Solving ../../benchmarks/true/isaplanner_prop4.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(count, F:
{() -> count([x, nil, z])
(count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab])
(count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)])}
(count([_bb, _cb, _db]) /\ count([_bb, _cb, _eb])) -> eq_nat([_db, _eb])
)
}

properties:
{(count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)])}


over-approximation: {count}
under-approximation: {}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 0  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 0  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 0
}


Solving took 30.312245 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1815, q_gen_1816, q_gen_1817, q_gen_1818, q_gen_1819, q_gen_1820, q_gen_1821, q_gen_1822, q_gen_1823, q_gen_1824, q_gen_1825, q_gen_1826, q_gen_1827, q_gen_1828, q_gen_1829, q_gen_1830, q_gen_1831, q_gen_1832, q_gen_1833, q_gen_1834, q_gen_1835, q_gen_1836, q_gen_1837, q_gen_1838, q_gen_1839, q_gen_1840, q_gen_1841, q_gen_1842, q_gen_1843, q_gen_1844, q_gen_1845, q_gen_1846, q_gen_1847, q_gen_1848, q_gen_1849, q_gen_1850, q_gen_1851, q_gen_1852, q_gen_1853, q_gen_1854, q_gen_1855, q_gen_1856, q_gen_1857, q_gen_1858, q_gen_1859, q_gen_1860, q_gen_1861, q_gen_1862, q_gen_1863, q_gen_1864, q_gen_1865, q_gen_1866, q_gen_1867, q_gen_1868, q_gen_1869, q_gen_1870, q_gen_1871, q_gen_1872, q_gen_1873, q_gen_1874, q_gen_1875, q_gen_1876, q_gen_1877, q_gen_1878, q_gen_1879, q_gen_1880, q_gen_1881, q_gen_1882, q_gen_1883, q_gen_1884, q_gen_1885, q_gen_1886, q_gen_1887, q_gen_1888, q_gen_1889, q_gen_1890, q_gen_1891, q_gen_1892, q_gen_1893, q_gen_1894, q_gen_1895, q_gen_1896, q_gen_1897, q_gen_1898, q_gen_1899, q_gen_1900, q_gen_1901, q_gen_1902, q_gen_1903, q_gen_1904, q_gen_1905, q_gen_1906, q_gen_1907, q_gen_1908, q_gen_1909, q_gen_1910, q_gen_1911, q_gen_1912, q_gen_1913, q_gen_1914, q_gen_1915, q_gen_1916, q_gen_1917, q_gen_1918, q_gen_1919, q_gen_1920, q_gen_1921, q_gen_1922, q_gen_1923, q_gen_1924, q_gen_1925, q_gen_1926, q_gen_1927, q_gen_1928, q_gen_1929, q_gen_1930, q_gen_1931, q_gen_1932, q_gen_1933, q_gen_1934, q_gen_1935, q_gen_1936, q_gen_1937, q_gen_1938, q_gen_1939, q_gen_1940, q_gen_1941, q_gen_1942, q_gen_1943, q_gen_1944, q_gen_1945, q_gen_1946, q_gen_1947, q_gen_1948, q_gen_1949, q_gen_1950, q_gen_1951, q_gen_1952, q_gen_1953, q_gen_1954, q_gen_1955, q_gen_1956, q_gen_1957, q_gen_1958, q_gen_1959, q_gen_1960, q_gen_1961, q_gen_1962, q_gen_1963, q_gen_1964, q_gen_1965, q_gen_1966, q_gen_1967, q_gen_1968, q_gen_1969, q_gen_1970, q_gen_1971, q_gen_1972, q_gen_1973, q_gen_1974, q_gen_1975, q_gen_1976, q_gen_1977, q_gen_1978, q_gen_1979, q_gen_1980, q_gen_1981, q_gen_1982, q_gen_1983, q_gen_1984, q_gen_1985, q_gen_1986},
Q_f={},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1847
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1857
<cons>(q_gen_1825, q_gen_1847) -> q_gen_1863
<s>(q_gen_1839) -> q_gen_1910
<cons>(q_gen_1825, q_gen_1857) -> q_gen_1913
<s>(q_gen_1910) -> q_gen_1929
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1935
<cons>(q_gen_1820, q_gen_1847) -> q_gen_1976
<cons>(q_gen_1820, q_gen_1830) -> q_gen_1979
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<b, s>(q_gen_1839) -> q_gen_1838
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1853
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1847) -> q_gen_1859
<cons, z>(q_gen_1825, q_gen_1857) -> q_gen_1865
<cons, z>(q_gen_1820, q_gen_1857) -> q_gen_1870
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1873
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1878
<cons, z>(q_gen_1820, q_gen_1847) -> q_gen_1881
<cons, s>(q_gen_1823, q_gen_1881) -> q_gen_1883
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1886
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1891
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1895
<cons, s>(q_gen_1823, q_gen_1865) -> q_gen_1900
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1906
<cons, s>(q_gen_1845, q_gen_1906) -> q_gen_1908
<a, s>(q_gen_1910) -> q_gen_1909
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1912
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1915
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1918
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1920
<cons, s>(q_gen_1823, q_gen_1859) -> q_gen_1922
<cons, s>(q_gen_1845, q_gen_1886) -> q_gen_1924
<cons, s>(q_gen_1927, q_gen_1924) -> q_gen_1926
<b, s>(q_gen_1910) -> q_gen_1927
<b, s>(q_gen_1929) -> q_gen_1928
<cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1931
<cons, s>(q_gen_1817, q_gen_1934) -> q_gen_1933
<cons, z>(q_gen_1820, q_gen_1935) -> q_gen_1934
<cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1938
<cons, s>(q_gen_1845, q_gen_1920) -> q_gen_1940
<cons, z>(q_gen_1825, q_gen_1935) -> q_gen_1943
<cons, s>(q_gen_1817, q_gen_1859) -> q_gen_1948
<cons, s>(q_gen_1823, q_gen_1943) -> q_gen_1951
<cons, z>(q_gen_1825, q_gen_1863) -> q_gen_1953
<cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1956
<cons, s>(q_gen_1817, q_gen_1870) -> q_gen_1958
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1961
<cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1964
<cons, s>(q_gen_1927, q_gen_1967) -> q_gen_1966
<cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1967
<cons, s>(q_gen_1845, q_gen_1878) -> q_gen_1970
<cons, z>(q_gen_1825, q_gen_1976) -> q_gen_1975
<cons, z>(q_gen_1820, q_gen_1979) -> q_gen_1978
<cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1982
<cons, s>(q_gen_1845, q_gen_1948) -> q_gen_1984
<cons, z>(q_gen_1825, q_gen_1979) -> q_gen_1986
<b, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1815
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1818
<a, nil, z>() -> q_gen_1821
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1822
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1824
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1827
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1829
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1831
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1832
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1834
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1835
<b, cons, s>(q_gen_1838, q_gen_1837) -> q_gen_1836
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1840
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1842
<a, cons, s>(q_gen_1845, q_gen_1837) -> q_gen_1844
<a, cons, z>(q_gen_1825, q_gen_1847) -> q_gen_1846
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1848
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1849
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1851
<a, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1852
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1854
<b, cons, z>(q_gen_1820, q_gen_1857) -> q_gen_1856
<b, cons, s>(q_gen_1817, q_gen_1859) -> q_gen_1858
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1860
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1861
<a, cons, z>(q_gen_1825, q_gen_1863) -> q_gen_1862
<a, cons, s>(q_gen_1823, q_gen_1865) -> q_gen_1864
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1866
<a, cons, s>(q_gen_1823, q_gen_1859) -> q_gen_1867
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1868
<a, cons, s>(q_gen_1817, q_gen_1870) -> q_gen_1869
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1871
<a, cons, s>(q_gen_1845, q_gen_1873) -> q_gen_1872
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1874
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1875
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1876
<a, cons, s>(q_gen_1845, q_gen_1878) -> q_gen_1877
<b, cons, s>(q_gen_1845, q_gen_1873) -> q_gen_1879
<b, cons, s>(q_gen_1823, q_gen_1881) -> q_gen_1880
<b, cons, s>(q_gen_1838, q_gen_1883) -> q_gen_1882
<b, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1884
<a, cons, s>(q_gen_1845, q_gen_1886) -> q_gen_1885
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1887
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1888
<b, cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1889
<a, cons, s>(q_gen_1845, q_gen_1891) -> q_gen_1890
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1892
<b, cons, s>(q_gen_1817, q_gen_1865) -> q_gen_1893
<b, cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1894
<a, cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1896
<a, cons, s>(q_gen_1838, q_gen_1878) -> q_gen_1897
<b, cons, s>(q_gen_1823, q_gen_1865) -> q_gen_1898
<b, cons, s>(q_gen_1838, q_gen_1900) -> q_gen_1899
<b, cons, s>(q_gen_1845, q_gen_1878) -> q_gen_1901
<b, cons, s>(q_gen_1838, q_gen_1891) -> q_gen_1902
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1903
<b, cons, s>(q_gen_1817, q_gen_1870) -> q_gen_1904
<a, cons, s>(q_gen_1845, q_gen_1906) -> q_gen_1905
<a, cons, s>(q_gen_1909, q_gen_1908) -> q_gen_1907
<b, cons, s>(q_gen_1823, q_gen_1912) -> q_gen_1911
<a, cons, s>(q_gen_1823, q_gen_1915) -> q_gen_1914
<a, cons, s>(q_gen_1817, q_gen_1865) -> q_gen_1916
<b, cons, s>(q_gen_1838, q_gen_1918) -> q_gen_1917
<b, cons, s>(q_gen_1845, q_gen_1920) -> q_gen_1919
<b, cons, s>(q_gen_1845, q_gen_1922) -> q_gen_1921
<b, cons, s>(q_gen_1909, q_gen_1924) -> q_gen_1923
<a, cons, s>(q_gen_1928, q_gen_1926) -> q_gen_1925
<a, cons, s>(q_gen_1838, q_gen_1931) -> q_gen_1930
<a, cons, s>(q_gen_1838, q_gen_1933) -> q_gen_1932
<b, cons, s>(q_gen_1817, q_gen_1915) -> q_gen_1936
<b, cons, s>(q_gen_1927, q_gen_1938) -> q_gen_1937
<b, cons, s>(q_gen_1927, q_gen_1940) -> q_gen_1939
<a, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1941
<a, cons, s>(q_gen_1817, q_gen_1943) -> q_gen_1942
<b, cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1944
<b, cons, s>(q_gen_1817, q_gen_1934) -> q_gen_1945
<b, cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1946
<b, cons, s>(q_gen_1845, q_gen_1948) -> q_gen_1947
<b, cons, s>(q_gen_1823, q_gen_1943) -> q_gen_1949
<b, cons, s>(q_gen_1838, q_gen_1951) -> q_gen_1950
<a, cons, s>(q_gen_1823, q_gen_1953) -> q_gen_1952
<a, cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1954
<b, cons, s>(q_gen_1838, q_gen_1956) -> q_gen_1955
<b, cons, s>(q_gen_1845, q_gen_1958) -> q_gen_1957
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1959
<a, cons, s>(q_gen_1838, q_gen_1961) -> q_gen_1960
<a, cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1962
<a, cons, s>(q_gen_1909, q_gen_1964) -> q_gen_1963
<a, cons, s>(q_gen_1928, q_gen_1966) -> q_gen_1965
<a, cons, s>(q_gen_1909, q_gen_1967) -> q_gen_1968
<a, cons, s>(q_gen_1927, q_gen_1970) -> q_gen_1969
<a, cons, s>(q_gen_1909, q_gen_1938) -> q_gen_1971
<a, cons, s>(q_gen_1909, q_gen_1924) -> q_gen_1972
<a, cons, s>(q_gen_1817, q_gen_1881) -> q_gen_1973
<a, cons, s>(q_gen_1817, q_gen_1975) -> q_gen_1974
<b, cons, s>(q_gen_1817, q_gen_1978) -> q_gen_1977
<a, cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1980
<b, cons, s>(q_gen_1909, q_gen_1982) -> q_gen_1981
<b, cons, s>(q_gen_1909, q_gen_1984) -> q_gen_1983
<a, cons, s>(q_gen_1823, q_gen_1986) -> q_gen_1985
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.011584 s (model generation: 0.010469,  model checking: 0.001115):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 1  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 1  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 1
}
Sat witness: Yes: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 1, which took 0.010720 s (model generation: 0.010354,  model checking: 0.000366):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814},
Q_f={q_gen_1814},
Delta=
{
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 1  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 1  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 4
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 2, which took 0.011336 s (model generation: 0.010799,  model checking: 0.000537):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817},
Q_f={q_gen_1814},
Delta=
{
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 1  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 4  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 4
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> a  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 3, which took 0.013187 s (model generation: 0.012479,  model checking: 0.000708):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 2  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 4  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 4
}
Sat witness: Yes: (() -> count([x, nil, z]), {
x -> a
})

-------------------------------------------
Step 4, which took 0.012759 s (model generation: 0.011650,  model checking: 0.001109):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 3  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 4  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 7
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 5, which took 0.013721 s (model generation: 0.012290,  model checking: 0.001431):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 4  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 7  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 7
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> b  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 6, which took 0.010249 s (model generation: 0.009474,  model checking: 0.000775):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1820
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 7  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 7  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 7
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> z  ;  _gb -> z  ;  l1 -> nil  ;  x -> a
})

-------------------------------------------
Step 7, which took 0.015883 s (model generation: 0.013491,  model checking: 0.002392):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1825, q_gen_1826},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 7  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 7  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 10
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 8, which took 0.016143 s (model generation: 0.014335,  model checking: 0.001808):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1825, q_gen_1826},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 7  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 10  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 10
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> b  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 9, which took 0.016152 s (model generation: 0.014989,  model checking: 0.001163):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1825, q_gen_1826},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 10  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 10  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 10
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 10, which took 0.015287 s (model generation: 0.013701,  model checking: 0.001586):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1825, q_gen_1826, q_gen_1828},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 8  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 10  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 10  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 13
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 11, which took 0.014879 s (model generation: 0.013889,  model checking: 0.000990):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1825, q_gen_1826, q_gen_1828},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, z>() -> q_gen_1817
<b, z>() -> q_gen_1817
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 9  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 10  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 13  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 13
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 12, which took 0.019373 s (model generation: 0.016116,  model checking: 0.003257):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 13  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 13  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 13
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 13, which took 0.024907 s (model generation: 0.017392,  model checking: 0.007515):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1833},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 13  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 13  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 16
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 14, which took 0.021518 s (model generation: 0.018204,  model checking: 0.003314):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1833, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 12  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 13  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 16  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 16
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> a  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 15, which took 0.014207 s (model generation: 0.012869,  model checking: 0.001338):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1833, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<z>() -> q_gen_1839
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 13  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 16  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 16  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 16
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 16, which took 0.024729 s (model generation: 0.014311,  model checking: 0.010418):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 14  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 16  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 16  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 19
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 17, which took 0.023288 s (model generation: 0.019129,  model checking: 0.004159):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 15  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 16  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 19  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 19
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.021205 s (model generation: 0.016245,  model checking: 0.004960):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 16  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 19  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 19  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 19
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 19, which took 0.021130 s (model generation: 0.019207,  model checking: 0.001923):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 17  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 19  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 19  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 22
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.028944 s (model generation: 0.023091,  model checking: 0.005853):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 18  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 19  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 22  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 22
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 21, which took 0.032298 s (model generation: 0.026649,  model checking: 0.005649):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 19  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 22  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 22  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 22
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 22, which took 0.027879 s (model generation: 0.024024,  model checking: 0.003855):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 20  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 22  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 22  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 25
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 23, which took 0.026120 s (model generation: 0.022354,  model checking: 0.003766):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 21  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 22  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 25  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 25
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> a  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.025532 s (model generation: 0.021296,  model checking: 0.004236):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 22  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 25  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 25  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 25
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 25, which took 0.028419 s (model generation: 0.026678,  model checking: 0.001741):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1841
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 23  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 25  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 25  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 28
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.023632 s (model generation: 0.020645,  model checking: 0.002987):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1841
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 24  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 25  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 28  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 28
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 27, which took 0.026747 s (model generation: 0.021775,  model checking: 0.004972):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 28  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 28  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 28
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 28, which took 0.026786 s (model generation: 0.025010,  model checking: 0.001776):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1841
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 26  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 28  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 28  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 31
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 29, which took 0.021042 s (model generation: 0.019686,  model checking: 0.001356):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 27  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 28  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 31  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 31
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 30, which took 0.035946 s (model generation: 0.022280,  model checking: 0.013666):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 28  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 29  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 31  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 34
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 31, which took 0.031847 s (model generation: 0.026415,  model checking: 0.005432):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 29  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 32  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 31  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 34
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 32, which took 0.031727 s (model generation: 0.030536,  model checking: 0.001191):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 30  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 32  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 34  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 34
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.032061 s (model generation: 0.026221,  model checking: 0.005840):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 31  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 35  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 34  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 34
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 34, which took 0.034782 s (model generation: 0.028556,  model checking: 0.006226):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 32  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 35  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 34  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 37
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 35, which took 0.041187 s (model generation: 0.038484,  model checking: 0.002703):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 33  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 35  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 37  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 37
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.046937 s (model generation: 0.040746,  model checking: 0.006191):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 34  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 38  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 37  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 37
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 37, which took 0.041608 s (model generation: 0.036040,  model checking: 0.005568):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 35  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 38  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 37  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 40
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, cons(a, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 38, which took 0.042567 s (model generation: 0.040417,  model checking: 0.002150):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 36  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 38  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 40  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 40
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 39, which took 0.054466 s (model generation: 0.043662,  model checking: 0.010804):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 37  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 41  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 40  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 40
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(s(z))  ;  _gb -> z  ;  l1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 40, which took 0.051446 s (model generation: 0.045242,  model checking: 0.006204):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 38  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 41  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 40  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 43
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.047986 s (model generation: 0.045685,  model checking: 0.002301):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 39  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 41  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 43  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 43
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 42, which took 0.069756 s (model generation: 0.061176,  model checking: 0.008580):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 40  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 44  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 43  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 43
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(s(z))  ;  _gb -> z  ;  l1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 43, which took 0.085177 s (model generation: 0.071763,  model checking: 0.013414):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 41  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 44  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 43  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 46
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.069468 s (model generation: 0.067951,  model checking: 0.001517):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 42  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 44  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 46  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 46
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 45, which took 0.080562 s (model generation: 0.072238,  model checking: 0.008324):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 43  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 47  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 46  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 46
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 46, which took 0.070761 s (model generation: 0.063554,  model checking: 0.007207):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1837, q_gen_1839, q_gen_1841},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1837
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1837
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1837
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1837
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1837) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1837) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 44  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 47  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 46  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 49
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 47, which took 0.083637 s (model generation: 0.079686,  model checking: 0.003951):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 45  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 47  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 49  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 49
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 48, which took 0.103895 s (model generation: 0.092181,  model checking: 0.011714):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 46  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 50  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 49  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 49
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(z))  ;  l1 -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 49, which took 0.108375 s (model generation: 0.098076,  model checking: 0.010299):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 47  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 50  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 49  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 52
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, cons(b, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.117449 s (model generation: 0.112902,  model checking: 0.004547):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 48  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 50  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 52  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 52
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 51, which took 0.126431 s (model generation: 0.113419,  model checking: 0.013012):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 49  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 53  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 52  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 52
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 52, which took 0.116299 s (model generation: 0.112138,  model checking: 0.004161):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 50  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 53  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 52  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 55
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 53, which took 0.119017 s (model generation: 0.115947,  model checking: 0.003070):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 51  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 53  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 55  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 55
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 54, which took 0.129937 s (model generation: 0.118834,  model checking: 0.011103):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 52  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 56  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 55  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 55
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 55, which took 0.149322 s (model generation: 0.131024,  model checking: 0.018298):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 53  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 56  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 55  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 58
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(a, cons(a, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 56, which took 0.143641 s (model generation: 0.137675,  model checking: 0.005966):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 54  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 56  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 58  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 58
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 57, which took 0.147716 s (model generation: 0.143400,  model checking: 0.004316):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 55  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 59  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 58  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 58
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 58, which took 0.304112 s (model generation: 0.295002,  model checking: 0.009110):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 56  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 59  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 58  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 61
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 59, which took 0.174165 s (model generation: 0.168602,  model checking: 0.005563):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 57  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 59  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 61  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 61
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 60, which took 0.200457 s (model generation: 0.186255,  model checking: 0.014202):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1853},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1816
<nil, z>() -> q_gen_1816
<a, s>(q_gen_1839) -> q_gen_1817
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1853
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 58  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 62  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 61  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 61
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(s(z)))  ;  l1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 61, which took 0.228954 s (model generation: 0.224327,  model checking: 0.004627):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1857},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1857) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1857
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1857) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1857) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1857) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 59  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 62  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 61  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 64
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 62, which took 0.241633 s (model generation: 0.238048,  model checking: 0.003585):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1853},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1853
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1853
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 60  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 62  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 64  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 64
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 63, which took 0.241231 s (model generation: 0.226001,  model checking: 0.015230):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 61  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 65  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 64  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 64
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 64, which took 0.236040 s (model generation: 0.212420,  model checking: 0.023620):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 62  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 65  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 67  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 65
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(b, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 65, which took 0.294026 s (model generation: 0.262935,  model checking: 0.031091):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 63  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 68  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 67  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 66
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 66, which took 0.345554 s (model generation: 0.322398,  model checking: 0.023156):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 64  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 68  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 70  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 67
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 67, which took 0.503232 s (model generation: 0.463344,  model checking: 0.039888):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 65  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 71  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 70  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 68
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(s(s(z)))  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 68, which took 0.465972 s (model generation: 0.412776,  model checking: 0.053196):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 66  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 71  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 70  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 71
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 69, which took 0.462635 s (model generation: 0.456225,  model checking: 0.006410):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1850) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1850) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 67  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 71  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 73  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 71
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 70, which took 1.153282 s (model generation: 1.136673,  model checking: 0.016609):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1838, q_gen_1850) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<a, s>(q_gen_1839) -> q_gen_1838
<b, s>(q_gen_1839) -> q_gen_1838
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1850
<cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1850) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 68  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 71  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 73  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 74
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 71, which took 0.467861 s (model generation: 0.452568,  model checking: 0.015293):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1841
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<b, s>(q_gen_1839) -> q_gen_1838
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1850) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1850) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 69  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 74  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 73  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 74
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 72, which took 0.491583 s (model generation: 0.485243,  model checking: 0.006340):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850, q_gen_1855},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1855
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 70  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 74  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 76  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 74
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 73, which took 0.482045 s (model generation: 0.473010,  model checking: 0.009035):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1850, q_gen_1855},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1850
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 71  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 74  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 76  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 77
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(z)  ;  t1 -> cons(a, cons(b, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 74, which took 0.627596 s (model generation: 0.602967,  model checking: 0.024629):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<b, s>(q_gen_1839) -> q_gen_1838
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 72  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 77  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 76  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 77
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 75, which took 0.790991 s (model generation: 0.785327,  model checking: 0.005664):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1855, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1855
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 73  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 77  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 79  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 77
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 76, which took 1.092440 s (model generation: 1.087741,  model checking: 0.004699):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1847, q_gen_1863},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1847
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1863
<cons>(q_gen_1825, q_gen_1847) -> q_gen_1863
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<cons, z>(q_gen_1825, q_gen_1847) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1863) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1847) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1863) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1847) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1863) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 74  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 77  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 79  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 80
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> z  ;  t1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 77, which took 0.800591 s (model generation: 0.787576,  model checking: 0.013015):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1855, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1819
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1855
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1855
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 75  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 80  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 79  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 80
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 78, which took 0.817891 s (model generation: 0.807738,  model checking: 0.010153):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<b, s>(q_gen_1839) -> q_gen_1838
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 76  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 80  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 82  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 80
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 79, which took 0.996508 s (model generation: 0.987727,  model checking: 0.008781):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, s>(q_gen_1839) -> q_gen_1823
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1833
<cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<b, s>(q_gen_1839) -> q_gen_1838
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 77  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 80  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 82  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 83
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 80, which took 1.306399 s (model generation: 1.277295,  model checking: 0.029104):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1839) -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 78  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 83  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 82  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 83
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 81, which took 1.315796 s (model generation: 1.298539,  model checking: 0.017257):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 79  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 83  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 85  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 83
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(s(z)))  ;  h1 -> b  ;  t1 -> cons(a, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 82, which took 2.952280 s (model generation: 2.813848,  model checking: 0.138432):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 80  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 86  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 85  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 84
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(s(s(z)))  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 83, which took 1.193431 s (model generation: 1.178649,  model checking: 0.014782):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 81  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 86  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 85  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 87
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 84, which took 2.380938 s (model generation: 2.365522,  model checking: 0.015416):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 82  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 86  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 88  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 87
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 85, which took 1.346773 s (model generation: 1.332505,  model checking: 0.014268):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1830) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 83  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 89  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 88  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 87
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 86, which took 1.635686 s (model generation: 1.620492,  model checking: 0.015194):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1830) -> q_gen_1913
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 84  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 89  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 88  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 90
}
Sat witness: Yes: ((count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]), {
_za -> s(s(z))  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 87, which took 1.885786 s (model generation: 1.869119,  model checking: 0.016667):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1913},
Q_f={q_gen_1814},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<s>(q_gen_1839) -> q_gen_1839
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1830) -> q_gen_1913
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1913
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1816
<cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, s>(q_gen_1839) -> q_gen_1817
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1833
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1843
<cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<cons, z>(q_gen_1820, q_gen_1913) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1843
<cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<a, nil, z>() -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<a, cons, z>(q_gen_1825, q_gen_1913) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1843) -> q_gen_1826
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1826
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 85  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 89  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 91  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 90
}
Sat witness: Yes: ((count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]), {
_ab -> s(s(s(z)))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 88, which took 1.035381 s (model generation: 1.017604,  model checking: 0.017777):

Model:
|_
{
count -> 
{{{
Q={q_gen_1814, q_gen_1815, q_gen_1816, q_gen_1817, q_gen_1819, q_gen_1820, q_gen_1823, q_gen_1825, q_gen_1826, q_gen_1828, q_gen_1830, q_gen_1833, q_gen_1838, q_gen_1839, q_gen_1841, q_gen_1843, q_gen_1845, q_gen_1850, q_gen_1852, q_gen_1853, q_gen_1855, q_gen_1861, q_gen_1868, q_gen_1877, q_gen_1886, q_gen_1895, q_gen_1906, q_gen_1909, q_gen_1910, q_gen_1920},
Q_f={q_gen_1814, q_gen_1815},
Delta=
{
<nil>() -> q_gen_1819
<a>() -> q_gen_1820
<b>() -> q_gen_1825
<cons>(q_gen_1820, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1819) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1830) -> q_gen_1830
<cons>(q_gen_1825, q_gen_1841) -> q_gen_1830
<z>() -> q_gen_1839
<cons>(q_gen_1820, q_gen_1819) -> q_gen_1841
<cons>(q_gen_1820, q_gen_1841) -> q_gen_1841
<s>(q_gen_1839) -> q_gen_1910
<s>(q_gen_1910) -> q_gen_1910
<cons, s>(q_gen_1845, q_gen_1906) -> q_gen_1816
<nil, z>() -> q_gen_1816
<b, z>() -> q_gen_1817
<a, z>() -> q_gen_1823
<b, s>(q_gen_1910) -> q_gen_1823
<cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1828
<cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1828
<cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1828
<cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1828
<cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1828
<cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1833
<cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1853) -> q_gen_1833
<cons, s>(q_gen_1845, q_gen_1920) -> q_gen_1833
<cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1833
<b, s>(q_gen_1839) -> q_gen_1838
<cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1843
<a, s>(q_gen_1839) -> q_gen_1845
<cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1850
<cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1853
<cons, z>(q_gen_1825, q_gen_1841) -> q_gen_1853
<cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1855
<cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1855
<cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1886
<cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1895
<cons, s>(q_gen_1845, q_gen_1886) -> q_gen_1895
<cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1906
<cons, s>(q_gen_1823, q_gen_1906) -> q_gen_1906
<cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1906
<a, s>(q_gen_1910) -> q_gen_1909
<cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1920
<cons, s>(q_gen_1823, q_gen_1895) -> q_gen_1920
<cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1920
<a, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1838, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1828) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1855) -> q_gen_1814
<a, cons, s>(q_gen_1845, q_gen_1886) -> q_gen_1814
<a, cons, s>(q_gen_1909, q_gen_1895) -> q_gen_1814
<a, cons, z>(q_gen_1825, q_gen_1830) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1814
<b, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1828) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1833) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1853) -> q_gen_1814
<b, cons, s>(q_gen_1845, q_gen_1855) -> q_gen_1814
<b, cons, z>(q_gen_1820, q_gen_1841) -> q_gen_1814
<b, nil, z>() -> q_gen_1814
<a, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1815
<a, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1815
<a, cons, z>(q_gen_1825, q_gen_1819) -> q_gen_1815
<a, nil, z>() -> q_gen_1815
<b, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1815
<b, cons, s>(q_gen_1909, q_gen_1828) -> q_gen_1815
<b, cons, s>(q_gen_1909, q_gen_1833) -> q_gen_1815
<b, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1815
<a, cons, s>(q_gen_1817, q_gen_1816) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1843) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1906) -> q_gen_1826
<a, cons, s>(q_gen_1838, q_gen_1895) -> q_gen_1826
<a, cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1826
<a, cons, s>(q_gen_1909, q_gen_1920) -> q_gen_1826
<a, cons, z>(q_gen_1820, q_gen_1819) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1843) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1826
<b, cons, s>(q_gen_1817, q_gen_1855) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1816) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1826
<b, cons, s>(q_gen_1823, q_gen_1920) -> q_gen_1826
<b, cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1826
<b, cons, s>(q_gen_1845, q_gen_1895) -> q_gen_1826
<b, cons, s>(q_gen_1909, q_gen_1895) -> q_gen_1826
<a, cons, s>(q_gen_1823, q_gen_1853) -> q_gen_1852
<a, cons, s>(q_gen_1817, q_gen_1850) -> q_gen_1861
<a, cons, s>(q_gen_1838, q_gen_1853) -> q_gen_1861
<b, cons, z>(q_gen_1820, q_gen_1830) -> q_gen_1861
<a, cons, s>(q_gen_1817, q_gen_1828) -> q_gen_1868
<a, cons, s>(q_gen_1817, q_gen_1853) -> q_gen_1868
<a, cons, s>(q_gen_1823, q_gen_1850) -> q_gen_1868
<a, cons, s>(q_gen_1845, q_gen_1906) -> q_gen_1868
<a, cons, s>(q_gen_1823, q_gen_1920) -> q_gen_1877
<a, cons, s>(q_gen_1838, q_gen_1886) -> q_gen_1877
<a, cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1877
<a, cons, s>(q_gen_1845, q_gen_1853) -> q_gen_1877
<a, cons, s>(q_gen_1909, q_gen_1816) -> q_gen_1877
<a, cons, s>(q_gen_1909, q_gen_1828) -> q_gen_1877
<a, cons, s>(q_gen_1909, q_gen_1906) -> q_gen_1877
<b, cons, s>(q_gen_1823, q_gen_1833) -> q_gen_1877
<b, cons, s>(q_gen_1823, q_gen_1855) -> q_gen_1877
<b, cons, s>(q_gen_1838, q_gen_1906) -> q_gen_1877
<b, cons, s>(q_gen_1838, q_gen_1920) -> q_gen_1877
<b, cons, s>(q_gen_1845, q_gen_1906) -> q_gen_1877
<b, cons, s>(q_gen_1845, q_gen_1920) -> q_gen_1877
}

Datatype: <elt, eltlist, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 86  ;  (count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]) -> 92  ;  (count([x, t1, _ab]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ab]) -> 91  ;  (count([x, t1, _za])) -> count([x, cons(x, t1), s(_za)]) -> 90
}
Sat witness: Yes: ((count([x, l1, _gb]) /\ count([x, cons(x, l1), _fb])) -> eq_nat([_fb, s(_gb)]), {
_fb -> s(z)  ;  _gb -> s(z)  ;  l1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

Total time: 30.312245
Reason for stopping: DontKnow. Stopped because: timeout