R
↳Dependency Pair Analysis
F(.(nil, y)) -> F(y)
F(.(.(x, y), z)) -> F(.(x, .(y, z)))
G(.(x, nil)) -> G(x)
G(.(x, .(y, z))) -> G(.(.(x, y), z))
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Remaining
F(.(.(x, y), z)) -> F(.(x, .(y, z)))
F(.(nil, y)) -> F(y)
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
F(.(nil, y)) -> F(y)
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
POL(g(x1)) = x1 POL(nil) = 1 POL(.(x1, x2)) = x1 + x2 POL(f(x1)) = x1 POL(F(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(.(.(x, y), z)) -> F(.(x, .(y, z)))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
one new Dependency Pair is created:
F(.(.(x, y), z)) -> F(.(x, .(y, z)))
F(.(.(x'', y0), .(y'', z''))) -> F(.(x'', .(y0, .(y'', z''))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Inst
...
→DP Problem 4
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(.(.(x'', y0), .(y'', z''))) -> F(.(x'', .(y0, .(y'', z''))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
one new Dependency Pair is created:
F(.(.(x'', y0), .(y'', z''))) -> F(.(x'', .(y0, .(y'', z''))))
F(.(.(x'''', y0''), .(y''0, .(y'''', z'''')))) -> F(.(x'''', .(y0'', .(y''0, .(y'''', z'''')))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Inst
...
→DP Problem 5
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(.(.(x'''', y0''), .(y''0, .(y'''', z'''')))) -> F(.(x'''', .(y0'', .(y''0, .(y'''', z'''')))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
one new Dependency Pair is created:
F(.(.(x'''', y0''), .(y''0, .(y'''', z'''')))) -> F(.(x'''', .(y0'', .(y''0, .(y'''', z'''')))))
F(.(.(x'''''', y0''''), .(y''0'', .(y''''0, .(y'''''', z''''''))))) -> F(.(x'''''', .(y0'''', .(y''0'', .(y''''0, .(y'''''', z''''''))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Inst
...
→DP Problem 6
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(.(.(x'''''', y0''''), .(y''0'', .(y''''0, .(y'''''', z''''''))))) -> F(.(x'''''', .(y0'''', .(y''0'', .(y''''0, .(y'''''', z''''''))))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
one new Dependency Pair is created:
F(.(.(x'''''', y0''''), .(y''0'', .(y''''0, .(y'''''', z''''''))))) -> F(.(x'''''', .(y0'''', .(y''0'', .(y''''0, .(y'''''', z''''''))))))
F(.(.(x'''''''', y0''''''), .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))) -> F(.(x'''''''', .(y0'''''', .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Inst
...
→DP Problem 7
↳Instantiation Transformation
→DP Problem 2
↳Remaining
F(.(.(x'''''''', y0''''''), .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))) -> F(.(x'''''''', .(y0'''''', .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
one new Dependency Pair is created:
F(.(.(x'''''''', y0''''''), .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))) -> F(.(x'''''''', .(y0'''''', .(y''0'''', .(y''''0'', .(y'''''''', .(y''''''''', z'''''''')))))))
F(.(.(x'''''''''', y0''''''''), .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))) -> F(.(x'''''''''', .(y0'''''''', .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
F(.(.(x'''''''''', y0''''''''), .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))) -> F(.(x'''''''''', .(y0'''''''', .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
G(.(x, .(y, z))) -> G(.(.(x, y), z))
G(.(x, nil)) -> G(x)
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Remaining Obligation(s)
F(.(.(x'''''''''', y0''''''''), .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))) -> F(.(x'''''''''', .(y0'''''''', .(y''0'''''', .(y''''0'''', .(y''''''''0, .(y'''''''''0, .(y'''''''''''', z''''''''''))))))))
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))
G(.(x, .(y, z))) -> G(.(.(x, y), z))
G(.(x, nil)) -> G(x)
f(nil) -> nil
f(.(nil, y)) -> .(nil, f(y))
f(.(.(x, y), z)) -> f(.(x, .(y, z)))
g(nil) -> nil
g(.(x, nil)) -> .(g(x), nil)
g(.(x, .(y, z))) -> g(.(.(x, y), z))