min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
↳ QTRS
↳ DependencyPairsProof
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
LOG(s(s(X))) → QUOT(X, s(s(0)))
QUOT(s(X), s(Y)) → QUOT(min(X, Y), s(Y))
LOG(s(s(X))) → LOG(s(quot(X, s(s(0)))))
MIN(s(X), s(Y)) → MIN(X, Y)
QUOT(s(X), s(Y)) → MIN(X, Y)
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
LOG(s(s(X))) → QUOT(X, s(s(0)))
QUOT(s(X), s(Y)) → QUOT(min(X, Y), s(Y))
LOG(s(s(X))) → LOG(s(quot(X, s(s(0)))))
MIN(s(X), s(Y)) → MIN(X, Y)
QUOT(s(X), s(Y)) → MIN(X, Y)
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
MIN(s(X), s(Y)) → MIN(X, Y)
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MIN(s(X), s(Y)) → MIN(X, Y)
The value of delta used in the strict ordering is 12.
POL(MIN(x1, x2)) = (3)x_2
POL(s(x1)) = 4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
QUOT(s(X), s(Y)) → QUOT(min(X, Y), s(Y))
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
QUOT(s(X), s(Y)) → QUOT(min(X, Y), s(Y))
The value of delta used in the strict ordering is 13.
POL(QUOT(x1, x2)) = (4)x_1
POL(s(x1)) = 13/4 + (5/4)x_1
POL(min(x1, x2)) = x_1
POL(0) = 0
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
LOG(s(s(X))) → LOG(s(quot(X, s(s(0)))))
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LOG(s(s(X))) → LOG(s(quot(X, s(s(0)))))
The value of delta used in the strict ordering is 16.
POL(LOG(x1)) = (2)x_1
POL(quot(x1, x2)) = x_1
POL(s(x1)) = 2 + (4)x_1
POL(min(x1, x2)) = x_1
POL(0) = 0
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
min(X, 0) → X
min(s(X), s(Y)) → min(X, Y)
quot(0, s(Y)) → 0
quot(s(X), s(Y)) → s(quot(min(X, Y), s(Y)))
log(s(0)) → 0
log(s(s(X))) → s(log(s(quot(X, s(s(0))))))