app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
↳ QTRS
↳ Non-Overlap Check
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(minus, x)
APP2(log, app2(s, app2(s, x))) -> APP2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0)))))
APP2(log, app2(s, app2(s, x))) -> APP2(quot, x)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(minus, x)
APP2(log, app2(s, app2(s, x))) -> APP2(app2(quot, x), app2(s, app2(s, 0)))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(app2(quot, x), app2(s, app2(s, 0))))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(s, 0))
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(quot, app2(app2(minus, x), y))
APP2(log, app2(s, app2(s, x))) -> APP2(s, 0)
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(app2(quot, app2(app2(minus, x), y)), app2(s, y))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(minus, x)
APP2(log, app2(s, app2(s, x))) -> APP2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0)))))
APP2(log, app2(s, app2(s, x))) -> APP2(quot, x)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(minus, x)
APP2(log, app2(s, app2(s, x))) -> APP2(app2(quot, x), app2(s, app2(s, 0)))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(app2(quot, x), app2(s, app2(s, 0))))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(s, 0))
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(quot, app2(app2(minus, x), y))
APP2(log, app2(s, app2(s, x))) -> APP2(s, 0)
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(app2(quot, app2(app2(minus, x), y)), app2(s, y))
APP2(log, app2(s, app2(s, x))) -> APP2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
The following pairs can be strictly oriented and are deleted.
The remaining pairs can at least by weakly be oriented.
APP2(app2(minus, app2(s, x)), app2(s, y)) -> APP2(app2(minus, x), y)
trivial
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
APP2(app2(quot, app2(s, x)), app2(s, y)) -> APP2(app2(quot, app2(app2(minus, x), y)), app2(s, y))
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
APP2(log, app2(s, app2(s, x))) -> APP2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0)))))
app2(app2(minus, x), 0) -> x
app2(app2(minus, app2(s, x)), app2(s, y)) -> app2(app2(minus, x), y)
app2(app2(quot, 0), app2(s, y)) -> 0
app2(app2(quot, app2(s, x)), app2(s, y)) -> app2(s, app2(app2(quot, app2(app2(minus, x), y)), app2(s, y)))
app2(log, app2(s, 0)) -> 0
app2(log, app2(s, app2(s, x))) -> app2(s, app2(log, app2(s, app2(app2(quot, x), app2(s, app2(s, 0))))))
app2(app2(minus, x0), 0)
app2(app2(minus, app2(s, x0)), app2(s, x1))
app2(app2(quot, 0), app2(s, x0))
app2(app2(quot, app2(s, x0)), app2(s, x1))
app2(log, app2(s, 0))
app2(log, app2(s, app2(s, x0)))