R
↳Dependency Pair Analysis
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, x), app(app(:, y), z))
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, y), z)
APP(app(:, app(app(:, x), y)), z) -> APP(:, y)
APP(app(:, app(app(+, x), y)), z) -> APP(app(+, app(app(:, x), z)), app(app(:, y), z))
APP(app(:, app(app(+, x), y)), z) -> APP(+, app(app(:, x), z))
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, x), z)
APP(app(:, app(app(+, x), y)), z) -> APP(:, x)
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, y), z)
APP(app(:, app(app(+, x), y)), z) -> APP(:, y)
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(:, app(app(g, z), y)), app(app(+, x), a))
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(:, app(app(g, z), y))
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(g, z), y)
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(g, z)
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(+, x), a)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(g, z), y)
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, y), z)
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, x), z)
APP(app(:, app(app(+, x), y)), z) -> APP(app(+, app(app(:, x), z)), app(app(:, y), z))
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, y), z)
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(:, app(app(g, z), y)), app(app(+, x), a))
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, x), app(app(:, y), z))
app(app(:, app(app(:, x), y)), z) -> app(app(:, x), app(app(:, y), z))
app(app(:, app(app(+, x), y)), z) -> app(app(+, app(app(:, x), z)), app(app(:, y), z))
app(app(:, z), app(app(+, x), app(f, y))) -> app(app(:, app(app(g, z), y)), app(app(+, x), a))
innermost
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(g, z), y)
APP(app(:, app(app(+, x), y)), z) -> APP(app(+, app(app(:, x), z)), app(app(:, y), z))
app(app(:, app(app(:, x), y)), z) -> app(app(:, x), app(app(:, y), z))
app(app(:, app(app(+, x), y)), z) -> app(app(+, app(app(:, x), z)), app(app(:, y), z))
app(app(:, z), app(app(+, x), app(f, y))) -> app(app(:, app(app(g, z), y)), app(app(+, x), a))
POL(:) = 1 POL(g) = 0 POL(+) = 0
APP(x1, x2) -> x1
app(x1, x2) -> x1
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Remaining Obligation(s)
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, y), z)
APP(app(:, app(app(+, x), y)), z) -> APP(app(:, x), z)
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, y), z)
APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(:, app(app(g, z), y)), app(app(+, x), a))
APP(app(:, app(app(:, x), y)), z) -> APP(app(:, x), app(app(:, y), z))
app(app(:, app(app(:, x), y)), z) -> app(app(:, x), app(app(:, y), z))
app(app(:, app(app(+, x), y)), z) -> app(app(+, app(app(:, x), z)), app(app(:, y), z))
app(app(:, z), app(app(+, x), app(f, y))) -> app(app(:, app(app(g, z), y)), app(app(+, x), a))
innermost