quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
↳ QTRS
↳ DependencyPairsProof
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
QUOT(s(x), s(y), z) → QUOT(x, y, z)
QUOT(x, 0, s(z)) → PLUS(z, s(0))
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
PLUS(s(x), y) → PLUS(x, y)
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
QUOT(s(x), s(y), z) → QUOT(x, y, z)
QUOT(x, 0, s(z)) → PLUS(z, s(0))
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
PLUS(s(x), y) → PLUS(x, y)
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
PLUS(s(x), y) → PLUS(x, y)
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
PLUS(s(x), y) → PLUS(x, y)
The value of delta used in the strict ordering is 4.
POL(PLUS(x1, x2)) = (4)x_1
POL(s(x1)) = 1 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
QUOT(s(x), s(y), z) → QUOT(x, y, z)
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
QUOT(s(x), s(y), z) → QUOT(x, y, z)
Used ordering: Polynomial interpretation [25,35]:
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
The value of delta used in the strict ordering is 16.
POL(plus(x1, x2)) = 3 + x_2
POL(QUOT(x1, x2, x3)) = (4)x_1
POL(s(x1)) = 4 + x_1
POL(0) = 1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
QUOT(x, 0, s(z)) → QUOT(x, plus(z, s(0)), s(z))
The value of delta used in the strict ordering is 9.
POL(plus(x1, x2)) = 1 + (2)x_2
POL(QUOT(x1, x2, x3)) = (3)x_2
POL(s(x1)) = 0
POL(0) = 4
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
quot(0, s(y), s(z)) → 0
quot(s(x), s(y), z) → quot(x, y, z)
plus(0, y) → y
plus(s(x), y) → s(plus(x, y))
quot(x, 0, s(z)) → s(quot(x, plus(z, s(0)), s(z)))