R
↳Dependency Pair Analysis
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(h, z), app(e, x)) -> APP(h, app(c, z))
APP(app(h, z), app(e, x)) -> APP(c, z)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(d, z)
APP(app(d, z), app(app(g, 0), 0)) -> APP(e, 0)
APP(app(d, z), app(app(g, x), y)) -> APP(app(g, app(e, x)), app(app(d, z), y))
APP(app(d, z), app(app(g, x), y)) -> APP(g, app(e, x))
APP(app(d, z), app(app(g, x), y)) -> APP(e, x)
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(g, app(app(d, app(c, z)), app(app(g, x), y)))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(d, z)
APP(app(g, app(e, x)), app(e, y)) -> APP(e, app(app(g, x), y))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(g, app(e, x)), app(e, y)) -> APP(g, x)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(d, z), app(app(g, x), y)) -> APP(app(g, app(e, x)), app(app(d, z), y))
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
three new Dependency Pairs are created:
APP(app(d, z), app(app(g, x), y)) -> APP(app(g, app(e, x)), app(app(d, z), y))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(d, z''), app(app(g, x), app(app(g, x''), y''))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(d, z''), y'')))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, x''), y''))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(d, z''), y'')))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
three new Dependency Pairs are created:
APP(app(d, z''), app(app(g, x), app(app(g, x''), y''))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(d, z''), y'')))
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, 0)))
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, x'''), y')))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(d, z'''), y'))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 3
↳Narrowing Transformation
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, x'''), y')))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(d, z'''), y'))))
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, 0)))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
one new Dependency Pair is created:
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, 0)))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 4
↳Narrowing Transformation
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, x'''), y')))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(d, z'''), y'))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
three new Dependency Pairs are created:
APP(app(d, z'''), app(app(g, x), app(app(g, x''), app(app(g, x'''), y')))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(d, z'''), y'))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, 0))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), y''))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(d, z''''), y'')))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 5
↳Narrowing Transformation
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), y''))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(d, z''''), y'')))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, 0))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
one new Dependency Pair is created:
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, 0))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, app(app(g, x''''), 0))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 6
↳Narrowing Transformation
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, app(app(g, x''''), 0))))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), y''))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(d, z''''), y'')))))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
three new Dependency Pairs are created:
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), y''))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(d, z''''), y'')))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(e, 0)))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), y')))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(d, z'''''), y'))))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, app(app(g, x'1), y')), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(app(d, app(c, z')), app(app(g, x'1), y'))), app(app(d, z'), app(app(g, x'1), y')))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 7
↳Narrowing Transformation
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, app(app(g, x'1), y')), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(app(d, app(c, z')), app(app(g, x'1), y'))), app(app(d, z'), app(app(g, x'1), y')))))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), y')))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(d, z'''''), y'))))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(e, 0)))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, app(app(g, x''''), 0))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
one new Dependency Pair is created:
APP(app(d, z''''), app(app(g, x), app(app(g, x''), app(app(g, x''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(e, app(app(g, x''''), 0))))
APP(app(d, z''''), app(app(g, x), app(app(g, x'''), app(app(g, x'''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), app(app(g, x'''''), 0))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 8
↳Narrowing Transformation
APP(app(d, z''''), app(app(g, x), app(app(g, x'''), app(app(g, x'''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), app(app(g, x'''''), 0))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), y')))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(d, z'''''), y'))))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(e, 0)))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, app(app(g, x'1), y')), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(app(d, app(c, z')), app(app(g, x'1), y'))), app(app(d, z'), app(app(g, x'1), y')))))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
one new Dependency Pair is created:
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(e, 0)))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0'), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, app(app(g, x'0'), 0)))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 9
↳Narrowing Transformation
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0'), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, app(app(g, x'0'), 0)))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, app(app(g, x'1), y')), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(app(d, app(c, z')), app(app(g, x'1), y'))), app(app(d, z'), app(app(g, x'1), y')))))))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), y')))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(d, z'''''), y'))))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, z''''), app(app(g, x), app(app(g, x'''), app(app(g, x'''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), app(app(g, x'''''), 0))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))
three new Dependency Pairs are created:
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), y')))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(d, z'''''), y'))))))
APP(app(d, z''''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, 0), 0))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(e, 0))))))
APP(app(d, z''''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, x'2), y''))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(g, app(e, x'2)), app(app(d, z''''''), y'')))))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, app(app(g, x'2), y'')), 0))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(g, app(app(d, app(c, z')), app(app(g, x'2), y''))), app(app(d, z'), app(app(g, x'2), y''))))))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 10
↳Remaining Obligation(s)
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, app(app(g, x'2), y'')), 0))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(g, app(app(d, app(c, z')), app(app(g, x'2), y''))), app(app(d, z'), app(app(g, x'2), y''))))))))
APP(app(d, z''''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, x'2), y''))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(app(g, app(e, x'2)), app(app(d, z''''''), y'')))))))
APP(app(d, z''''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, x'1), app(app(g, 0), 0))))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(e, x'1)), app(e, 0))))))
APP(app(d, z''''), app(app(g, x), app(app(g, x'''), app(app(g, x'''''), app(app(g, 0), 0))))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), app(app(g, x'''''), 0))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0), app(app(g, app(app(g, x'1), y')), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(e, x'0)), app(app(g, app(app(d, app(c, z')), app(app(g, x'1), y'))), app(app(d, z'), app(app(g, x'1), y')))))))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, app(app(g, x'0), y'')), 0))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(app(g, app(app(d, app(c, z')), app(app(g, x'0), y''))), app(app(d, z'), app(app(g, x'0), y''))))))
APP(app(d, z'''), app(app(g, x), app(app(g, x'''), app(app(g, 0), 0)))) -> APP(app(g, app(e, x)), app(e, app(app(g, x'''), 0)))
APP(app(d, app(c, z')), app(app(g, x), app(app(g, x''), app(app(g, app(app(g, x'''), y')), 0)))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(app(d, app(c, z')), app(app(g, x'''), y'))), app(app(d, z'), app(app(g, x'''), y')))))
APP(app(d, app(c, z'')), app(app(g, x), app(app(g, app(app(g, x''), y'')), 0))) -> APP(app(g, app(e, x)), app(app(g, app(app(d, app(c, z'')), app(app(g, x''), y''))), app(app(d, z''), app(app(g, x''), y''))))
APP(app(d, z''), app(app(g, x), app(app(g, 0), 0))) -> APP(app(g, app(e, x)), app(e, 0))
APP(app(g, app(e, x)), app(e, y)) -> APP(app(g, x), y)
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, z), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(d, app(c, z)), app(app(g, x), y))
APP(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> APP(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
APP(app(d, z), app(app(g, x), y)) -> APP(app(d, z), y)
APP(app(h, z), app(e, x)) -> APP(app(d, z), x)
APP(app(h, z), app(e, x)) -> APP(app(h, app(c, z)), app(app(d, z), x))
APP(app(d, z'''''), app(app(g, x), app(app(g, x''), app(app(g, x'''), app(app(g, x'0'), app(app(g, 0), 0)))))) -> APP(app(g, app(e, x)), app(app(g, app(e, x'')), app(app(g, app(e, x''')), app(e, app(app(g, x'0'), 0)))))
app(app(h, z), app(e, x)) -> app(app(h, app(c, z)), app(app(d, z), x))
app(app(d, z), app(app(g, 0), 0)) -> app(e, 0)
app(app(d, z), app(app(g, x), y)) -> app(app(g, app(e, x)), app(app(d, z), y))
app(app(d, app(c, z)), app(app(g, app(app(g, x), y)), 0)) -> app(app(g, app(app(d, app(c, z)), app(app(g, x), y))), app(app(d, z), app(app(g, x), y)))
app(app(g, app(e, x)), app(e, y)) -> app(e, app(app(g, x), y))