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