YES Time: 1.063739 TRS: { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)), app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs), app(app(app(f(), x), y), z) -> 2(), app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), x), x), x), app(app(app(g(), x), x), y) -> y, app(app(app(g(), x), y), y) -> x, app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app(app(map(), fun), nil()) -> nil(), app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs), app(app(filter(), fun), nil()) -> nil(), 0() -> 2(), 1() -> 2()} DP: DP: { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))} TRS: { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)), app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs), app(app(app(f(), x), y), z) -> 2(), app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), x), x), x), app(app(app(g(), x), x), y) -> y, app(app(app(g(), x), y), y) -> x, app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app(app(map(), fun), nil()) -> nil(), app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs), app(app(filter(), fun), nil()) -> nil(), 0() -> 2(), 1() -> 2()} EDG: { (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(f(), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), x), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), x), x), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) 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xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs))) (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x))) (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)) (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)) (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x)) (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun)) (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))} STATUS: arrows: 0.845679 SCCS (1): Scc: { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)} SCC (6): Strict: { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)} Weak: { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)), app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs), app(app(app(f(), x), y), z) -> 2(), app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), x), x), x), app(app(app(g(), x), x), y) -> y, app(app(app(g(), x), y), y) -> x, app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app(app(map(), fun), nil()) -> nil(), app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs), app(app(filter(), fun), nil()) -> nil(), 0() -> 2(), 1() -> 2()} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [app](x0, x1) = x0 + x1, [f] = 0, [0] = 0, [1] = 0, [2] = 0, [g] = 0, [nil] = 0, [map] = 0, [cons] = 1, [filter] = 0, [filter2] = 0, [true] = 0, [false] = 0, [app#](x0, x1) = x0 Strict: app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs) 1 + 1x + 0fun + 1xs >= 0 + 0x + 0fun + 1xs app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x) 1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs) 1 + 1x + 0fun + 1xs >= 0 + 0fun + 1xs app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x) 1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs) 0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs) 0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs Weak: 1() -> 2() 0 >= 0 0() -> 2() 0 >= 0 app(app(filter(), fun), nil()) -> nil() 0 + 1fun >= 0 app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs) 1 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs app(app(map(), fun), nil()) -> nil() 0 + 1fun >= 0 app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)) 1 + 1x + 1fun + 1xs >= 1 + 1x + 2fun + 1xs app(app(app(g(), x), y), y) -> x 0 + 1x + 2y >= 1x app(app(app(g(), x), x), y) -> y 0 + 2x + 1y >= 1y app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), x), x), x) 0 + 1x >= 0 + 3x app(app(app(f(), x), y), z) -> 2() 0 + 1x + 1y + 1z >= 0 app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs) 0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)) 0 + 1x + 1fun + 1xs >= 1 + 1x + 1fun + 1xs SCCS (0):