R
↳Dependency Pair Analysis
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(if, app(p, x))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(cons, x), app(app(filter, p), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
eight new Dependency Pairs are created:
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(app(if, app(p'', x)), app(app(cons, x), nil)), app(app(filter, p''), nil))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(filter, p''), app(app(cons, x''), xs'')))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), nil))), nil)
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), app(app(cons, x''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rewriting Transformation
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), app(app(cons, x''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(filter, p''), app(app(cons, x''), xs'')))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(app(if, app(p'', x)), app(app(cons, x), nil)), app(app(filter, p''), nil))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
one new Dependency Pair is created:
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(app(if, app(p'', x)), app(app(cons, x), nil)), app(app(filter, p''), nil))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(app(if, app(p'', x)), app(app(cons, x), nil)), nil)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rw
...
→DP Problem 3
↳Rewriting Transformation
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(filter, p''), app(app(cons, x''), xs'')))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), app(app(cons, x''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
one new Dependency Pair is created:
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(filter, p''), app(app(cons, x''), xs'')))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rw
...
→DP Problem 4
↳Rewriting Transformation
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), app(app(cons, x''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
one new Dependency Pair is created:
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(filter, p''), app(app(cons, x''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rw
...
→DP Problem 5
↳Narrowing Transformation
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
six new Dependency Pairs are created:
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs)))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs)))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(if, app(p'', x)), app(app(cons, x), nil))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rw
...
→DP Problem 6
↳Forward Instantiation Transformation
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(if, app(p'', x)), app(app(cons, x), nil))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs)))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs)))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost
seven new Dependency Pairs are created:
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(filter, p''), app(app(cons, x''), xs''))
APP(app(filter, app(filter, app(app(if, true), xs''''))), app(app(cons, app(app(cons, x'''), xs'')), xs)) -> APP(app(filter, app(app(if, true), xs'''')), app(app(cons, x'''), xs''))
APP(app(filter, app(filter, app(app(if, false), xs''''))), app(app(cons, app(app(cons, x'''), xs'')), xs)) -> APP(app(filter, app(app(if, false), xs'''')), app(app(cons, x'''), xs''))
APP(app(filter, app(filter, app(filter, p''''))), app(app(cons, app(app(cons, nil), xs'')), xs)) -> APP(app(filter, app(filter, p'''')), app(app(cons, nil), xs''))
APP(app(filter, app(filter, app(filter, p''''))), app(app(cons, app(app(cons, app(app(cons, x''''), xs'''')), xs'')), xs)) -> APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''''), xs'''')), xs''))
APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''), app(app(cons, x''''), xs''''))), xs)) -> APP(app(filter, p''''), app(app(cons, x''), app(app(cons, x''''), xs'''')))
APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''), nil)), xs)) -> APP(app(filter, p''''), app(app(cons, x''), nil))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Rw
...
→DP Problem 7
↳Remaining Obligation(s)
APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''), nil)), xs)) -> APP(app(filter, p''''), app(app(cons, x''), nil))
APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''), app(app(cons, x''''), xs''''))), xs)) -> APP(app(filter, p''''), app(app(cons, x''), app(app(cons, x''''), xs'''')))
APP(app(filter, app(filter, app(filter, p''''))), app(app(cons, app(app(cons, app(app(cons, x''''), xs'''')), xs'')), xs)) -> APP(app(filter, app(filter, p'''')), app(app(cons, app(app(cons, x''''), xs'''')), xs''))
APP(app(filter, app(filter, app(filter, p''''))), app(app(cons, app(app(cons, nil), xs'')), xs)) -> APP(app(filter, app(filter, p'''')), app(app(cons, nil), xs''))
APP(app(filter, app(filter, app(app(if, false), xs''''))), app(app(cons, app(app(cons, x'''), xs'')), xs)) -> APP(app(filter, app(app(if, false), xs'''')), app(app(cons, x'''), xs''))
APP(app(filter, app(filter, app(app(if, true), xs''''))), app(app(cons, app(app(cons, x'''), xs'')), xs)) -> APP(app(filter, app(app(if, true), xs'''')), app(app(cons, x'''), xs''))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(filter, p''), app(app(cons, x''), xs''))
APP(app(filter, p''), app(app(cons, x), nil)) -> APP(app(if, app(p'', x)), app(app(cons, x), nil))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs)))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs)))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs)))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs'')))
APP(app(filter, app(filter, p'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(app(if, app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))), app(app(cons, app(app(cons, x''), xs'')), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(filter, p'')), app(app(cons, nil), xs)) -> APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, p'')), xs))), app(app(filter, app(filter, p'')), xs))
APP(app(filter, app(app(if, false), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, x'), app(app(cons, x'), app(app(filter, app(app(if, false), xs'')), xs))), app(app(filter, app(app(if, false), xs'')), xs))
APP(app(filter, app(app(if, true), xs'')), app(app(cons, x'), xs)) -> APP(app(app(if, xs''), app(app(cons, x'), app(app(filter, app(app(if, true), xs'')), xs))), app(app(filter, app(app(if, true), xs'')), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(if, app(p'', x)), app(app(cons, x), app(app(app(if, app(p'', x'')), app(app(cons, x''), app(app(filter, p''), xs''))), app(app(filter, p''), xs''))))
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
innermost