:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)
↳ QTRS
↳ DependencyPairsProof
:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)
:1(i(x), :(y, :(x, z))) → :1(i(z), y)
:1(e, x) → I(x)
:1(i(x), :(y, :(x, z))) → I(z)
:1(:(x, y), z) → :1(z, i(y))
:1(:(x, y), z) → :1(x, :(z, i(y)))
:1(x, :(y, :(i(x), z))) → I(z)
:1(:(x, y), z) → I(y)
I(:(x, y)) → :1(y, x)
:1(i(x), :(y, x)) → I(y)
:1(x, :(y, i(x))) → I(y)
:1(x, :(y, :(i(x), z))) → :1(i(z), y)
:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
:1(i(x), :(y, :(x, z))) → :1(i(z), y)
:1(e, x) → I(x)
:1(i(x), :(y, :(x, z))) → I(z)
:1(:(x, y), z) → :1(z, i(y))
:1(:(x, y), z) → :1(x, :(z, i(y)))
:1(x, :(y, :(i(x), z))) → I(z)
:1(:(x, y), z) → I(y)
I(:(x, y)) → :1(y, x)
:1(i(x), :(y, x)) → I(y)
:1(x, :(y, i(x))) → I(y)
:1(x, :(y, :(i(x), z))) → :1(i(z), y)
:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
:1(i(x), :(y, :(x, z))) → :1(i(z), y)
:1(e, x) → I(x)
:1(i(x), :(y, :(x, z))) → I(z)
:1(:(x, y), z) → :1(z, i(y))
:1(x, :(y, :(i(x), z))) → I(z)
:1(:(x, y), z) → I(y)
I(:(x, y)) → :1(y, x)
:1(i(x), :(y, x)) → I(y)
:1(x, :(y, i(x))) → I(y)
:1(x, :(y, :(i(x), z))) → :1(i(z), y)
Used ordering: Polynomial interpretation [25,35]:
:1(:(x, y), z) → :1(x, :(z, i(y)))
The value of delta used in the strict ordering is 4.
POL(i(x1)) = x_1
POL(:(x1, x2)) = 4 + x_1 + x_2
POL(:1(x1, x2)) = (4)x_1 + (4)x_2
POL(e) = 2
POL(I(x1)) = 4 + (4)x_1
:(x, x) → e
:(x, e) → x
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(:(x, y), z) → :(x, :(z, i(y)))
:(i(x), :(y, :(x, z))) → :(i(z), y)
i(:(x, y)) → :(y, x)
:(e, x) → i(x)
:(i(x), :(y, x)) → i(y)
i(i(x)) → x
i(e) → e
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
:1(:(x, y), z) → :1(x, :(z, i(y)))
:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
:1(:(x, y), z) → :1(x, :(z, i(y)))
The value of delta used in the strict ordering is 1/16.
POL(i(x1)) = 0
POL(:(x1, x2)) = 1/4 + x_1
POL(:1(x1, x2)) = (1/4)x_1
POL(e) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
:(x, x) → e
:(x, e) → x
i(:(x, y)) → :(y, x)
:(:(x, y), z) → :(x, :(z, i(y)))
:(e, x) → i(x)
i(i(x)) → x
i(e) → e
:(x, :(y, i(x))) → i(y)
:(x, :(y, :(i(x), z))) → :(i(z), y)
:(i(x), :(y, x)) → i(y)
:(i(x), :(y, :(x, z))) → :(i(z), y)