambda(x), y) → A(x, a(y, t))
A(lambda(x), y) → LAMBDA(a(x, a(y, t)))
A(lambda(x), y) → A(x, 1)
A(a(x, y), z) → A(x, a(y, z))
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(a(x, y), z) → A(y, z)
A(lambda(x), y) → A(y, t)
A(lambda(x), y) → LAMBDA(a(x, 1))
A(lambda(x), y) → A(x, a(y, t))
A(lambda(x), y) → LAMBDA(a(x, a(y, t)))
A(lambda(x), y) → A(x, 1)
A(a(x, y), z) → A(x, a(y, z))
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
A(a(x, y), z) → A(y, z)
A(lambda(x), y) → A(y, t)
A(lambda(x), y) → A(x, a(y, t))
A(lambda(x), y) → A(x, 1)
A(a(x, y), z) → A(x, a(y, z))
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(lambda(x), y) → A(y, t)
A(lambda(x), y) → A(x, a(y, t))
A(lambda(x), y) → A(x, 1)
Used ordering: Polynomial interpretation [25,35]:
A(a(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
The value of delta used in the strict ordering is 1.
POL(lambda(x1)) = 4 + x_1
POL(t) = 0
POL(a(x1, x2)) = x_1 + x_2
POL(A(x1, x2)) = (1/4)x_1 + (1/4)x_2
POL(1) = 0
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
The value of delta used in the strict ordering is 1/8.
POL(lambda(x1)) = 0
POL(t) = 0
POL(a(x1, x2)) = 1/4 + (4)x_1 + (4)x_2
POL(A(x1, x2)) = (1/2)x_1
POL(1) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(lambda(x), y) → lambda(a(x, 1))
a(lambda(x), y) → lambda(a(x, a(y, t)))
a(a(x, y), z) → a(x, a(y, z))
lambda(x) → x
a(x, y) → x
a(x, y) → y