Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: right


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(butlast, F:
{() -> butlast([cons(y, nil), nil])
() -> butlast([nil, nil])
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)])}
(butlast([_th, _uh]) /\ butlast([_th, _vh])) -> eq_eltlist([_uh, _vh])
)
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)])}
(append([_xh, _yh, _ai]) /\ append([_xh, _yh, _zh])) -> eq_eltlist([_zh, _ai])
)
(butlastconcat, F:
{(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di])
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi])}
(butlastconcat([_ei, _fi, _gi]) /\ butlastconcat([_ei, _fi, _hi])) -> eq_eltlist([_gi, _hi])
)
}

properties:
{(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki])}


over-approximation: {append, butlast, butlastconcat}
under-approximation: {}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 0
() -> butlast([nil, nil]) -> 0
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 0
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 0
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 0
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 0
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 0
}


Solving took 63.967669 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1703, q_gen_1704, q_gen_1705, q_gen_1708, q_gen_1709, q_gen_1710, q_gen_1717, q_gen_1720, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1735, q_gen_1736, q_gen_1737, q_gen_1741, q_gen_1742, q_gen_1744, q_gen_1745, q_gen_1750, q_gen_1751, q_gen_1752, q_gen_1753, q_gen_1755, q_gen_1756, q_gen_1757, q_gen_1758, q_gen_1759, q_gen_1760, q_gen_1763, q_gen_1764, q_gen_1766, q_gen_1769, q_gen_1770, q_gen_1771, q_gen_1772, q_gen_1773, q_gen_1774, q_gen_1780, q_gen_1781, q_gen_1782, q_gen_1783, q_gen_1784, q_gen_1785, q_gen_1786, q_gen_1790, q_gen_1791, q_gen_1792, q_gen_1794, q_gen_1797, q_gen_1798, q_gen_1799, q_gen_1800, q_gen_1801, q_gen_1802, q_gen_1804, q_gen_1805, q_gen_1806, q_gen_1807, q_gen_1810, q_gen_1814, q_gen_1815, q_gen_1820, q_gen_1821, q_gen_1826, q_gen_1827, q_gen_1828, q_gen_1830, q_gen_1831, q_gen_1832, q_gen_1837, q_gen_1838, q_gen_1839, q_gen_1840, q_gen_1841, q_gen_1842, q_gen_1844, q_gen_1849, q_gen_1851, q_gen_1852, q_gen_1853, q_gen_1854, q_gen_1855, q_gen_1856, q_gen_1857, q_gen_1859, q_gen_1863, q_gen_1864, q_gen_1866, q_gen_1867, q_gen_1871, q_gen_1872, q_gen_1876, q_gen_1877, q_gen_1878, q_gen_1879, q_gen_1880, q_gen_1881, q_gen_1883, q_gen_1887, q_gen_1888, q_gen_1889, q_gen_1890, q_gen_1891, q_gen_1892, q_gen_1893, q_gen_1897, q_gen_1898, q_gen_1899, q_gen_1904, q_gen_1905},
Q_f={},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<a>() -> q_gen_1758
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1800
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1709
<a, a>() -> q_gen_1710
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1737
<cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1745
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1753
<b, a>() -> q_gen_1783
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1791
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1807
<nil, cons>(q_gen_1758, q_gen_1722) -> q_gen_1840
<cons, cons>(q_gen_1783, q_gen_1737) -> q_gen_1842
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1703
<nil, cons, cons>(q_gen_1710, q_gen_1709) -> q_gen_1708
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1717
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1720
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1736
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1741
<a, b, a>() -> q_gen_1742
<cons, nil, cons>(q_gen_1705, q_gen_1745) -> q_gen_1744
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<cons, cons, cons>(q_gen_1724, q_gen_1752) -> q_gen_1751
<cons, nil, cons>(q_gen_1705, q_gen_1753) -> q_gen_1752
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1755
<cons, cons, cons>(q_gen_1759, q_gen_1757) -> q_gen_1756
<nil, nil, cons>(q_gen_1758, q_gen_1722) -> q_gen_1757
<b, a, b>() -> q_gen_1759
<cons, nil, cons>(q_gen_1705, q_gen_1737) -> q_gen_1760
<cons, cons, cons>(q_gen_1764, q_gen_1757) -> q_gen_1763
<a, a, a>() -> q_gen_1764
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1766
<cons, cons, cons>(q_gen_1742, q_gen_1735) -> q_gen_1769
<cons, cons, cons>(q_gen_1742, q_gen_1771) -> q_gen_1770
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1771
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1774
<nil, cons, cons>(q_gen_1710, q_gen_1737) -> q_gen_1780
<cons, cons, cons>(q_gen_1764, q_gen_1782) -> q_gen_1781
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1782
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1784
<cons, cons, cons>(q_gen_1724, q_gen_1786) -> q_gen_1785
<cons, cons, cons>(q_gen_1724, q_gen_1760) -> q_gen_1786
<cons, nil, cons>(q_gen_1705, q_gen_1791) -> q_gen_1790
<cons, nil, cons>(q_gen_1783, q_gen_1737) -> q_gen_1792
<nil, cons, cons>(q_gen_1705, q_gen_1753) -> q_gen_1794
<nil, cons, cons>(q_gen_1705, q_gen_1791) -> q_gen_1797
<cons, cons, cons>(q_gen_1742, q_gen_1799) -> q_gen_1798
<nil, nil, cons>(q_gen_1723, q_gen_1800) -> q_gen_1799
<nil, cons, cons>(q_gen_1705, q_gen_1745) -> q_gen_1801
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1802
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1804
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1805
<nil, cons, cons>(q_gen_1783, q_gen_1807) -> q_gen_1806
<cons, cons, cons>(q_gen_1724, q_gen_1792) -> q_gen_1810
<cons, cons, cons>(q_gen_1742, q_gen_1815) -> q_gen_1814
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1815
<cons, cons, cons>(q_gen_1724, q_gen_1821) -> q_gen_1820
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1821
<cons, cons, cons>(q_gen_1759, q_gen_1721) -> q_gen_1826
<cons, cons, cons>(q_gen_1764, q_gen_1729) -> q_gen_1827
<cons, cons, cons>(q_gen_1724, q_gen_1774) -> q_gen_1828
<cons, cons, cons>(q_gen_1724, q_gen_1831) -> q_gen_1830
<cons, cons, cons>(q_gen_1724, q_gen_1832) -> q_gen_1831
<cons, cons, cons>(q_gen_1724, q_gen_1720) -> q_gen_1832
<nil, cons, cons>(q_gen_1705, q_gen_1807) -> q_gen_1837
<cons, cons, cons>(q_gen_1742, q_gen_1839) -> q_gen_1838
<nil, cons, cons>(q_gen_1705, q_gen_1840) -> q_gen_1839
<cons, nil, cons>(q_gen_1705, q_gen_1842) -> q_gen_1841
<cons, cons, cons>(q_gen_1724, q_gen_1785) -> q_gen_1844
<cons, cons, cons>(q_gen_1724, q_gen_1810) -> q_gen_1849
<cons, cons, cons>(q_gen_1759, q_gen_1852) -> q_gen_1851
<nil, cons, cons>(q_gen_1710, q_gen_1807) -> q_gen_1852
<cons, cons, cons>(q_gen_1764, q_gen_1854) -> q_gen_1853
<cons, cons, cons>(q_gen_1759, q_gen_1855) -> q_gen_1854
<nil, cons, cons>(q_gen_1783, q_gen_1840) -> q_gen_1855
<cons, cons, cons>(q_gen_1724, q_gen_1857) -> q_gen_1856
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1857
<cons, cons, cons>(q_gen_1724, q_gen_1757) -> q_gen_1859
<cons, cons, cons>(q_gen_1724, q_gen_1864) -> q_gen_1863
<cons, nil, cons>(q_gen_1710, q_gen_1791) -> q_gen_1864
<cons, cons, cons>(q_gen_1724, q_gen_1867) -> q_gen_1866
<cons, nil, cons>(q_gen_1710, q_gen_1842) -> q_gen_1867
<cons, cons, cons>(q_gen_1724, q_gen_1744) -> q_gen_1871
<cons, cons, cons>(q_gen_1742, q_gen_1855) -> q_gen_1872
<cons, cons, cons>(q_gen_1764, q_gen_1877) -> q_gen_1876
<cons, cons, cons>(q_gen_1724, q_gen_1878) -> q_gen_1877
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1878
<cons, cons, cons>(q_gen_1759, q_gen_1880) -> q_gen_1879
<cons, cons, cons>(q_gen_1742, q_gen_1881) -> q_gen_1880
<cons, nil, cons>(q_gen_1705, q_gen_1807) -> q_gen_1881
<cons, cons, cons>(q_gen_1742, q_gen_1792) -> q_gen_1883
<cons, cons, cons>(q_gen_1759, q_gen_1888) -> q_gen_1887
<nil, cons, cons>(q_gen_1783, q_gen_1791) -> q_gen_1888
<cons, cons, cons>(q_gen_1759, q_gen_1890) -> q_gen_1889
<cons, cons, cons>(q_gen_1724, q_gen_1891) -> q_gen_1890
<nil, nil, cons>(q_gen_1758, q_gen_1800) -> q_gen_1891
<cons, cons, cons>(q_gen_1724, q_gen_1799) -> q_gen_1892
<cons, cons, cons>(q_gen_1742, q_gen_1806) -> q_gen_1893
<cons, cons, cons>(q_gen_1742, q_gen_1857) -> q_gen_1897
<cons, cons, cons>(q_gen_1724, q_gen_1899) -> q_gen_1898
<cons, cons, cons>(q_gen_1742, q_gen_1703) -> q_gen_1899
<cons, cons, cons>(q_gen_1724, q_gen_1905) -> q_gen_1904
<cons, nil, cons>(q_gen_1705, q_gen_1840) -> q_gen_1905
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1697, q_gen_1698, q_gen_1706, q_gen_1707, q_gen_1711, q_gen_1712, q_gen_1713, q_gen_1725, q_gen_1726, q_gen_1731, q_gen_1738, q_gen_1808, q_gen_1816, q_gen_1833, q_gen_1843, q_gen_1846, q_gen_1847},
Q_f={},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1697
<b, b>() -> q_gen_1698
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1706
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1711) -> q_gen_1712
<a, a>() -> q_gen_1713
<cons, cons>(q_gen_1698, q_gen_1706) -> q_gen_1725
<cons, cons>(q_gen_1698, q_gen_1725) -> q_gen_1726
<cons, cons>(q_gen_1713, q_gen_1693) -> q_gen_1731
<cons, cons>(q_gen_1698, q_gen_1697) -> q_gen_1738
<cons, cons>(q_gen_1713, q_gen_1706) -> q_gen_1808
<cons, cons>(q_gen_1698, q_gen_1738) -> q_gen_1816
<cons, cons>(q_gen_1698, q_gen_1816) -> q_gen_1833
<cons, cons>(q_gen_1698, q_gen_1731) -> q_gen_1843
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1846
<cons, cons>(q_gen_1698, q_gen_1846) -> q_gen_1847
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1718, q_gen_1719, q_gen_1727, q_gen_1728, q_gen_1732, q_gen_1733, q_gen_1734, q_gen_1739, q_gen_1740, q_gen_1743, q_gen_1746, q_gen_1747, q_gen_1748, q_gen_1749, q_gen_1754, q_gen_1761, q_gen_1762, q_gen_1765, q_gen_1767, q_gen_1768, q_gen_1775, q_gen_1776, q_gen_1777, q_gen_1778, q_gen_1779, q_gen_1787, q_gen_1788, q_gen_1789, q_gen_1793, q_gen_1795, q_gen_1796, q_gen_1803, q_gen_1809, q_gen_1811, q_gen_1812, q_gen_1813, q_gen_1817, q_gen_1818, q_gen_1819, q_gen_1822, q_gen_1823, q_gen_1824, q_gen_1825, q_gen_1829, q_gen_1834, q_gen_1835, q_gen_1836, q_gen_1845, q_gen_1848, q_gen_1850, q_gen_1858, q_gen_1860, q_gen_1861, q_gen_1862, q_gen_1865, q_gen_1868, q_gen_1869, q_gen_1870, q_gen_1873, q_gen_1874, q_gen_1875, q_gen_1882, q_gen_1884, q_gen_1885, q_gen_1886, q_gen_1894, q_gen_1895, q_gen_1896, q_gen_1900, q_gen_1901, q_gen_1902, q_gen_1903},
Q_f={},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<a>() -> q_gen_1719
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<a, a>() -> q_gen_1734
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1740
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1748
<cons, cons>(q_gen_1716, q_gen_1779) -> q_gen_1778
<cons, nil>(q_gen_1719, q_gen_1701) -> q_gen_1779
<cons, cons>(q_gen_1716, q_gen_1748) -> q_gen_1796
<cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1818
<b, a>() -> q_gen_1862
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1875
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1896
<a, b>() -> q_gen_1903
<nil, nil, nil>() -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, nil>(q_gen_1719, q_gen_1701) -> q_gen_1718
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1727
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1728
<cons, nil, cons>(q_gen_1734, q_gen_1733) -> q_gen_1732
<nil, cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1739
<cons, nil, cons>(q_gen_1716, q_gen_1740) -> q_gen_1743
<cons, cons, cons>(q_gen_1749, q_gen_1747) -> q_gen_1746
<cons, nil, cons>(q_gen_1716, q_gen_1748) -> q_gen_1747
<b, b, b>() -> q_gen_1749
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1754
<cons, cons, cons>(q_gen_1762, q_gen_1699) -> q_gen_1761
<b, a, b>() -> q_gen_1762
<cons, cons, cons>(q_gen_1749, q_gen_1727) -> q_gen_1765
<cons, cons, cons>(q_gen_1768, q_gen_1699) -> q_gen_1767
<a, b, a>() -> q_gen_1768
<cons, cons, cons>(q_gen_1776, q_gen_1699) -> q_gen_1775
<a, a, a>() -> q_gen_1776
<cons, nil, cons>(q_gen_1716, q_gen_1778) -> q_gen_1777
<cons, cons, cons>(q_gen_1749, q_gen_1788) -> q_gen_1787
<cons, cons, cons>(q_gen_1749, q_gen_1789) -> q_gen_1788
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1789
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1793
<nil, cons, cons>(q_gen_1716, q_gen_1796) -> q_gen_1795
<nil, cons, cons>(q_gen_1734, q_gen_1748) -> q_gen_1803
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1809
<cons, cons, cons>(q_gen_1749, q_gen_1812) -> q_gen_1811
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1812
<b, b, a>() -> q_gen_1813
<cons, nil, cons>(q_gen_1716, q_gen_1818) -> q_gen_1817
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1819
<cons, cons, cons>(q_gen_1749, q_gen_1823) -> q_gen_1822
<cons, cons, cons>(q_gen_1749, q_gen_1824) -> q_gen_1823
<nil, cons, cons>(q_gen_1716, q_gen_1748) -> q_gen_1824
<cons, cons, cons>(q_gen_1749, q_gen_1728) -> q_gen_1825
<cons, cons, cons>(q_gen_1813, q_gen_1819) -> q_gen_1829
<cons, cons, cons>(q_gen_1749, q_gen_1835) -> q_gen_1834
<cons, cons, cons>(q_gen_1749, q_gen_1836) -> q_gen_1835
<cons, cons, cons>(q_gen_1749, q_gen_1825) -> q_gen_1836
<cons, cons, cons>(q_gen_1749, q_gen_1787) -> q_gen_1845
<cons, nil, cons>(q_gen_1716, q_gen_1796) -> q_gen_1848
<cons, cons, cons>(q_gen_1749, q_gen_1811) -> q_gen_1850
<cons, cons, cons>(q_gen_1749, q_gen_1754) -> q_gen_1858
<cons, cons, cons>(q_gen_1749, q_gen_1861) -> q_gen_1860
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1861
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1865
<cons, cons, cons>(q_gen_1749, q_gen_1869) -> q_gen_1868
<cons, cons, cons>(q_gen_1768, q_gen_1870) -> q_gen_1869
<cons, nil, cons>(q_gen_1862, q_gen_1748) -> q_gen_1870
<cons, cons, cons>(q_gen_1768, q_gen_1874) -> q_gen_1873
<nil, cons, cons>(q_gen_1862, q_gen_1875) -> q_gen_1874
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1882
<cons, cons, cons>(q_gen_1768, q_gen_1885) -> q_gen_1884
<cons, cons, cons>(q_gen_1886, q_gen_1714) -> q_gen_1885
<b, a, a>() -> q_gen_1886
<cons, cons, cons>(q_gen_1768, q_gen_1895) -> q_gen_1894
<nil, cons, cons>(q_gen_1862, q_gen_1896) -> q_gen_1895
<cons, cons, cons>(q_gen_1886, q_gen_1699) -> q_gen_1900
<cons, cons, cons>(q_gen_1749, q_gen_1902) -> q_gen_1901
<nil, cons, cons>(q_gen_1903, q_gen_1715) -> q_gen_1902
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006112 s (model generation: 0.005627,  model checking: 0.000485):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 0
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 1
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 1
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 1
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 1
}
Sat witness: Found: (() -> butlast([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.004875 s (model generation: 0.004701,  model checking: 0.000174):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692},
Q_f={q_gen_1692},
Delta=
{
<nil, nil>() -> q_gen_1692
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 1
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 1
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 1
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 1
}
Sat witness: Found: (() -> butlast([cons(y, nil), nil]), {
y -> b
})

-------------------------------------------
Step 2, which took 0.004761 s (model generation: 0.004368,  model checking: 0.000393):

Model:
|_
{
append -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 1
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 1
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 1
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.005164 s (model generation: 0.004885,  model checking: 0.000279):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696},
Q_f={q_gen_1696},
Delta=
{
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 1
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 1
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 1
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> nil  ;  x2 -> b  ;  x3 -> nil  ;  y -> b
})

-------------------------------------------
Step 4, which took 0.004935 s (model generation: 0.004800,  model checking: 0.000135):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696},
Q_f={q_gen_1696},
Delta=
{
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 1
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 1
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> nil  ;  x -> nil
})

-------------------------------------------
Step 5, which took 0.005145 s (model generation: 0.004795,  model checking: 0.000350):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696},
Q_f={q_gen_1696},
Delta=
{
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699},
Q_f={q_gen_1699},
Delta=
{
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 1
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 2
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> nil  ;  x -> nil  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 6, which took 0.007889 s (model generation: 0.007566,  model checking: 0.000323):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696},
Q_f={q_gen_1696},
Delta=
{
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 2
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 7, which took 0.012035 s (model generation: 0.011564,  model checking: 0.000471):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 3
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: (() -> butlast([cons(y, nil), nil]), {
y -> a
})

-------------------------------------------
Step 8, which took 0.007356 s (model generation: 0.006728,  model checking: 0.000628):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 4
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 9, which took 0.013326 s (model generation: 0.012869,  model checking: 0.000457):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 4
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 4
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> cons(b, nil)  ;  x2 -> b  ;  x3 -> nil  ;  y -> a
})

-------------------------------------------
Step 10, which took 0.005540 s (model generation: 0.005038,  model checking: 0.000502):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 4
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(b, nil)  ;  x -> cons(b, nil)
})

-------------------------------------------
Step 11, which took 0.012942 s (model generation: 0.012333,  model checking: 0.000609):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 4
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, nil)  ;  _ji -> cons(b, nil)  ;  _ki -> nil  ;  xs -> nil  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 12, which took 0.015462 s (model generation: 0.014010,  model checking: 0.001452):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 4
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> nil  ;  x -> nil  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 13, which took 0.016720 s (model generation: 0.014668,  model checking: 0.002052):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705},
Q_f={q_gen_1696},
Delta=
{
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.016500 s (model generation: 0.015602,  model checking: 0.000898):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1717, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1709
<cons, cons, cons>(q_gen_1724, q_gen_1717) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1717
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1717
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1694, q_gen_1695, q_gen_1698},
Q_f={q_gen_1692},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 5
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 7
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.017161 s (model generation: 0.016177,  model checking: 0.000984):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 6
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 7
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 10
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> cons(b, nil)  ;  x2 -> b  ;  x3 -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 16, which took 0.014284 s (model generation: 0.013771,  model checking: 0.000513):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 7
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 10
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 10
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> nil  ;  x -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.011135 s (model generation: 0.010246,  model checking: 0.000889):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 7
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 10
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 10
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 10
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, nil)  ;  _ji -> nil  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 18, which took 0.019873 s (model generation: 0.017839,  model checking: 0.002034):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 7
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 10
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 10
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 10
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 10
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(b, nil)  ;  x -> nil  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 19, which took 0.018975 s (model generation: 0.017729,  model checking: 0.001246):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 10
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 10
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 10
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 10
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.022529 s (model generation: 0.018507,  model checking: 0.004022):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 8
() -> butlast([nil, nil]) -> 8
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 10
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 10
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 10
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 13
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 11
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(a, nil)  ;  x -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 21, which took 0.022215 s (model generation: 0.020555,  model checking: 0.001660):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 9
() -> butlast([nil, nil]) -> 9
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 10
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 10
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 13
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 13
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 11
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> nil  ;  xs -> nil  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 22, which took 0.023296 s (model generation: 0.020889,  model checking: 0.002407):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711, q_gen_1713},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1693) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1711) -> q_gen_1711
<a, a>() -> q_gen_1713
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 10
() -> butlast([nil, nil]) -> 10
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 10
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 13
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 13
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 13
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 11
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, nil))  ;  _di -> cons(b, cons(b, nil))  ;  x -> nil  ;  x2 -> cons(b, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 23, which took 0.026189 s (model generation: 0.023922,  model checking: 0.002267):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711, q_gen_1713},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1693) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1711) -> q_gen_1711
<a, a>() -> q_gen_1713
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 10
() -> butlast([nil, nil]) -> 10
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 13
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 13
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 13
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 13
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 11
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.028894 s (model generation: 0.024886,  model checking: 0.004008):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> butlast([cons(y, nil), nil]) -> 11
() -> butlast([nil, nil]) -> 11
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 13
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 13
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 13
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 16
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 12
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 25, which took 0.031481 s (model generation: 0.026169,  model checking: 0.005312):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> butlast([cons(y, nil), nil]) -> 12
() -> butlast([nil, nil]) -> 12
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 13
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 13
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 16
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 16
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 13
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> nil  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 26, which took 0.031737 s (model generation: 0.025326,  model checking: 0.006411):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> butlast([cons(y, nil), nil]) -> 13
() -> butlast([nil, nil]) -> 13
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 13
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 16
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 16
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 16
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 14
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(b, nil)))  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 27, which took 0.034892 s (model generation: 0.028194,  model checking: 0.006698):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> butlast([cons(y, nil), nil]) -> 13
() -> butlast([nil, nil]) -> 13
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 16
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 16
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 16
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 16
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 14
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 28, which took 0.042484 s (model generation: 0.032082,  model checking: 0.010402):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> butlast([cons(y, nil), nil]) -> 14
() -> butlast([nil, nil]) -> 14
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 16
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 19
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 17
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 17
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 15
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(b, nil)  ;  x -> cons(b, nil)  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 29, which took 0.039436 s (model generation: 0.032439,  model checking: 0.006997):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> butlast([cons(y, nil), nil]) -> 15
() -> butlast([nil, nil]) -> 15
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 19
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 19
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 17
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 17
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 16
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 30, which took 0.045949 s (model generation: 0.037882,  model checking: 0.008067):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> butlast([cons(y, nil), nil]) -> 16
() -> butlast([nil, nil]) -> 16
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 19
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 19
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 20
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 18
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 17
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> cons(b, cons(b, nil))  ;  xs -> cons(b, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 31, which took 0.050546 s (model generation: 0.043047,  model checking: 0.007499):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> butlast([cons(y, nil), nil]) -> 17
() -> butlast([nil, nil]) -> 17
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 19
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 22
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 20
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 19
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 18
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(b, nil)  ;  x -> cons(b, nil)  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 32, which took 0.047397 s (model generation: 0.041489,  model checking: 0.005908):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> butlast([cons(y, nil), nil]) -> 18
() -> butlast([nil, nil]) -> 18
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 22
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 22
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 20
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 20
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 19
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 33, which took 0.033177 s (model generation: 0.023568,  model checking: 0.009609):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> butlast([cons(y, nil), nil]) -> 19
() -> butlast([nil, nil]) -> 19
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 22
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 22
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 23
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 21
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 20
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, nil)))  ;  _ji -> cons(b, cons(b, nil))  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 34, which took 0.044807 s (model generation: 0.043097,  model checking: 0.001710):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1707, q_gen_1711, q_gen_1713},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1693) -> q_gen_1711
<cons, cons>(q_gen_1713, q_gen_1711) -> q_gen_1711
<a, a>() -> q_gen_1713
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> butlast([cons(y, nil), nil]) -> 20
() -> butlast([nil, nil]) -> 20
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 22
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 22
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 23
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 21
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 23
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> nil  ;  x2 -> b  ;  x3 -> nil  ;  y -> a
})

-------------------------------------------
Step 35, which took 0.050441 s (model generation: 0.044523,  model checking: 0.005918):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1727, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1727},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1727) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1727
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1727
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1727
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1727
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> butlast([cons(y, nil), nil]) -> 21
() -> butlast([nil, nil]) -> 21
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 22
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 25
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 23
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 22
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 23
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(a, nil)  ;  x -> cons(a, nil)  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 36, which took 0.063232 s (model generation: 0.048549,  model checking: 0.014683):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1727, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1727},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1727) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1727
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1727
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1727
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1727
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> butlast([cons(y, nil), nil]) -> 22
() -> butlast([nil, nil]) -> 22
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 25
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 25
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 23
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 23
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 23
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 37, which took 0.068577 s (model generation: 0.063055,  model checking: 0.005522):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> butlast([cons(y, nil), nil]) -> 23
() -> butlast([nil, nil]) -> 23
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 25
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 25
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 26
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 24
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 24
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, nil)))  ;  _ji -> cons(b, cons(b, nil))  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, nil)  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 38, which took 0.079800 s (model generation: 0.078333,  model checking: 0.001467):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1707, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1692
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1734, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<b, b>() -> q_gen_1716
<a, a>() -> q_gen_1734
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1734, q_gen_1715) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> butlast([cons(y, nil), nil]) -> 24
() -> butlast([nil, nil]) -> 24
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 25
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 25
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 26
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 24
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 27
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> nil  ;  x2 -> a  ;  x3 -> nil  ;  y -> b
})

-------------------------------------------
Step 39, which took 0.078955 s (model generation: 0.072855,  model checking: 0.006100):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> butlast([cons(y, nil), nil]) -> 25
() -> butlast([nil, nil]) -> 25
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 25
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 28
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 26
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 25
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 27
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> nil  ;  _di -> cons(a, nil)  ;  x -> cons(a, nil)  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 40, which took 0.078622 s (model generation: 0.077736,  model checking: 0.000886):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1706, q_gen_1707, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693, q_gen_1706},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1706) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1706
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> butlast([cons(y, nil), nil]) -> 25
() -> butlast([nil, nil]) -> 25
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 25
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 28
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 26
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 28
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 27
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, cons(a, nil)))
})

-------------------------------------------
Step 41, which took 0.096094 s (model generation: 0.075597,  model checking: 0.020497):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1706, q_gen_1707, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693, q_gen_1706},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1706) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1706
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> butlast([cons(y, nil), nil]) -> 25
() -> butlast([nil, nil]) -> 25
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 28
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 28
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 26
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 28
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 27
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 42, which took 0.068965 s (model generation: 0.067419,  model checking: 0.001546):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1706, q_gen_1707, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693, q_gen_1706},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1706) -> q_gen_1706
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1706
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> butlast([cons(y, nil), nil]) -> 26
() -> butlast([nil, nil]) -> 26
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 28
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 28
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 29
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 28
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 27
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(a, nil)  ;  _ji -> nil  ;  _ki -> cons(a, nil)  ;  xs -> cons(a, nil)  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 43, which took 0.090194 s (model generation: 0.087350,  model checking: 0.002844):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> butlast([cons(y, nil), nil]) -> 27
() -> butlast([nil, nil]) -> 27
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 28
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 31
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 29
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 29
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 28
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, nil))  ;  _di -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x2 -> cons(b, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 44, which took 0.106387 s (model generation: 0.099715,  model checking: 0.006672):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> butlast([cons(y, nil), nil]) -> 28
() -> butlast([nil, nil]) -> 28
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 31
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 31
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 29
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 29
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 29
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 45, which took 0.100907 s (model generation: 0.098125,  model checking: 0.002782):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> butlast([cons(y, nil), nil]) -> 29
() -> butlast([nil, nil]) -> 29
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 31
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 31
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 32
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 30
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 30
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(a, cons(b, nil))  ;  _ji -> cons(a, nil)  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 46, which took 0.105137 s (model generation: 0.103509,  model checking: 0.001628):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> butlast([cons(y, nil), nil]) -> 30
() -> butlast([nil, nil]) -> 30
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 31
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 34
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 32
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 31
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 31
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, nil))  ;  _di -> cons(b, cons(b, cons(b, nil)))  ;  x -> nil  ;  x2 -> cons(b, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 47, which took 0.110009 s (model generation: 0.101472,  model checking: 0.008537):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1727, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1727},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1727) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1727
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1727
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1727
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> butlast([cons(y, nil), nil]) -> 31
() -> butlast([nil, nil]) -> 31
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 34
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 34
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 32
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 32
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 32
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 48, which took 0.146350 s (model generation: 0.145954,  model checking: 0.000396):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1709
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1730
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 32
() -> butlast([nil, nil]) -> 32
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 34
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 34
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 32
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 32
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 32
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 49, which took 0.109760 s (model generation: 0.108282,  model checking: 0.001478):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1709
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1709
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1709) -> q_gen_1696
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 32
() -> butlast([nil, nil]) -> 32
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 34
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 34
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 35
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 33
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 33
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, nil)))  ;  _ji -> cons(b, cons(b, nil))  ;  _ki -> nil  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 50, which took 0.113356 s (model generation: 0.111911,  model checking: 0.001445):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1709
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1709
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1709) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 33
() -> butlast([nil, nil]) -> 33
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 34
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 37
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 35
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 34
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 34
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(a, nil)  ;  _di -> cons(a, cons(b, nil))  ;  x -> nil  ;  x2 -> cons(b, nil)  ;  z -> a
})

-------------------------------------------
Step 51, which took 0.157567 s (model generation: 0.156080,  model checking: 0.001487):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1709
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1709
<a, a>() -> q_gen_1710
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1709) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 34
() -> butlast([nil, nil]) -> 34
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 37
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 37
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 35
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 35
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 35
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 52, which took 0.141745 s (model generation: 0.141350,  model checking: 0.000395):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1709
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1709
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1709
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1709) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> butlast([cons(y, nil), nil]) -> 35
() -> butlast([nil, nil]) -> 35
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 37
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 37
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 35
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 35
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 35
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 53, which took 0.114496 s (model generation: 0.111782,  model checking: 0.002714):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> butlast([cons(y, nil), nil]) -> 35
() -> butlast([nil, nil]) -> 35
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 37
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 37
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 36
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 36
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(a, cons(a, nil))  ;  _ji -> cons(a, nil)  ;  _ki -> cons(b, nil)  ;  xs -> nil  ;  ys -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 54, which took 0.200886 s (model generation: 0.198365,  model checking: 0.002521):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> butlast([cons(y, nil), nil]) -> 36
() -> butlast([nil, nil]) -> 36
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 37
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 37
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 37
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(b, cons(a, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(b, nil)))  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 55, which took 0.218558 s (model generation: 0.216218,  model checking: 0.002340):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> butlast([cons(y, nil), nil]) -> 37
() -> butlast([nil, nil]) -> 37
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 38
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 38
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 56, which took 0.157135 s (model generation: 0.156668,  model checking: 0.000467):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 38
() -> butlast([nil, nil]) -> 38
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 38
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 38
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 57, which took 0.199513 s (model generation: 0.198369,  model checking: 0.001144):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1735
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1706, q_gen_1707, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693, q_gen_1706},
Delta=
{
<nil>() -> q_gen_1694
<b>() -> q_gen_1695
<a>() -> q_gen_1707
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1706) -> q_gen_1706
<cons, nil>(q_gen_1707, q_gen_1694) -> q_gen_1706
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 38
() -> butlast([nil, nil]) -> 38
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 38
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 41
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> cons(b, nil)  ;  x2 -> b  ;  x3 -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 58, which took 0.173560 s (model generation: 0.173110,  model checking: 0.000450):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1740, q_gen_1749},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1740
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 38
() -> butlast([nil, nil]) -> 38
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 38
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 41
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 41
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 59, which took 0.122400 s (model generation: 0.121538,  model checking: 0.000862):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 38
() -> butlast([nil, nil]) -> 38
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 40
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 41
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 41
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 41
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> cons(a, nil)  ;  xs -> cons(b, nil)  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 60, which took 0.259867 s (model generation: 0.258325,  model checking: 0.001542):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1735
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 39
() -> butlast([nil, nil]) -> 39
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 40
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 43
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 41
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 41
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 41
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, cons(b, nil)))  ;  _di -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> cons(b, cons(b, nil))  ;  x2 -> cons(b, cons(b, cons(b, nil)))  ;  z -> b
})

-------------------------------------------
Step 61, which took 0.284851 s (model generation: 0.284368,  model checking: 0.000483):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1740, q_gen_1749, q_gen_1768},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1740
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1768, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1768, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1714
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<a, a, a>() -> q_gen_1768
<a, b, a>() -> q_gen_1768
<b, b, a>() -> q_gen_1768
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 40
() -> butlast([nil, nil]) -> 40
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 43
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 43
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 41
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 41
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 41
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> nil  ;  h1 -> a  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 62, which took 0.336917 s (model generation: 0.333921,  model checking: 0.002996):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> butlast([cons(y, nil), nil]) -> 41
() -> butlast([nil, nil]) -> 41
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 43
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 43
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 44
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 42
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 42
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(a, cons(b, nil))  ;  _ji -> cons(a, nil)  ;  _ki -> nil  ;  xs -> nil  ;  ys -> cons(a, nil)
})

-------------------------------------------
Step 63, which took 0.290715 s (model generation: 0.288341,  model checking: 0.002374):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> butlast([cons(y, nil), nil]) -> 42
() -> butlast([nil, nil]) -> 42
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 43
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 46
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 44
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 43
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 43
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(b, cons(b, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 64, which took 0.195951 s (model generation: 0.191631,  model checking: 0.004320):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> butlast([cons(y, nil), nil]) -> 43
() -> butlast([nil, nil]) -> 43
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 46
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 46
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 44
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 44
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 44
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 65, which took 0.278363 s (model generation: 0.275184,  model checking: 0.003179):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> butlast([cons(y, nil), nil]) -> 44
() -> butlast([nil, nil]) -> 44
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 46
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 46
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 47
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 45
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 45
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ji -> cons(b, cons(b, cons(b, nil)))  ;  _ki -> cons(a, cons(a, nil))  ;  xs -> cons(b, cons(b, nil))  ;  ys -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 66, which took 0.238518 s (model generation: 0.235161,  model checking: 0.003357):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> butlast([cons(y, nil), nil]) -> 45
() -> butlast([nil, nil]) -> 45
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 46
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 49
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 47
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 46
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 46
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _di -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x2 -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  z -> b
})

-------------------------------------------
Step 67, which took 0.322279 s (model generation: 0.318044,  model checking: 0.004235):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> butlast([cons(y, nil), nil]) -> 46
() -> butlast([nil, nil]) -> 46
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 49
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 49
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 47
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 47
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 47
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 68, which took 0.382712 s (model generation: 0.378928,  model checking: 0.003784):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> butlast([cons(y, nil), nil]) -> 47
() -> butlast([nil, nil]) -> 47
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 49
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 49
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 50
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 48
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 48
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(a, cons(b, nil)))  ;  _ji -> cons(b, cons(a, nil))  ;  _ki -> cons(b, cons(b, nil))  ;  xs -> cons(b, cons(b, cons(b, nil)))  ;  ys -> nil
})

-------------------------------------------
Step 69, which took 0.487795 s (model generation: 0.484664,  model checking: 0.003131):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> butlast([cons(y, nil), nil]) -> 48
() -> butlast([nil, nil]) -> 48
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 49
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 52
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 50
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 49
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 49
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, cons(b, nil)))  ;  _di -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x2 -> cons(b, cons(b, cons(b, nil)))  ;  z -> b
})

-------------------------------------------
Step 70, which took 0.353017 s (model generation: 0.351755,  model checking: 0.001262):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1692
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> butlast([cons(y, nil), nil]) -> 49
() -> butlast([nil, nil]) -> 49
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 49
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 52
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 50
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 49
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 52
}
Sat witness: Found: ((butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]), {
_sh -> cons(b, cons(b, nil))  ;  x2 -> b  ;  x3 -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 71, which took 0.402753 s (model generation: 0.399602,  model checking: 0.003151):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1735
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> butlast([cons(y, nil), nil]) -> 49
() -> butlast([nil, nil]) -> 49
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 52
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 52
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 50
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 50
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 52
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 72, which took 0.555942 s (model generation: 0.554248,  model checking: 0.001694):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> butlast([cons(y, nil), nil]) -> 50
() -> butlast([nil, nil]) -> 50
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 52
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 52
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 53
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 51
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 52
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, nil)  ;  _ji -> nil  ;  _ki -> cons(b, nil)  ;  xs -> nil  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 73, which took 0.466414 s (model generation: 0.465586,  model checking: 0.000828):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> butlast([cons(y, nil), nil]) -> 51
() -> butlast([nil, nil]) -> 51
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 52
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 52
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 53
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 54
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 52
}
Sat witness: Found: ((butlast([x, _bi])) -> butlastconcat([x, nil, _bi]), {
_bi -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 74, which took 0.520730 s (model generation: 0.517822,  model checking: 0.002908):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> butlast([cons(y, nil), nil]) -> 52
() -> butlast([nil, nil]) -> 52
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 52
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 55
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 53
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 54
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 53
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, nil))  ;  _di -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x2 -> cons(b, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 75, which took 0.875400 s (model generation: 0.871893,  model checking: 0.003507):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> butlast([cons(y, nil), nil]) -> 52
() -> butlast([nil, nil]) -> 52
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 55
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 55
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 53
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 54
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 53
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(a, cons(b, nil)))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 76, which took 0.806695 s (model generation: 0.801802,  model checking: 0.004893):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1709, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1709
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1709
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1709) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1709) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1709) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1783, q_gen_1709) -> q_gen_1772
<nil, cons, cons>(q_gen_1783, q_gen_1709) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> butlast([cons(y, nil), nil]) -> 53
() -> butlast([nil, nil]) -> 53
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 55
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 55
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 56
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 54
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 54
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> cons(b, cons(b, nil))  ;  xs -> cons(b, cons(b, nil))  ;  ys -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 77, which took 0.726490 s (model generation: 0.721218,  model checking: 0.005272):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 54
() -> butlast([cons(y, nil), nil]) -> 54
() -> butlast([nil, nil]) -> 54
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 55
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 58
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 56
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 55
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 55
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(b, cons(a, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 78, which took 0.934033 s (model generation: 0.931111,  model checking: 0.002922):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1703, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696, q_gen_1703},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1703) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1703) -> q_gen_1703
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1703
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1703
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> butlast([cons(y, nil), nil]) -> 55
() -> butlast([nil, nil]) -> 55
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 58
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 58
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 56
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 56
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 56
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 79, which took 0.871050 s (model generation: 0.865013,  model checking: 0.006037):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 56
() -> butlast([cons(y, nil), nil]) -> 56
() -> butlast([nil, nil]) -> 56
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 58
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 58
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 59
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 57
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 57
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> cons(a, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 80, which took 1.265604 s (model generation: 1.265074,  model checking: 0.000530):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1737, q_gen_1772, q_gen_1773},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<b, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1710, q_gen_1737) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1737
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1737
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1737) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1710, q_gen_1737) -> q_gen_1772
<nil, cons, cons>(q_gen_1710, q_gen_1737) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1740, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1740
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1740) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> butlast([cons(y, nil), nil]) -> 57
() -> butlast([nil, nil]) -> 57
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 58
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 58
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 59
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 57
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 57
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 81, which took 1.087640 s (model generation: 1.083810,  model checking: 0.003830):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1737, q_gen_1760, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1737) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1737
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1737) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1760) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1737) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, nil, cons>(q_gen_1705, q_gen_1737) -> q_gen_1760
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1760
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> butlast([cons(y, nil), nil]) -> 58
() -> butlast([nil, nil]) -> 58
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 58
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 61
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 59
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 58
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 58
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  x -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 82, which took 1.079499 s (model generation: 1.074772,  model checking: 0.004727):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1710, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1737, q_gen_1759, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1704
<cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<b, b>() -> q_gen_1705
<a, a>() -> q_gen_1710
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1737) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1737
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1737
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1737
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1759, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1759, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<cons, nil, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1737) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1710, q_gen_1737) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, cons, cons>(q_gen_1759, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1737) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1710, q_gen_1737) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1710, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, b, a>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1783, q_gen_1737) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1737) -> q_gen_1729
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1729
<a, a, a>() -> q_gen_1759
<b, a, b>() -> q_gen_1759
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> butlast([cons(y, nil), nil]) -> 58
() -> butlast([nil, nil]) -> 58
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 61
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 61
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 59
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 59
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 59
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 83, which took 1.363182 s (model generation: 1.360153,  model checking: 0.003029):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1703, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696, q_gen_1703},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1703) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1703
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1703
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<a, a, a>() -> q_gen_1724
<a, b, a>() -> q_gen_1724
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1700, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699, q_gen_1700},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1700
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1700
<cons, cons, cons>(q_gen_1749, q_gen_1700) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> butlast([cons(y, nil), nil]) -> 59
() -> butlast([nil, nil]) -> 59
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 61
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 61
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 62
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 60
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 60
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, nil)))  ;  _ji -> cons(b, cons(b, nil))  ;  _ki -> cons(b, cons(a, nil))  ;  xs -> cons(b, nil)  ;  ys -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 84, which took 1.968642 s (model generation: 1.961921,  model checking: 0.006721):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1750, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1750) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1750) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1750
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 60
() -> butlast([cons(y, nil), nil]) -> 60
() -> butlast([nil, nil]) -> 60
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 61
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 64
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 62
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 61
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 61
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, nil))  ;  _di -> cons(a, cons(a, cons(a, nil)))  ;  x -> cons(a, nil)  ;  x2 -> cons(b, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 85, which took 1.170548 s (model generation: 1.165520,  model checking: 0.005028):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 61
() -> butlast([cons(y, nil), nil]) -> 61
() -> butlast([nil, nil]) -> 61
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 64
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 64
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 62
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 62
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 62
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, cons(a, nil)))  ;  h1 -> b  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 86, which took 2.872569 s (model generation: 2.869860,  model checking: 0.002709):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1772
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 62
() -> butlast([cons(y, nil), nil]) -> 62
() -> butlast([nil, nil]) -> 62
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 64
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 64
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 65
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 63
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 63
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, nil)  ;  _ji -> nil  ;  _ki -> cons(a, nil)  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 87, which took 1.441289 s (model generation: 1.434992,  model checking: 0.006297):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1750, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1750) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1742, q_gen_1750) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1750
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1750
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 63
() -> butlast([cons(y, nil), nil]) -> 63
() -> butlast([nil, nil]) -> 63
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 64
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 67
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 65
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 64
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 64
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(a, cons(a, cons(b, nil)))  ;  x -> cons(a, cons(b, cons(b, nil)))  ;  x2 -> cons(a, nil)  ;  z -> b
})

-------------------------------------------
Step 88, which took 2.675048 s (model generation: 2.664550,  model checking: 0.010498):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 64
() -> butlast([cons(y, nil), nil]) -> 64
() -> butlast([nil, nil]) -> 64
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 67
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 67
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 65
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 65
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 65
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  h1 -> b  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 89, which took 3.045819 s (model generation: 3.038411,  model checking: 0.007408):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1722
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1772
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, a, a>() -> q_gen_1813
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 65
() -> butlast([cons(y, nil), nil]) -> 65
() -> butlast([nil, nil]) -> 65
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 67
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 67
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 68
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 66
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 66
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ji -> cons(b, cons(b, cons(b, nil)))  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, nil)  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 90, which took 2.284198 s (model generation: 2.277543,  model checking: 0.006655):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1750, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1750) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1742, q_gen_1750) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1750
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1750
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, a, a>() -> q_gen_1813
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 66
() -> butlast([cons(y, nil), nil]) -> 66
() -> butlast([nil, nil]) -> 66
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 67
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 70
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 68
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 67
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 67
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, cons(b, cons(b, nil)))  ;  _di -> cons(a, cons(a, cons(a, nil)))  ;  x -> cons(a, nil)  ;  x2 -> cons(b, cons(b, cons(b, nil)))  ;  z -> b
})

-------------------------------------------
Step 91, which took 2.998226 s (model generation: 2.995004,  model checking: 0.003222):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1772
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 67
() -> butlast([cons(y, nil), nil]) -> 67
() -> butlast([nil, nil]) -> 67
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 70
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 70
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 68
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 68
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 68
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(a, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 92, which took 3.579490 s (model generation: 3.573111,  model checking: 0.006379):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1750, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1750) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<cons, cons, cons>(q_gen_1724, q_gen_1750) -> q_gen_1750
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1750
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 68
() -> butlast([cons(y, nil), nil]) -> 68
() -> butlast([nil, nil]) -> 68
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 70
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 70
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 71
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 69
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 69
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, cons(b, nil))  ;  _ji -> cons(b, nil)  ;  _ki -> cons(a, nil)  ;  xs -> cons(b, nil)  ;  ys -> cons(a, nil)
})

-------------------------------------------
Step 93, which took 7.157166 s (model generation: 7.147338,  model checking: 0.009828):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1772, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1772) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1772) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1772
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1772
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, a, a>() -> q_gen_1813
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 69
() -> butlast([cons(y, nil), nil]) -> 69
() -> butlast([nil, nil]) -> 69
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 70
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 73
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 71
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 70
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 70
}
Sat witness: Found: ((append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]), {
_ci -> cons(b, nil)  ;  _di -> cons(b, cons(b, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(a, nil)  ;  z -> b
})

-------------------------------------------
Step 94, which took 4.638246 s (model generation: 4.636162,  model checking: 0.002084):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1729, q_gen_1730, q_gen_1742, q_gen_1750, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1729) -> q_gen_1696
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1750) -> q_gen_1721
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1729
<cons, cons, cons>(q_gen_1742, q_gen_1750) -> q_gen_1729
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1729
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1729
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
<cons, cons, cons>(q_gen_1724, q_gen_1729) -> q_gen_1750
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1750
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<a, b>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, a, a>() -> q_gen_1813
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 70
() -> butlast([cons(y, nil), nil]) -> 70
() -> butlast([nil, nil]) -> 70
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 73
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 73
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 71
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 71
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 71
}
Sat witness: Found: ((append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]), {
_wh -> cons(b, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 95, which took 7.473648 s (model generation: 7.470905,  model checking: 0.002743):

Model:
|_
{
append -> 
{{{
Q={q_gen_1696, q_gen_1703, q_gen_1704, q_gen_1705, q_gen_1721, q_gen_1722, q_gen_1723, q_gen_1724, q_gen_1730, q_gen_1735, q_gen_1742, q_gen_1773, q_gen_1783},
Q_f={q_gen_1696, q_gen_1703},
Delta=
{
<nil>() -> q_gen_1722
<a>() -> q_gen_1723
<b>() -> q_gen_1723
<cons>(q_gen_1723, q_gen_1722) -> q_gen_1773
<cons>(q_gen_1723, q_gen_1773) -> q_gen_1773
<cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1704
<nil, nil>() -> q_gen_1704
<a, a>() -> q_gen_1705
<b, b>() -> q_gen_1705
<cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1730
<cons, cons>(q_gen_1783, q_gen_1704) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1730
<nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1730
<b, a>() -> q_gen_1783
<cons, cons, cons>(q_gen_1724, q_gen_1721) -> q_gen_1696
<cons, cons, cons>(q_gen_1742, q_gen_1703) -> q_gen_1696
<nil, cons, cons>(q_gen_1705, q_gen_1704) -> q_gen_1696
<nil, nil, nil>() -> q_gen_1696
<cons, cons, cons>(q_gen_1724, q_gen_1696) -> q_gen_1703
<cons, cons, cons>(q_gen_1742, q_gen_1721) -> q_gen_1703
<cons, cons, cons>(q_gen_1742, q_gen_1735) -> q_gen_1703
<cons, nil, cons>(q_gen_1705, q_gen_1704) -> q_gen_1703
<cons, cons, cons>(q_gen_1742, q_gen_1696) -> q_gen_1721
<cons, nil, cons>(q_gen_1705, q_gen_1730) -> q_gen_1721
<cons, nil, cons>(q_gen_1783, q_gen_1704) -> q_gen_1721
<nil, nil, cons>(q_gen_1723, q_gen_1722) -> q_gen_1721
<b, a, b>() -> q_gen_1724
<b, b, b>() -> q_gen_1724
<cons, cons, cons>(q_gen_1724, q_gen_1703) -> q_gen_1735
<cons, cons, cons>(q_gen_1724, q_gen_1735) -> q_gen_1735
<nil, cons, cons>(q_gen_1705, q_gen_1730) -> q_gen_1735
<nil, cons, cons>(q_gen_1783, q_gen_1730) -> q_gen_1735
<nil, nil, cons>(q_gen_1723, q_gen_1773) -> q_gen_1735
<a, a, a>() -> q_gen_1742
<a, b, a>() -> q_gen_1742
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}
  ;  butlast -> 
{{{
Q={q_gen_1692, q_gen_1693, q_gen_1694, q_gen_1695, q_gen_1698, q_gen_1711},
Q_f={q_gen_1692, q_gen_1693},
Delta=
{
<nil>() -> q_gen_1694
<a>() -> q_gen_1695
<b>() -> q_gen_1695
<nil, nil>() -> q_gen_1692
<cons, cons>(q_gen_1698, q_gen_1693) -> q_gen_1693
<cons, nil>(q_gen_1695, q_gen_1694) -> q_gen_1693
<a, a>() -> q_gen_1698
<b, b>() -> q_gen_1698
<cons, cons>(q_gen_1698, q_gen_1692) -> q_gen_1711
<cons, cons>(q_gen_1698, q_gen_1711) -> q_gen_1711
}

Datatype: <eltlist, eltlist>
Convolution form: right
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_1699, q_gen_1701, q_gen_1702, q_gen_1714, q_gen_1715, q_gen_1716, q_gen_1727, q_gen_1733, q_gen_1749, q_gen_1813, q_gen_1862},
Q_f={q_gen_1699, q_gen_1727},
Delta=
{
<nil>() -> q_gen_1701
<a>() -> q_gen_1702
<b>() -> q_gen_1702
<cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1715
<cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1715
<nil, nil>() -> q_gen_1715
<a, a>() -> q_gen_1716
<a, b>() -> q_gen_1716
<b, b>() -> q_gen_1716
<cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1733
<cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1733
<cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1733
<b, a>() -> q_gen_1862
<cons, cons, cons>(q_gen_1749, q_gen_1699) -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1714) -> q_gen_1699
<cons, nil, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1716, q_gen_1733) -> q_gen_1699
<nil, cons, cons>(q_gen_1862, q_gen_1715) -> q_gen_1699
<nil, cons, nil>(q_gen_1702, q_gen_1701) -> q_gen_1699
<nil, nil, nil>() -> q_gen_1699
<cons, cons, cons>(q_gen_1749, q_gen_1727) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1699) -> q_gen_1714
<cons, cons, cons>(q_gen_1813, q_gen_1714) -> q_gen_1714
<cons, nil, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1715) -> q_gen_1714
<cons, nil, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<nil, cons, cons>(q_gen_1716, q_gen_1715) -> q_gen_1714
<nil, cons, cons>(q_gen_1862, q_gen_1733) -> q_gen_1714
<cons, nil, nil>(q_gen_1702, q_gen_1701) -> q_gen_1727
<a, a, a>() -> q_gen_1749
<a, b, a>() -> q_gen_1749
<b, a, b>() -> q_gen_1749
<b, b, b>() -> q_gen_1749
<b, a, a>() -> q_gen_1813
<b, b, a>() -> q_gen_1813
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 71
() -> butlast([cons(y, nil), nil]) -> 71
() -> butlast([nil, nil]) -> 71
(append([t1, l2, _wh])) -> append([cons(h1, t1), l2, cons(h1, _wh)]) -> 73
(append([x, _ci, _di]) /\ butlast([cons(z, x2), _ci])) -> butlastconcat([x, cons(z, x2), _di]) -> 73
(append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]) -> 74
(butlast([x, _bi])) -> butlastconcat([x, nil, _bi]) -> 72
(butlast([cons(x2, x3), _sh])) -> butlast([cons(y, cons(x2, x3)), cons(y, _sh)]) -> 72
}
Sat witness: Found: ((append([xs, ys, _ii]) /\ butlast([_ii, _ji]) /\ butlastconcat([xs, ys, _ki])) -> eq_eltlist([_ji, _ki]), {
_ii -> cons(b, nil)  ;  _ji -> nil  ;  _ki -> cons(b, nil)  ;  xs -> cons(b, nil)  ;  ys -> cons(b, nil)
})

Total time: 63.967669
Reason for stopping: DontKnow. Stopped because: timeout