app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
↳ QTRS
↳ DependencyPairsProof
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(g, x)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(app(app(insert, f), g), z), app(app(g, x), y))
APP(app(min, app(s, x)), app(s, y)) → APP(app(min, x), y)
APP(asort, z) → APP(app(sort, min), max)
APP(app(min, app(s, x)), app(s, y)) → APP(min, x)
APP(dsort, z) → APP(app(sort, max), min)
APP(app(app(app(insert, f), g), nil), y) → APP(app(cons, y), nil)
APP(asort, z) → APP(app(app(sort, min), max), z)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(insert, f), g)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(app(insert, f), g), z)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(insert, f), g), app(app(app(sort, f), g), y))
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(g, x), y)
APP(app(max, app(s, x)), app(s, y)) → APP(max, x)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(insert, f)
APP(app(app(app(insert, f), g), nil), y) → APP(cons, y)
APP(asort, z) → APP(sort, min)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(f, x)
APP(dsort, z) → APP(app(app(sort, max), min), z)
APP(app(max, app(s, x)), app(s, y)) → APP(app(max, x), y)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(sort, f), g), y)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(cons, app(app(f, x), y))
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(f, x), y)
APP(dsort, z) → APP(sort, max)
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(g, x)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(app(app(insert, f), g), z), app(app(g, x), y))
APP(app(min, app(s, x)), app(s, y)) → APP(app(min, x), y)
APP(asort, z) → APP(app(sort, min), max)
APP(app(min, app(s, x)), app(s, y)) → APP(min, x)
APP(dsort, z) → APP(app(sort, max), min)
APP(app(app(app(insert, f), g), nil), y) → APP(app(cons, y), nil)
APP(asort, z) → APP(app(app(sort, min), max), z)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(insert, f), g)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(app(insert, f), g), z)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(insert, f), g), app(app(app(sort, f), g), y))
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(g, x), y)
APP(app(max, app(s, x)), app(s, y)) → APP(max, x)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(insert, f)
APP(app(app(app(insert, f), g), nil), y) → APP(cons, y)
APP(asort, z) → APP(sort, min)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(f, x)
APP(dsort, z) → APP(app(app(sort, max), min), z)
APP(app(max, app(s, x)), app(s, y)) → APP(app(max, x), y)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(sort, f), g), y)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(cons, app(app(f, x), y))
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(f, x), y)
APP(dsort, z) → APP(sort, max)
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
APP(app(min, app(s, x)), app(s, y)) → APP(app(min, x), y)
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(min, app(s, x)), app(s, y)) → APP(app(min, x), y)
The value of delta used in the strict ordering is 1.
POL(APP(x1, x2)) = (4)x_1
POL(app(x1, x2)) = (1/4)x_1 + (4)x_2
POL(s) = 1/4
POL(min) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
APP(app(max, app(s, x)), app(s, y)) → APP(app(max, x), y)
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(max, app(s, x)), app(s, y)) → APP(app(max, x), y)
The value of delta used in the strict ordering is 1.
POL(APP(x1, x2)) = (4)x_1
POL(max) = 0
POL(app(x1, x2)) = (1/4)x_1 + (4)x_2
POL(s) = 1/4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(g, x)
APP(dsort, z) → APP(app(app(sort, max), min), z)
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(sort, f), g), y)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(app(app(insert, f), g), z), app(app(g, x), y))
APP(app(app(sort, f), g), app(app(cons, x), y)) → APP(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(g, x), y)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(app(f, x), y)
APP(app(app(app(insert, f), g), app(app(cons, x), z)), y) → APP(f, x)
APP(asort, z) → APP(app(app(sort, min), max), z)
app(app(app(sort, f), g), nil) → nil
app(app(app(sort, f), g), app(app(cons, x), y)) → app(app(app(app(insert, f), g), app(app(app(sort, f), g), y)), x)
app(app(app(app(insert, f), g), nil), y) → app(app(cons, y), nil)
app(app(app(app(insert, f), g), app(app(cons, x), z)), y) → app(app(cons, app(app(f, x), y)), app(app(app(app(insert, f), g), z), app(app(g, x), y)))
app(app(max, 0), y) → y
app(app(max, x), 0) → x
app(app(max, app(s, x)), app(s, y)) → app(app(max, x), y)
app(app(min, 0), y) → 0
app(app(min, x), 0) → 0
app(app(min, app(s, x)), app(s, y)) → app(app(min, x), y)
app(asort, z) → app(app(app(sort, min), max), z)
app(dsort, z) → app(app(app(sort, max), min), z)