:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
↳ QTRS
↳ DependencyPairsProof
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
:1(z, +(x, f(y))) → :1(g(z, y), +(x, a))
:1(+(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(x, :(y, z))
:1(+(x, y), z) → :1(x, z)
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
:1(z, +(x, f(y))) → :1(g(z, y), +(x, a))
:1(+(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(x, :(y, z))
:1(+(x, y), z) → :1(x, z)
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
:1(+(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(x, :(y, z))
:1(+(x, y), z) → :1(x, z)
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
:1(:(x, y), z) → :1(y, z)
:1(:(x, y), z) → :1(x, :(y, z))
Used ordering: Polynomial interpretation [25,35]:
:1(+(x, y), z) → :1(y, z)
:1(+(x, y), z) → :1(x, z)
The value of delta used in the strict ordering is 9/16.
POL(f(x1)) = 1
POL(a) = 3
POL(:(x1, x2)) = 9/4 + x_1 + (2)x_2
POL(g(x1, x2)) = 4 + (9/4)x_1 + (3/4)x_2
POL(:1(x1, x2)) = (1/4)x_1
POL(+(x1, x2)) = x_1 + (3/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
:1(+(x, y), z) → :1(y, z)
:1(+(x, y), z) → :1(x, z)
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
:1(+(x, y), z) → :1(y, z)
:1(+(x, y), z) → :1(x, z)
The value of delta used in the strict ordering is 4.
POL(:1(x1, x2)) = (4)x_1
POL(+(x1, x2)) = 1 + (4)x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
:(:(x, y), z) → :(x, :(y, z))
:(+(x, y), z) → +(:(x, z), :(y, z))
:(z, +(x, f(y))) → :(g(z, y), +(x, a))