R
↳Dependency Pair Analysis
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, x) -> F'(t, g(x))
F(t, x) -> G(x)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F'(triple(a, b, c), A) -> F''(foldB(triple(s(a), 0, c), b))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
FOLD(t, x, s(n)) -> F(fold(t, x, n), x)
FOLD(t, x, s(n)) -> FOLD(t, x, n)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
FOLDC(t, s(n)) -> FOLDC(t, n)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a, b, c), A) -> F''(foldB(triple(s(a), 0, c), b))
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, x) -> F'(t, g(x))
FOLDB(t, s(n)) -> F(foldB(t, n), B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F(t, x) -> F'(t, g(x))
F(t, A) -> F'(t, A)
F(t, B) -> F'(t, A)
F(t, B) -> F'(t, B)
F(t, C) -> F'(t, A)
F(t, C) -> F'(t, B)
F(t, C) -> F'(t, C)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, A) -> F'(t, A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a, b, c), A) -> F''(foldB(triple(s(a), 0, c), b))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a, b, c), A) -> F''(foldB(triple(s(a), 0, c), b))
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a', s(n'), c'), A) -> F''(f(foldB(triple(s(a'), 0, c'), n'), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 4
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a', s(n'), c'), A) -> F''(f(foldB(triple(s(a'), 0, c'), n'), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, A) -> F'(t, A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a', s(n'), c'), A) -> F''(f(foldB(triple(s(a'), 0, c'), n'), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), g(B)))
F'(triple(a'', s(0), c''), A) -> F''(f(triple(s(a''), 0, c''), B))
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 5
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, A) -> F'(t, A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
F'(triple(a'', s(0), c''), A) -> F''(f(triple(s(a''), 0, c''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F(t, A) -> F'(t, A)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 6
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
F'(triple(a'', s(0), c''), A) -> F''(f(triple(s(a''), 0, c''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
four new Dependency Pairs are created:
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 7
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
F'(triple(a'', s(0), c''), A) -> F''(f(triple(s(a''), 0, c''), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a'', s(0), c''), A) -> F''(f(triple(s(a''), 0, c''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 8
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
four new Dependency Pairs are created:
F'(triple(a'', s(s(n'')), c''), A) -> F''(f(f(foldB(triple(s(a''), 0, c''), n''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 9
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 10
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
five new Dependency Pairs are created:
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 11
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 12
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a'', s(n''), c''), A) -> F''(f'(foldB(triple(s(a''), 0, c''), n''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 13
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 14
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
five new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 15
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
five new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 16
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
two new Dependency Pairs are created:
F'(triple(a''', s(s(0)), c'''), A) -> F''(f(f(triple(s(a'''), 0, c'''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 17
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
five new Dependency Pairs are created:
F'(triple(a''', s(s(s(n'))), c'''), A) -> F''(f(f(f(foldB(triple(s(a'''), 0, c'''), n'), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 18
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 19
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 20
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 21
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 22
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 23
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 24
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 25
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 26
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 27
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 28
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 29
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 30
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
one new Dependency Pair is created:
F'(triple(a''', s(0), c'''), A) -> F''(f'(triple(s(a'''), 0, c'''), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 31
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 32
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 33
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 34
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 35
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f'(f(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 36
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 37
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 38
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 39
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 40
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a''', s(s(n''')), c'''), A) -> F''(f(f'(foldB(triple(s(a'''), 0, c'''), n'''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 41
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 42
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), g(B)), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 43
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 44
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 45
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), A), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 46
↳Narrowing Transformation
→DP Problem 2
↳Remaining
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), A), B), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
three new Dependency Pairs are created:
F'(triple(a'''', s(s(s(0))), c''''), A) -> F''(f(f(f(triple(s(a''''), 0, c''''), B), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 3
↳Nar
...
→DP Problem 47
↳Narrowing Transformation
→DP Problem 2
↳Remaining
F(t, B) -> F'(t, B)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, C) -> F'(t, B)
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), A), B), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
FOLDB(t, s(n)) -> FOLDB(t, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
six new Dependency Pairs are created:
F'(triple(a'''', s(s(s(s(n'')))), c''''), A) -> F''(f(f(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), B), B))
F'(triple(a''''', s(s(s(s(0)))), c'''''), A) -> F''(f(f(f(f(triple(s(a'''''), 0, c'''''), B), B), B), B))
F'(triple(a''''', s(s(s(s(s(n'))))), c'''''), A) -> F''(f(f(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), B), B))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''''', s(s(s(s(s(n'))))), c'''''), A) -> F''(f(f(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), B), B))
F'(triple(a''''', s(s(s(s(0)))), c'''''), A) -> F''(f(f(f(f(triple(s(a'''''), 0, c'''''), B), B), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), A), B), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
FOLD(t, x, s(n)) -> FOLD(t, x, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
FOLDB(t, s(n)) -> FOLDB(t, n)
FOLDC(t, s(n)) -> FOLDC(t, n)
F(t, C) -> F'(t, B)
F'(triple(a''''', s(s(s(s(s(n'))))), c'''''), A) -> F''(f(f(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), B), B))
F'(triple(a''''', s(s(s(s(0)))), c'''''), A) -> F''(f(f(f(f(triple(s(a'''''), 0, c'''''), B), B), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), B), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(s(n''')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f(f'(foldB(triple(s(a''''), 0, c''''), n''), A), B), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), B), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f(f'(triple(s(a'''''), 0, c'''''), g(B)), B), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n''), B), A), B))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f(f'(f(foldB(triple(s(a''''), 0, c''''), n'), B), A), B))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f(f'(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), g(B)), B))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f(f'(f(triple(s(a'''''), 0, c'''''), B), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f(f'(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), g(B)), B))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f(f'(triple(s(a''''), 0, c''''), A), B))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), B))
F'(triple(a'''', s(s(s(n'))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n'), B), B), A))
F'(triple(a''''', s(s(s(s(n'')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), B))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), g(B)), A))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), B), g(B)))
F'(triple(a'''', s(s(n'''')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), B))
F'(triple(a'''', s(s(s(n''))), c''''), A) -> F''(f'(f(f(foldB(triple(s(a''''), 0, c''''), n''), B), B), A))
F'(triple(a''''', s(s(s(s(n')))), c'''''), A) -> F''(f'(f(f(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), B), B), g(B)))
F'(triple(a''''', s(s(s(0))), c'''''), A) -> F''(f'(f(f(triple(s(a'''''), 0, c'''''), B), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f(f'(foldB(triple(s(a'''''), 0, c'''''), n'''), g(B)), B), g(B)))
F'(triple(a''''', s(s(s(n'''))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'''), B), g(B)), g(B)))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), B))
F'(triple(a'''', s(s(0)), c''''), A) -> F''(f'(f(triple(s(a''''), 0, c''''), B), A))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), B))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), g(B)), A))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), B), g(B)))
F'(triple(a'''', s(s(n'')), c''''), A) -> F''(f'(f'(foldB(triple(s(a''''), 0, c''''), n''), A), g(B)))
F'(triple(a''''', s(s(s(n'))), c'''''), A) -> F''(f'(f'(f(foldB(triple(s(a'''''), 0, c'''''), n'), B), g(B)), g(B)))
F'(triple(a''''', s(s(0)), c'''''), A) -> F''(f'(f'(triple(s(a'''''), 0, c'''''), g(B)), g(B)))
F'(triple(a'''', s(0), c''''), A) -> F''(f(triple(s(a''''), 0, c''''), A))
F'(triple(a'''', s(0), c''''), A) -> F''(f''(foldB(triple(s(s(a'''')), 0, c''''), 0)))
F(t, C) -> F'(t, A)
FOLDC(t, s(n)) -> F(foldC(t, n), C)
F''(triple(a, b, c)) -> FOLDC(triple(a, b, 0), c)
F'(triple(a', 0, c'), A) -> F''(triple(s(a'), 0, c'))
F(t, B) -> F'(t, A)
FOLDB(t, s(n)) -> F(foldB(t, n), B)
F'(triple(a, b, c), A) -> FOLDB(triple(s(a), 0, c), b)
F(triple(a'', b'', c''), A) -> F'(triple(a'', b'', c''), A)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, B) -> F'(t, B)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)
FOLD(t, x, s(n)) -> FOLD(t, x, n)
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldB(t, 0) -> t
foldB(t, s(n)) -> f(foldB(t, n), B)
foldC(t, 0) -> t
foldC(t, s(n)) -> f(foldC(t, n), C)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, s(c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldB(triple(s(a), 0, c), b))
f''(triple(a, b, c)) -> foldC(triple(a, b, 0), c)
fold(t, x, 0) -> t
fold(t, x, s(n)) -> f(fold(t, x, n), x)