MAYBE Time: 0.067381 TRS: { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)), app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs), app(app(app(quot(), x), 0()), app(s(), z)) -> app(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app(app(app(quot(), 0()), app(s(), y)), app(s(), z)) -> 0(), app(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app(app(app(quot(), x), y), z), app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs), app(app(filter(), f), nil()) -> nil()} DP: DP: { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))} TRS: { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)), app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs), app(app(app(quot(), x), 0()), app(s(), z)) -> app(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app(app(app(quot(), 0()), app(s(), y)), app(s(), z)) -> 0(), app(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app(app(app(quot(), x), y), z), app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs), app(app(filter(), f), nil()) -> nil()} UR: { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)), app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs), app(app(app(quot(), x), 0()), app(s(), z)) -> app(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app(app(app(quot(), 0()), app(s(), y)), app(s(), z)) -> 0(), app(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app(app(app(quot(), x), y), z), app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs), app(app(filter(), f), nil()) -> nil()} EDG: { (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), 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-> app#(filter(), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) 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app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(filter(), f), 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app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z)))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f)) (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))) } STATUS: arrows: 0.000000 SCCS (1): Scc: { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))} SCC (21): Strict: { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(app(quot(), x), app(s(), z)), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(app(quot(), x), app(s(), z)), app#(app(app(quot(), x), 0()), app(s(), z)) -> app#(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(app(quot(), x), y), z), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(app(quot(), x), y), app#(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app#(quot(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))} Weak: { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)), app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs), app(app(app(quot(), x), 0()), app(s(), z)) -> app(s(), app(app(app(quot(), x), app(s(), z)), app(s(), z))), app(app(app(quot(), 0()), app(s(), y)), app(s(), z)) -> 0(), app(app(app(quot(), app(s(), x)), app(s(), y)), z) -> app(app(app(quot(), x), y), z), app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs), app(app(filter(), f), nil()) -> nil()} Open