R
↳Dependency Pair Analysis
G(g(x)) -> G(h(g(x)))
G(g(x)) -> H(g(x))
H(h(x)) -> H(f(h(x), x))
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
G(g(x)) -> G(h(g(x)))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
two new Dependency Pairs are created:
G(g(x)) -> G(h(g(x)))
G(g(h(g(x'')))) -> G(h(g(x'')))
G(g(g(x''))) -> G(h(g(h(g(x'')))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
G(g(g(x''))) -> G(h(g(h(g(x'')))))
G(g(h(g(x'')))) -> G(h(g(x'')))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
two new Dependency Pairs are created:
G(g(h(g(x'')))) -> G(h(g(x'')))
G(g(h(g(h(g(x')))))) -> G(h(g(x')))
G(g(h(g(g(x'))))) -> G(h(g(h(g(x')))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 3
↳Narrowing Transformation
G(g(h(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(h(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(x''))) -> G(h(g(h(g(x'')))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(x''))) -> G(h(g(h(g(x'')))))
G(g(g(x'''))) -> G(h(g(x''')))
G(g(g(h(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(x')))) -> G(h(g(h(g(h(g(x')))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 4
↳Argument Filtering and Ordering
G(g(g(g(x')))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(h(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(x'''))) -> G(h(g(x''')))
G(g(h(g(h(g(x')))))) -> G(h(g(x')))
G(g(h(g(g(x'))))) -> G(h(g(h(g(x')))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
G(g(g(h(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(x'''))) -> G(h(g(x''')))
G(g(h(g(h(g(x')))))) -> G(h(g(x')))
G(g(h(g(g(x'))))) -> G(h(g(h(g(x')))))
h(h(x)) -> h(f(h(x), x))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
G(x1) -> G(x1)
g(x1) -> g(x1)
h(x1) -> x1
f(x1, x2) -> x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 5
↳Narrowing Transformation
G(g(g(g(x')))) -> G(h(g(h(g(h(g(x')))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(x')))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(x'')))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 6
↳Narrowing Transformation
G(g(g(g(g(x''))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(x'')))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(x'')))) -> G(h(g(h(g(x'')))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(x'')))) -> G(h(g(h(g(x'')))))
G(g(g(g(x''')))) -> G(h(g(x''')))
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 7
↳Narrowing Transformation
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(x''')))) -> G(h(g(x''')))
G(g(g(g(h(g(x'')))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(h(g(x'')))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 8
↳Narrowing Transformation
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(x''')))) -> G(h(g(x''')))
G(g(g(g(g(x''))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(g(x''))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 9
↳Narrowing Transformation
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(x''')))) -> G(h(g(x''')))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
two new Dependency Pairs are created:
G(g(g(g(x''')))) -> G(h(g(x''')))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 10
↳Narrowing Transformation
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(h(g(x')))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 11
↳Narrowing Transformation
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(g(x'))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 12
↳Narrowing Transformation
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(h(g(x''')))))) -> G(h(g(h(g(x''')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 13
↳Narrowing Transformation
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 14
↳Narrowing Transformation
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 15
↳Narrowing Transformation
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(g(x'''))))) -> G(h(g(h(g(h(g(x''')))))))
G(g(g(g(g(x''''))))) -> G(h(g(h(g(x'''')))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 16
↳Narrowing Transformation
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x''''))))) -> G(h(g(h(g(x'''')))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(h(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 17
↳Narrowing Transformation
G(g(g(g(g(h(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(g(h(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x''''))))) -> G(h(g(h(g(x'''')))))
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
three new Dependency Pairs are created:
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(h(g(x')))))))))))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(g(h(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(g(g(g(x''))))))) -> G(h(g(h(g(h(g(h(g(h(g(h(g(x'')))))))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 18
↳Argument Filtering and Ordering
G(g(g(g(g(g(g(x''))))))) -> G(h(g(h(g(h(g(h(g(h(g(h(g(x'')))))))))))))
G(g(g(g(g(g(h(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x''''))))) -> G(h(g(h(g(x'''')))))
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(h(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))
G(g(g(g(g(g(h(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(g(g(x'')))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(g(h(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(g(g(x')))))) -> G(h(g(h(g(h(g(h(g(x')))))))))
G(g(g(g(g(h(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(g(x''''))))) -> G(h(g(h(g(x'''')))))
G(g(g(g(h(g(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
G(g(g(g(h(g(g(h(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(g(x''))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(g(x''))))))))) -> G(h(g(h(g(h(g(h(g(x'')))))))))
G(g(g(g(h(g(h(g(h(g(x'')))))))))) -> G(h(g(h(g(h(g(x'')))))))
G(g(g(g(h(g(h(g(x'')))))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(g(x'))))))) -> G(h(g(h(g(h(g(x')))))))
G(g(g(g(h(g(h(g(x')))))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x'''')))))) -> G(h(g(x'''')))
G(g(g(g(g(x''))))) -> G(h(g(h(g(x'')))))
G(g(g(g(h(g(x'')))))) -> G(h(g(x'')))
G(g(g(g(g(x'))))) -> G(h(g(h(g(x')))))
G(g(g(g(h(g(x')))))) -> G(h(g(x')))
G(g(g(g(g(h(g(g(x'')))))))) -> G(h(g(h(g(h(g(h(g(h(g(x'')))))))))))
h(h(x)) -> h(f(h(x), x))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
G(x1) -> G(x1)
g(x1) -> g(x1)
h(x1) -> x1
f(x1, x2) -> x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 19
↳Remaining Obligation(s)
G(g(g(g(g(g(g(x''))))))) -> G(h(g(h(g(h(g(h(g(h(g(h(g(x'')))))))))))))
g(h(g(x))) -> g(x)
g(g(x)) -> g(h(g(x)))
h(h(x)) -> h(f(h(x), x))